id	sid	tid	token	lemma	pos
ejpam-804	1	1	10_xxx_joyeux.dvi	10_xxx_joyeux.dvi	PROPN
ejpam-804	1	2	european	european	PROPN
ejpam-804	1	3	journal	journal	PROPN
ejpam-804	1	4	of	of	ADP
ejpam-804	1	5	pure	pure	ADJ
ejpam-804	1	6	and	and	CCONJ
ejpam-804	1	7	applied	apply	VERB
ejpam-804	1	8	mathematics	mathematic	NOUN
ejpam-804	1	9	vol	vol	NOUN
ejpam-804	1	10	.	.	PUNCT
ejpam-804	2	1	3	3	NUM
ejpam-804	2	2	,	,	PUNCT
ejpam-804	2	3	no	no	INTJ
ejpam-804	2	4	.	.	NOUN
ejpam-804	2	5	3	3	NUM
ejpam-804	2	6	,	,	PUNCT
ejpam-804	2	7	2010	2010	NUM
ejpam-804	2	8	,	,	PUNCT
ejpam-804	2	9	519	519	NUM
ejpam-804	2	10	-	-	SYM
ejpam-804	2	11	530	530	NUM
ejpam-804	2	12	issn	issn	PROPN
ejpam-804	2	13	1307	1307	NUM
ejpam-804	2	14	-	-	SYM
ejpam-804	2	15	5543	5543	NUM
ejpam-804	2	16	–	–	PUNCT
ejpam-804	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-804	2	18	special	special	ADJ
ejpam-804	2	19	issue	issue	NOUN
ejpam-804	2	20	on	on	ADP
ejpam-804	2	21	granger	granger	PROPN
ejpam-804	2	22	econometrics	econometric	NOUN
ejpam-804	2	23	and	and	CCONJ
ejpam-804	2	24	statistical	statistical	ADJ
ejpam-804	2	25	modeling	modeling	NOUN
ejpam-804	2	26	dedicated	dedicate	VERB
ejpam-804	2	27	to	to	ADP
ejpam-804	2	28	the	the	DET
ejpam-804	2	29	memory	memory	NOUN
ejpam-804	2	30	of	of	ADP
ejpam-804	2	31	prof	prof	NOUN
ejpam-804	2	32	.	.	PUNCT
ejpam-804	3	1	sir	sir	PROPN
ejpam-804	3	2	clive	clive	PROPN
ejpam-804	3	3	w.j	w.j	PROPN
ejpam-804	3	4	.	.	PROPN
ejpam-804	4	1	granger	granger	PROPN
ejpam-804	4	2	a	a	DET
ejpam-804	4	3	generalization	generalization	NOUN
ejpam-804	4	4	of	of	ADP
ejpam-804	4	5	the	the	DET
ejpam-804	4	6	concept	concept	NOUN
ejpam-804	4	7	of	of	ADP
ejpam-804	4	8	cointegration	cointegration	NOUN
ejpam-804	4	9	to	to	ADP
ejpam-804	4	10	harmonizable	harmonizable	ADJ
ejpam-804	4	11	and	and	CCONJ
ejpam-804	4	12	class	class	NOUN
ejpam-804	4	13	(	(	PUNCT
ejpam-804	4	14	kf	kf	NOUN
ejpam-804	4	15	)	)	PUNCT
ejpam-804	4	16	processes	process	VERB
ejpam-804	4	17	roselyne	roselyne	PROPN
ejpam-804	4	18	joyeux	joyeux	PROPN
ejpam-804	4	19	faculty	faculty	NOUN
ejpam-804	4	20	of	of	ADP
ejpam-804	4	21	business	business	NOUN
ejpam-804	4	22	and	and	CCONJ
ejpam-804	4	23	economics	economic	NOUN
ejpam-804	4	24	,	,	PUNCT
ejpam-804	4	25	macquarie	macquarie	PROPN
ejpam-804	4	26	university	university	PROPN
ejpam-804	4	27	,	,	PUNCT
ejpam-804	4	28	sydney	sydney	PROPN
ejpam-804	4	29	2109	2109	NUM
ejpam-804	4	30	,	,	PUNCT
ejpam-804	4	31	australia	australia	PROPN
ejpam-804	4	32	abstract	abstract	NOUN
ejpam-804	4	33	.	.	PUNCT
ejpam-804	5	1	in	in	ADP
ejpam-804	5	2	this	this	DET
ejpam-804	5	3	paper	paper	NOUN
ejpam-804	5	4	we	we	PRON
ejpam-804	5	5	consider	consider	VERB
ejpam-804	5	6	the	the	DET
ejpam-804	5	7	generalization	generalization	NOUN
ejpam-804	5	8	of	of	ADP
ejpam-804	5	9	the	the	DET
ejpam-804	5	10	concept	concept	NOUN
ejpam-804	5	11	of	of	ADP
ejpam-804	5	12	cointegration	cointegration	NOUN
ejpam-804	5	13	to	to	ADP
ejpam-804	5	14	non	non	ADJ
ejpam-804	5	15	-	-	ADJ
ejpam-804	5	16	stationary	stationary	ADJ
ejpam-804	5	17	processes	process	NOUN
ejpam-804	5	18	which	which	PRON
ejpam-804	5	19	are	be	AUX
ejpam-804	5	20	not	not	PART
ejpam-804	5	21	necessarily	necessarily	ADV
ejpam-804	5	22	i(d	i(d	NOUN
ejpam-804	5	23	)	)	PUNCT
ejpam-804	5	24	.	.	PUNCT
ejpam-804	6	1	two	two	NUM
ejpam-804	6	2	cases	case	NOUN
ejpam-804	6	3	are	be	AUX
ejpam-804	6	4	of	of	ADP
ejpam-804	6	5	special	special	ADJ
ejpam-804	6	6	interest	interest	NOUN
ejpam-804	6	7	.	.	PUNCT
ejpam-804	7	1	first	first	ADV
ejpam-804	7	2	the	the	DET
ejpam-804	7	3	case	case	NOUN
ejpam-804	7	4	of	of	ADP
ejpam-804	7	5	nonstationary	nonstationary	ADJ
ejpam-804	7	6	processes	process	NOUN
ejpam-804	7	7	which	which	PRON
ejpam-804	7	8	adjust	adjust	VERB
ejpam-804	7	9	to	to	ADP
ejpam-804	7	10	an	an	DET
ejpam-804	7	11	equilibrium	equilibrium	NOUN
ejpam-804	7	12	not	not	PART
ejpam-804	7	13	necessarily	necessarily	ADV
ejpam-804	7	14	according	accord	VERB
ejpam-804	7	15	to	to	ADP
ejpam-804	7	16	a	a	DET
ejpam-804	7	17	linear	linear	ADJ
ejpam-804	7	18	adjustment	adjustment	NOUN
ejpam-804	7	19	process	process	NOUN
ejpam-804	7	20	.	.	PUNCT
ejpam-804	8	1	second	second	ADJ
ejpam-804	8	2	the	the	DET
ejpam-804	8	3	case	case	NOUN
ejpam-804	8	4	of	of	ADP
ejpam-804	8	5	non	non	ADJ
ejpam-804	8	6	-	-	ADJ
ejpam-804	8	7	stationary	stationary	ADJ
ejpam-804	8	8	(	(	PUNCT
ejpam-804	8	9	possibly	possibly	ADV
ejpam-804	8	10	i(1	i(1	PROPN
ejpam-804	8	11	)	)	PUNCT
ejpam-804	8	12	)	)	PUNCT
ejpam-804	8	13	series	serie	NOUN
ejpam-804	8	14	which	which	PRON
ejpam-804	8	15	co	co	VERB
ejpam-804	8	16	-	-	NOUN
ejpam-804	8	17	move	move	NOUN
ejpam-804	8	18	according	accord	VERB
ejpam-804	8	19	to	to	ADP
ejpam-804	8	20	a	a	DET
ejpam-804	8	21	non	non	ADJ
ejpam-804	8	22	linear	linear	ADJ
ejpam-804	8	23	or	or	CCONJ
ejpam-804	8	24	heteroscedastic	heteroscedastic	ADJ
ejpam-804	8	25	adjustment	adjustment	NOUN
ejpam-804	8	26	process	process	NOUN
ejpam-804	8	27	.	.	PUNCT
ejpam-804	9	1	the	the	DET
ejpam-804	9	2	non	non	ADJ
ejpam-804	9	3	-	-	ADJ
ejpam-804	9	4	stationary	stationary	ADJ
ejpam-804	9	5	processes	process	NOUN
ejpam-804	9	6	considered	consider	VERB
ejpam-804	9	7	here	here	ADV
ejpam-804	9	8	belong	belong	VERB
ejpam-804	9	9	to	to	ADP
ejpam-804	9	10	the	the	DET
ejpam-804	9	11	kampé	kampé	PROPN
ejpam-804	9	12	de	de	PROPN
ejpam-804	9	13	fériet	fériet	PROPN
ejpam-804	9	14	(	(	PUNCT
ejpam-804	9	15	kf	kf	NOUN
ejpam-804	9	16	)	)	PUNCT
ejpam-804	9	17	class	class	NOUN
ejpam-804	9	18	.	.	PUNCT
ejpam-804	10	1	2000	2000	NUM
ejpam-804	10	2	mathematics	mathematic	NOUN
ejpam-804	10	3	subject	subject	NOUN
ejpam-804	10	4	classifications	classification	NOUN
ejpam-804	10	5	:	:	PUNCT
ejpam-804	10	6	91b84,62m10,42b10,42a38	91b84,62m10,42b10,42a38	NUM
ejpam-804	10	7	key	key	ADJ
ejpam-804	10	8	words	word	NOUN
ejpam-804	10	9	and	and	CCONJ
ejpam-804	10	10	phrases	phrase	NOUN
ejpam-804	10	11	:	:	PUNCT
ejpam-804	10	12	kampé	kampé	PROPN
ejpam-804	10	13	de	de	PROPN
ejpam-804	10	14	fériet	fériet	PROPN
ejpam-804	10	15	processes	process	NOUN
ejpam-804	10	16	,	,	PUNCT
ejpam-804	10	17	non	non	ADJ
ejpam-804	10	18	-	-	ADJ
ejpam-804	10	19	stationary	stationary	ADJ
ejpam-804	10	20	,	,	PUNCT
ejpam-804	10	21	harmonizable	harmonizable	ADJ
ejpam-804	10	22	,	,	PUNCT
ejpam-804	10	23	cointegration	cointegration	NOUN
ejpam-804	10	24	,	,	PUNCT
ejpam-804	10	25	asymptotically	asymptotically	ADV
ejpam-804	10	26	stationary	stationary	ADJ
ejpam-804	10	27	1	1	NUM
ejpam-804	10	28	.	.	PUNCT
ejpam-804	11	1	introduction	introduction	NOUN
ejpam-804	11	2	the	the	DET
ejpam-804	11	3	theory	theory	NOUN
ejpam-804	11	4	of	of	ADP
ejpam-804	11	5	cointegration	cointegration	NOUN
ejpam-804	11	6	as	as	SCONJ
ejpam-804	11	7	introduced	introduce	VERB
ejpam-804	11	8	by	by	ADP
ejpam-804	11	9	engle	engle	PROPN
ejpam-804	11	10	and	and	CCONJ
ejpam-804	11	11	granger	granger	NOUN
ejpam-804	12	1	[	[	X
ejpam-804	12	2	7	7	X
ejpam-804	12	3	]	]	PUNCT
ejpam-804	12	4	refers	refer	VERB
ejpam-804	12	5	to	to	ADP
ejpam-804	12	6	the	the	DET
ejpam-804	12	7	situation	situation	NOUN
ejpam-804	12	8	where	where	SCONJ
ejpam-804	12	9	multiple	multiple	ADJ
ejpam-804	12	10	i(d	i(d	NOUN
ejpam-804	12	11	)	)	PUNCT
ejpam-804	12	12	series	series	NOUN
ejpam-804	12	13	can	can	AUX
ejpam-804	12	14	be	be	AUX
ejpam-804	12	15	combined	combine	VERB
ejpam-804	12	16	to	to	PART
ejpam-804	12	17	produce	produce	VERB
ejpam-804	12	18	an	an	DET
ejpam-804	12	19	i(k	i(k	PROPN
ejpam-804	12	20	)	)	PUNCT
ejpam-804	12	21	series	series	NOUN
ejpam-804	12	22	,	,	PUNCT
ejpam-804	12	23	where	where	SCONJ
ejpam-804	12	24	k	k	PROPN
ejpam-804	12	25	can	can	AUX
ejpam-804	12	26	range	range	VERB
ejpam-804	12	27	from	from	ADP
ejpam-804	12	28	0	0	NUM
ejpam-804	12	29	to	to	ADP
ejpam-804	12	30	d	d	NOUN
ejpam-804	12	31	−	−	PROPN
ejpam-804	12	32	1	1	NUM
ejpam-804	12	33	.	.	PUNCT
ejpam-804	13	1	in	in	ADP
ejpam-804	13	2	the	the	DET
ejpam-804	13	3	case	case	NOUN
ejpam-804	13	4	where	where	SCONJ
ejpam-804	13	5	d	d	NOUN
ejpam-804	13	6	=	=	SYM
ejpam-804	13	7	1	1	NUM
ejpam-804	13	8	two	two	NUM
ejpam-804	13	9	series	serie	NOUN
ejpam-804	13	10	are	be	AUX
ejpam-804	13	11	said	say	VERB
ejpam-804	13	12	to	to	PART
ejpam-804	13	13	be	be	AUX
ejpam-804	13	14	cointegrated	cointegrate	VERB
ejpam-804	13	15	if	if	SCONJ
ejpam-804	13	16	they	they	PRON
ejpam-804	13	17	are	be	AUX
ejpam-804	13	18	non	non	ADJ
ejpam-804	13	19	-	-	ADJ
ejpam-804	13	20	stationary	stationary	ADJ
ejpam-804	13	21	in	in	ADP
ejpam-804	13	22	levels	level	NOUN
ejpam-804	13	23	,	,	PUNCT
ejpam-804	13	24	stationary	stationary	ADJ
ejpam-804	13	25	in	in	ADP
ejpam-804	13	26	first	first	ADJ
ejpam-804	13	27	differences	difference	NOUN
ejpam-804	13	28	and	and	CCONJ
ejpam-804	13	29	there	there	PRON
ejpam-804	13	30	exists	exist	VERB
ejpam-804	13	31	a	a	DET
ejpam-804	13	32	linear	linear	ADJ
ejpam-804	13	33	combination	combination	NOUN
ejpam-804	13	34	of	of	ADP
ejpam-804	13	35	the	the	DET
ejpam-804	13	36	levels	level	NOUN
ejpam-804	13	37	which	which	PRON
ejpam-804	13	38	is	be	AUX
ejpam-804	13	39	stationary	stationary	ADJ
ejpam-804	13	40	.	.	PUNCT
ejpam-804	14	1	although	although	SCONJ
ejpam-804	14	2	this	this	DET
ejpam-804	14	3	approach	approach	NOUN
ejpam-804	14	4	has	have	AUX
ejpam-804	14	5	proved	prove	VERB
ejpam-804	14	6	to	to	PART
ejpam-804	14	7	be	be	AUX
ejpam-804	14	8	extremely	extremely	ADV
ejpam-804	14	9	fruitful	fruitful	ADJ
ejpam-804	14	10	in	in	ADP
ejpam-804	14	11	applications	application	NOUN
ejpam-804	14	12	,	,	PUNCT
ejpam-804	14	13	it	it	PRON
ejpam-804	14	14	has	have	AUX
ejpam-804	14	15	also	also	ADV
ejpam-804	14	16	frustrated	frustrate	VERB
ejpam-804	14	17	researchers	researcher	NOUN
ejpam-804	14	18	because	because	SCONJ
ejpam-804	14	19	of	of	ADP
ejpam-804	14	20	its	its	PRON
ejpam-804	14	21	limitations	limitation	NOUN
ejpam-804	14	22	.	.	PUNCT
ejpam-804	15	1	one	one	NUM
ejpam-804	15	2	limitation	limitation	NOUN
ejpam-804	15	3	is	be	AUX
ejpam-804	15	4	that	that	SCONJ
ejpam-804	15	5	it	it	PRON
ejpam-804	15	6	is	be	AUX
ejpam-804	15	7	assumed	assume	VERB
ejpam-804	15	8	that	that	SCONJ
ejpam-804	15	9	economic	economic	ADJ
ejpam-804	15	10	time	time	NOUN
ejpam-804	15	11	series	series	PROPN
ejpam-804	15	12	exhibiting	exhibit	VERB
ejpam-804	15	13	a	a	DET
ejpam-804	15	14	trending	trend	VERB
ejpam-804	15	15	behavior	behavior	NOUN
ejpam-804	15	16	can	can	AUX
ejpam-804	15	17	be	be	AUX
ejpam-804	15	18	well	well	ADV
ejpam-804	15	19	approximated	approximate	VERB
ejpam-804	15	20	by	by	ADP
ejpam-804	15	21	processes	process	NOUN
ejpam-804	15	22	that	that	PRON
ejpam-804	15	23	are	be	AUX
ejpam-804	15	24	integrated	integrate	VERB
ejpam-804	15	25	,	,	PUNCT
ejpam-804	15	26	usually	usually	ADV
ejpam-804	15	27	of	of	ADP
ejpam-804	15	28	order	order	NOUN
ejpam-804	15	29	one	one	NUM
ejpam-804	15	30	.	.	PUNCT
ejpam-804	16	1	a	a	DET
ejpam-804	16	2	second	second	ADJ
ejpam-804	16	3	limitation	limitation	NOUN
ejpam-804	16	4	is	be	AUX
ejpam-804	16	5	that	that	SCONJ
ejpam-804	16	6	cointegrated	cointegrate	VERB
ejpam-804	16	7	series	series	PROPN
ejpam-804	16	8	co	co	NOUN
ejpam-804	16	9	-	-	NOUN
ejpam-804	16	10	move	move	NOUN
ejpam-804	16	11	according	accord	VERB
ejpam-804	16	12	to	to	ADP
ejpam-804	16	13	a	a	DET
ejpam-804	16	14	stationary	stationary	ADJ
ejpam-804	16	15	process	process	NOUN
ejpam-804	16	16	.	.	PUNCT
ejpam-804	17	1	harris	harris	PROPN
ejpam-804	17	2	et	et	PROPN
ejpam-804	17	3	al	al	PROPN
ejpam-804	17	4	.	.	PUNCT
ejpam-804	18	1	[	[	X
ejpam-804	18	2	12	12	NUM
ejpam-804	18	3	]	]	PUNCT
ejpam-804	18	4	remark	remark	NOUN
ejpam-804	18	5	that	that	SCONJ
ejpam-804	18	6	higher	high	ADJ
ejpam-804	18	7	frequency	frequency	NOUN
ejpam-804	18	8	data	datum	NOUN
ejpam-804	18	9	appear	appear	VERB
ejpam-804	18	10	to	to	PART
ejpam-804	18	11	be	be	AUX
ejpam-804	18	12	more	more	ADV
ejpam-804	18	13	volatile	volatile	ADJ
ejpam-804	18	14	than	than	SCONJ
ejpam-804	18	15	would	would	AUX
ejpam-804	18	16	be	be	AUX
ejpam-804	18	17	expected	expect	VERB
ejpam-804	18	18	from	from	ADP
ejpam-804	18	19	i(1	i(1	PROPN
ejpam-804	18	20	)	)	PUNCT
ejpam-804	18	21	processes	process	NOUN
ejpam-804	18	22	.	.	PUNCT
ejpam-804	19	1	they	they	PRON
ejpam-804	19	2	also	also	ADV
ejpam-804	19	3	note	note	VERB
ejpam-804	19	4	that	that	SCONJ
ejpam-804	19	5	series	series	NOUN
ejpam-804	19	6	,	,	PUNCT
ejpam-804	19	7	which	which	PRON
ejpam-804	19	8	should	should	AUX
ejpam-804	19	9	co	co	VERB
ejpam-804	19	10	-	-	VERB
ejpam-804	19	11	move	move	ADJ
ejpam-804	19	12	,	,	PUNCT
ejpam-804	19	13	often	often	ADV
ejpam-804	19	14	deviate	deviate	VERB
ejpam-804	19	15	email	email	NOUN
ejpam-804	19	16	address	address	NOUN
ejpam-804	19	17	:	:	PUNCT
ejpam-804	19	18	rjoyeux�efs.mq.edu.au	rjoyeux�efs.mq.edu.au	X
ejpam-804	19	19	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-804	20	1	519	519	NUM
ejpam-804	20	2	c	c	X
ejpam-804	20	3	©	©	PROPN
ejpam-804	20	4	2010	2010	NUM
ejpam-804	20	5	ejpam	ejpam	NOUN
ejpam-804	20	6	all	all	DET
ejpam-804	20	7	rights	right	NOUN
ejpam-804	20	8	reserved	reserve	VERB
ejpam-804	20	9	.	.	PUNCT
ejpam-804	21	1	r.	r.	PROPN
ejpam-804	21	2	joyeux	joyeux	PROPN
ejpam-804	21	3	/	/	SYM
ejpam-804	21	4	eur	eur	PROPN
ejpam-804	21	5	.	.	PUNCT
ejpam-804	22	1	j.	j.	PROPN
ejpam-804	22	2	pure	pure	PROPN
ejpam-804	22	3	appl	appl	PROPN
ejpam-804	22	4	.	.	PROPN
ejpam-804	22	5	math	math	PROPN
ejpam-804	22	6	,	,	PUNCT
ejpam-804	22	7	3	3	NUM
ejpam-804	22	8	(	(	PUNCT
ejpam-804	22	9	2010	2010	NUM
ejpam-804	22	10	)	)	PUNCT
ejpam-804	22	11	,	,	PUNCT
ejpam-804	22	12	519	519	NUM
ejpam-804	22	13	-	-	SYM
ejpam-804	22	14	530	530	NUM
ejpam-804	22	15	520	520	NUM
ejpam-804	22	16	substantially	substantially	ADV
ejpam-804	22	17	for	for	ADP
ejpam-804	22	18	short	short	ADJ
ejpam-804	22	19	periods	period	NOUN
ejpam-804	22	20	of	of	ADP
ejpam-804	22	21	time	time	NOUN
ejpam-804	22	22	.	.	PUNCT
ejpam-804	23	1	they	they	PRON
ejpam-804	23	2	addresses	address	VERB
ejpam-804	23	3	those	those	DET
ejpam-804	23	4	issues	issue	NOUN
ejpam-804	23	5	by	by	ADP
ejpam-804	23	6	introducing	introduce	VERB
ejpam-804	23	7	the	the	DET
ejpam-804	23	8	concept	concept	NOUN
ejpam-804	23	9	of	of	ADP
ejpam-804	23	10	stochastic	stochastic	ADJ
ejpam-804	23	11	integration	integration	NOUN
ejpam-804	23	12	and	and	CCONJ
ejpam-804	23	13	stochastic	stochastic	ADJ
ejpam-804	23	14	cointegration	cointegration	NOUN
ejpam-804	23	15	.	.	PUNCT
ejpam-804	24	1	briefly	briefly	NOUN
ejpam-804	24	2	a	a	DET
ejpam-804	24	3	process	process	NOUN
ejpam-804	24	4	is	be	AUX
ejpam-804	24	5	stochastically	stochastically	ADV
ejpam-804	24	6	integrated	integrate	VERB
ejpam-804	24	7	if	if	SCONJ
ejpam-804	24	8	it	it	PRON
ejpam-804	24	9	consists	consist	VERB
ejpam-804	24	10	of	of	ADP
ejpam-804	24	11	a	a	DET
ejpam-804	24	12	non	non	ADJ
ejpam-804	24	13	-	-	ADJ
ejpam-804	24	14	mean	mean	ADJ
ejpam-804	24	15	reverting∗	reverting∗	NOUN
ejpam-804	24	16	i(1	i(1	NOUN
ejpam-804	24	17	)	)	PUNCT
ejpam-804	24	18	stochastic	stochastic	ADJ
ejpam-804	24	19	trend	trend	NOUN
ejpam-804	24	20	plus	plus	CCONJ
ejpam-804	24	21	a	a	DET
ejpam-804	24	22	heteroskedastic	heteroskedastic	ADJ
ejpam-804	24	23	shock	shock	NOUN
ejpam-804	24	24	term	term	NOUN
ejpam-804	24	25	.	.	PUNCT
ejpam-804	25	1	the	the	DET
ejpam-804	25	2	first	first	ADJ
ejpam-804	25	3	difference	difference	NOUN
ejpam-804	25	4	of	of	ADP
ejpam-804	25	5	such	such	DET
ejpam-804	25	6	a	a	DET
ejpam-804	25	7	process	process	NOUN
ejpam-804	25	8	is	be	AUX
ejpam-804	25	9	mean	mean	VERB
ejpam-804	25	10	reverting	revert	VERB
ejpam-804	25	11	but	but	CCONJ
ejpam-804	25	12	not	not	PART
ejpam-804	25	13	i(0	i(0	PROPN
ejpam-804	25	14	)	)	PUNCT
ejpam-804	25	15	.	.	PUNCT
ejpam-804	26	1	two	two	NUM
ejpam-804	26	2	processes	process	NOUN
ejpam-804	26	3	are	be	AUX
ejpam-804	26	4	stochastically	stochastically	ADV
ejpam-804	26	5	cointegrated	cointegrate	VERB
ejpam-804	26	6	if	if	SCONJ
ejpam-804	26	7	they	they	PRON
ejpam-804	26	8	are	be	AUX
ejpam-804	26	9	stochastically	stochastically	ADV
ejpam-804	26	10	integrated	integrate	VERB
ejpam-804	26	11	and	and	CCONJ
ejpam-804	26	12	there	there	PRON
ejpam-804	26	13	exists	exist	VERB
ejpam-804	26	14	a	a	DET
ejpam-804	26	15	linear	linear	ADJ
ejpam-804	26	16	combination	combination	NOUN
ejpam-804	26	17	of	of	ADP
ejpam-804	26	18	the	the	DET
ejpam-804	26	19	two	two	NUM
ejpam-804	26	20	which	which	PRON
ejpam-804	26	21	is	be	AUX
ejpam-804	26	22	mean	mean	VERB
ejpam-804	26	23	reverting	revert	VERB
ejpam-804	26	24	but	but	CCONJ
ejpam-804	26	25	not	not	PART
ejpam-804	26	26	necessarily	necessarily	ADV
ejpam-804	26	27	i(0	i(0	PROPN
ejpam-804	26	28	)	)	PUNCT
ejpam-804	26	29	.	.	PUNCT
ejpam-804	27	1	in	in	ADP
ejpam-804	27	2	particular	particular	ADJ
ejpam-804	27	3	heteroskedastic	heteroskedastic	ADJ
ejpam-804	27	4	error	error	NOUN
ejpam-804	27	5	correction	correction	NOUN
ejpam-804	27	6	terms	term	NOUN
ejpam-804	27	7	are	be	AUX
ejpam-804	27	8	allowed	allow	VERB
ejpam-804	27	9	.	.	PUNCT
ejpam-804	28	1	a	a	DET
ejpam-804	28	2	third	third	ADJ
ejpam-804	28	3	limitation	limitation	NOUN
ejpam-804	28	4	is	be	AUX
ejpam-804	28	5	that	that	SCONJ
ejpam-804	28	6	most	most	ADJ
ejpam-804	28	7	tests	test	NOUN
ejpam-804	28	8	for	for	ADP
ejpam-804	28	9	unit	unit	NOUN
ejpam-804	28	10	roots	root	NOUN
ejpam-804	28	11	and	and	CCONJ
ejpam-804	28	12	cointegration	cointegration	NOUN
ejpam-804	28	13	assume	assume	VERB
ejpam-804	28	14	a	a	DET
ejpam-804	28	15	linear	linear	ADJ
ejpam-804	28	16	arima	arima	NOUN
ejpam-804	28	17	or	or	CCONJ
ejpam-804	28	18	var	var	NOUN
ejpam-804	28	19	framework	framework	NOUN
ejpam-804	28	20	.	.	PUNCT
ejpam-804	29	1	for	for	ADP
ejpam-804	29	2	example	example	NOUN
ejpam-804	29	3	in	in	ADP
ejpam-804	29	4	the	the	DET
ejpam-804	29	5	dickey	dickey	NOUN
ejpam-804	29	6	and	and	CCONJ
ejpam-804	29	7	fuller	full	ADJ
ejpam-804	29	8	[	[	X
ejpam-804	29	9	5	5	NUM
ejpam-804	29	10	]	]	PUNCT
ejpam-804	29	11	test	test	NOUN
ejpam-804	29	12	for	for	ADP
ejpam-804	29	13	a	a	DET
ejpam-804	29	14	unit	unit	NOUN
ejpam-804	29	15	root	root	NOUN
ejpam-804	29	16	assumes	assume	VERB
ejpam-804	29	17	a	a	DET
ejpam-804	29	18	linear	linear	ADJ
ejpam-804	29	19	arima	arima	PROPN
ejpam-804	29	20	model	model	NOUN
ejpam-804	29	21	.	.	PUNCT
ejpam-804	30	1	if	if	SCONJ
ejpam-804	30	2	the	the	DET
ejpam-804	30	3	series	series	NOUN
ejpam-804	30	4	is	be	AUX
ejpam-804	30	5	generated	generate	VERB
ejpam-804	30	6	by	by	ADP
ejpam-804	30	7	a	a	DET
ejpam-804	30	8	non	non	ADJ
ejpam-804	30	9	-	-	ADJ
ejpam-804	30	10	linear	linear	ADJ
ejpam-804	30	11	model	model	NOUN
ejpam-804	30	12	,	,	PUNCT
ejpam-804	30	13	the	the	DET
ejpam-804	30	14	dickey	dickey	NOUN
ejpam-804	30	15	-	-	PUNCT
ejpam-804	30	16	fuller	full	ADJ
ejpam-804	30	17	test	test	NOUN
ejpam-804	30	18	can	can	AUX
ejpam-804	30	19	lead	lead	VERB
ejpam-804	30	20	us	we	PRON
ejpam-804	30	21	to	to	PART
ejpam-804	30	22	conclude	conclude	VERB
ejpam-804	30	23	erroneously	erroneously	ADV
ejpam-804	30	24	that	that	SCONJ
ejpam-804	30	25	the	the	DET
ejpam-804	30	26	series	series	NOUN
ejpam-804	30	27	has	have	VERB
ejpam-804	30	28	a	a	DET
ejpam-804	30	29	unit	unit	NOUN
ejpam-804	30	30	root	root	NOUN
ejpam-804	30	31	.	.	PUNCT
ejpam-804	31	1	a	a	DET
ejpam-804	31	2	linear	linear	ADJ
ejpam-804	31	3	relationship	relationship	NOUN
ejpam-804	31	4	is	be	AUX
ejpam-804	31	5	also	also	ADV
ejpam-804	31	6	assumed	assume	VERB
ejpam-804	31	7	as	as	ADP
ejpam-804	31	8	the	the	DET
ejpam-804	31	9	basis	basis	NOUN
ejpam-804	31	10	for	for	ADP
ejpam-804	31	11	the	the	DET
ejpam-804	31	12	engle	engle	NOUN
ejpam-804	31	13	-	-	PUNCT
ejpam-804	31	14	granger	granger	PROPN
ejpam-804	31	15	and	and	CCONJ
ejpam-804	31	16	the	the	DET
ejpam-804	31	17	johansen	johansen	PROPN
ejpam-804	31	18	’s	’s	PART
ejpam-804	31	19	tests	test	NOUN
ejpam-804	31	20	for	for	ADP
ejpam-804	31	21	cointegration	cointegration	NOUN
ejpam-804	31	22	[	[	X
ejpam-804	31	23	7	7	NUM
ejpam-804	31	24	,	,	PUNCT
ejpam-804	31	25	13	13	NUM
ejpam-804	31	26	]	]	PUNCT
ejpam-804	31	27	.	.	PUNCT
ejpam-804	32	1	those	those	DET
ejpam-804	32	2	tests	test	NOUN
ejpam-804	32	3	might	might	AUX
ejpam-804	32	4	fail	fail	VERB
ejpam-804	32	5	to	to	PART
ejpam-804	32	6	detect	detect	VERB
ejpam-804	32	7	an	an	DET
ejpam-804	32	8	adjustment	adjustment	NOUN
ejpam-804	32	9	to	to	ADP
ejpam-804	32	10	equilibrium	equilibrium	NOUN
ejpam-804	32	11	if	if	SCONJ
ejpam-804	32	12	such	such	DET
ejpam-804	32	13	an	an	DET
ejpam-804	32	14	adjustment	adjustment	NOUN
ejpam-804	32	15	is	be	AUX
ejpam-804	32	16	non	non	ADJ
ejpam-804	32	17	-	-	ADJ
ejpam-804	32	18	linear	linear	ADJ
ejpam-804	32	19	.	.	PUNCT
ejpam-804	33	1	enders	ender	NOUN
ejpam-804	33	2	and	and	CCONJ
ejpam-804	33	3	ludlow	ludlow	NOUN
ejpam-804	34	1	[	[	X
ejpam-804	34	2	6	6	NUM
ejpam-804	34	3	]	]	PUNCT
ejpam-804	34	4	develop	develop	VERB
ejpam-804	34	5	a	a	DET
ejpam-804	34	6	test	test	NOUN
ejpam-804	34	7	for	for	ADP
ejpam-804	34	8	reversion	reversion	NOUN
ejpam-804	34	9	that	that	PRON
ejpam-804	34	10	does	do	AUX
ejpam-804	34	11	not	not	PART
ejpam-804	34	12	a	a	DET
ejpam-804	34	13	priori	priori	ADV
ejpam-804	34	14	impose	impose	VERB
ejpam-804	34	15	a	a	DET
ejpam-804	34	16	particular	particular	ADJ
ejpam-804	34	17	dynamic	dynamic	ADJ
ejpam-804	34	18	structure	structure	NOUN
ejpam-804	34	19	of	of	ADP
ejpam-804	34	20	the	the	DET
ejpam-804	34	21	adjustment	adjustment	NOUN
ejpam-804	34	22	coefficients	coefficient	NOUN
ejpam-804	34	23	.	.	PUNCT
ejpam-804	35	1	they	they	PRON
ejpam-804	35	2	use	use	VERB
ejpam-804	35	3	a	a	DET
ejpam-804	35	4	first	first	ADJ
ejpam-804	35	5	order	order	NOUN
ejpam-804	35	6	fourier	fourier	NOUN
ejpam-804	35	7	approximation	approximation	NOUN
ejpam-804	35	8	which	which	PRON
ejpam-804	35	9	allows	allow	VERB
ejpam-804	35	10	for	for	ADP
ejpam-804	35	11	non	non	ADJ
ejpam-804	35	12	-	-	ADJ
ejpam-804	35	13	linear	linear	ADJ
ejpam-804	35	14	decay	decay	NOUN
ejpam-804	35	15	.	.	PUNCT
ejpam-804	36	1	because	because	SCONJ
ejpam-804	36	2	of	of	ADP
ejpam-804	36	3	these	these	DET
ejpam-804	36	4	limitations	limitation	NOUN
ejpam-804	36	5	there	there	PRON
ejpam-804	36	6	is	be	VERB
ejpam-804	36	7	a	a	DET
ejpam-804	36	8	need	need	NOUN
ejpam-804	36	9	to	to	PART
ejpam-804	36	10	study	study	VERB
ejpam-804	36	11	a	a	DET
ejpam-804	36	12	larger	large	ADJ
ejpam-804	36	13	class	class	NOUN
ejpam-804	36	14	of	of	ADP
ejpam-804	36	15	processes	process	NOUN
ejpam-804	36	16	besides	besides	SCONJ
ejpam-804	36	17	i(d	i(d	NOUN
ejpam-804	36	18	)	)	PUNCT
ejpam-804	36	19	processes	process	NOUN
ejpam-804	36	20	and	and	CCONJ
ejpam-804	36	21	to	to	PART
ejpam-804	36	22	develop	develop	VERB
ejpam-804	36	23	tools	tool	NOUN
ejpam-804	36	24	to	to	PART
ejpam-804	36	25	study	study	VERB
ejpam-804	36	26	those	those	DET
ejpam-804	36	27	processes	process	NOUN
ejpam-804	36	28	.	.	PUNCT
ejpam-804	37	1	in	in	ADP
ejpam-804	37	2	particular	particular	ADJ
ejpam-804	37	3	the	the	DET
ejpam-804	37	4	cointegration	cointegration	NOUN
ejpam-804	37	5	concept	concept	NOUN
ejpam-804	37	6	needs	need	VERB
ejpam-804	37	7	to	to	PART
ejpam-804	37	8	be	be	AUX
ejpam-804	37	9	generalized	generalize	VERB
ejpam-804	37	10	to	to	ADP
ejpam-804	37	11	non	non	ADJ
ejpam-804	37	12	-	-	ADJ
ejpam-804	37	13	stationary	stationary	ADJ
ejpam-804	37	14	series	series	NOUN
ejpam-804	37	15	which	which	PRON
ejpam-804	37	16	are	be	AUX
ejpam-804	37	17	not	not	PART
ejpam-804	37	18	necessarily	necessarily	ADV
ejpam-804	37	19	integrated	integrate	VERB
ejpam-804	37	20	and	and	CCONJ
ejpam-804	37	21	whose	whose	DET
ejpam-804	37	22	co	co	NOUN
ejpam-804	37	23	-	-	NOUN
ejpam-804	37	24	movements	movement	NOUN
ejpam-804	37	25	are	be	AUX
ejpam-804	37	26	not	not	PART
ejpam-804	37	27	necessarily	necessarily	ADV
ejpam-804	37	28	according	accord	VERB
ejpam-804	37	29	to	to	ADP
ejpam-804	37	30	i(0	i(0	PROPN
ejpam-804	37	31	)	)	PUNCT
ejpam-804	37	32	processes	process	NOUN
ejpam-804	37	33	.	.	PUNCT
ejpam-804	38	1	other	other	ADJ
ejpam-804	38	2	generalisations	generalisation	NOUN
ejpam-804	38	3	of	of	ADP
ejpam-804	38	4	cointegration	cointegration	NOUN
ejpam-804	38	5	have	have	AUX
ejpam-804	38	6	been	be	AUX
ejpam-804	38	7	proposed	propose	VERB
ejpam-804	38	8	previously	previously	ADV
ejpam-804	38	9	.	.	PUNCT
ejpam-804	39	1	gregoir	gregoir	PROPN
ejpam-804	40	1	[	[	X
ejpam-804	40	2	9	9	NUM
ejpam-804	40	3	,	,	PUNCT
ejpam-804	40	4	10	10	NUM
ejpam-804	40	5	]	]	PUNCT
ejpam-804	40	6	uses	use	VERB
ejpam-804	40	7	the	the	DET
ejpam-804	40	8	framework	framework	NOUN
ejpam-804	40	9	introduced	introduce	VERB
ejpam-804	40	10	by	by	ADP
ejpam-804	40	11	gregoir	gregoir	NOUN
ejpam-804	40	12	and	and	CCONJ
ejpam-804	40	13	laroque	laroque	NOUN
ejpam-804	40	14	[	[	X
ejpam-804	40	15	11	11	NUM
ejpam-804	40	16	]	]	PUNCT
ejpam-804	40	17	to	to	PART
ejpam-804	40	18	define	define	VERB
ejpam-804	40	19	integral	integral	ADJ
ejpam-804	40	20	operators	operator	NOUN
ejpam-804	40	21	to	to	PART
ejpam-804	40	22	build	build	VERB
ejpam-804	40	23	up	up	ADP
ejpam-804	40	24	nonstationary	nonstationary	ADJ
ejpam-804	40	25	time	time	NOUN
ejpam-804	40	26	series	series	NOUN
ejpam-804	40	27	.	.	PUNCT
ejpam-804	41	1	this	this	DET
ejpam-804	41	2	type	type	NOUN
ejpam-804	41	3	of	of	ADP
ejpam-804	41	4	specification	specification	NOUN
ejpam-804	41	5	may	may	AUX
ejpam-804	41	6	occur	occur	VERB
ejpam-804	41	7	for	for	ADP
ejpam-804	41	8	time	time	NOUN
ejpam-804	41	9	series	series	NOUN
ejpam-804	41	10	models	model	NOUN
ejpam-804	41	11	with	with	ADP
ejpam-804	41	12	more	more	ADJ
ejpam-804	41	13	than	than	ADP
ejpam-804	41	14	one	one	NUM
ejpam-804	41	15	unit	unit	NOUN
ejpam-804	41	16	root	root	NOUN
ejpam-804	41	17	at	at	ADP
ejpam-804	41	18	frequency	frequency	NOUN
ejpam-804	41	19	zero	zero	NUM
ejpam-804	41	20	and	and	CCONJ
ejpam-804	41	21	some	some	DET
ejpam-804	41	22	seasonal	seasonal	ADJ
ejpam-804	41	23	unit	unit	NOUN
ejpam-804	41	24	roots	root	NOUN
ejpam-804	41	25	.	.	PUNCT
ejpam-804	42	1	in	in	ADP
ejpam-804	42	2	this	this	DET
ejpam-804	42	3	paper	paper	NOUN
ejpam-804	42	4	we	we	PRON
ejpam-804	42	5	consider	consider	VERB
ejpam-804	42	6	a	a	DET
ejpam-804	42	7	class	class	NOUN
ejpam-804	42	8	of	of	ADP
ejpam-804	42	9	processes	process	NOUN
ejpam-804	42	10	which	which	PRON
ejpam-804	42	11	are	be	AUX
ejpam-804	42	12	non	non	ADJ
ejpam-804	42	13	-	-	ADJ
ejpam-804	42	14	stationary	stationary	ADJ
ejpam-804	42	15	and	and	CCONJ
ejpam-804	42	16	includes	include	VERB
ejpam-804	42	17	the	the	DET
ejpam-804	42	18	class	class	NOUN
ejpam-804	42	19	of	of	ADP
ejpam-804	42	20	stationary	stationary	ADJ
ejpam-804	42	21	processes	process	NOUN
ejpam-804	42	22	as	as	ADP
ejpam-804	42	23	a	a	DET
ejpam-804	42	24	subset	subset	NOUN
ejpam-804	42	25	.	.	PUNCT
ejpam-804	43	1	this	this	PRON
ejpam-804	43	2	is	be	AUX
ejpam-804	43	3	the	the	DET
ejpam-804	43	4	class	class	NOUN
ejpam-804	43	5	of	of	ADP
ejpam-804	43	6	kampé	kampé	PROPN
ejpam-804	43	7	de	de	PROPN
ejpam-804	43	8	fériet	fériet	PROPN
ejpam-804	43	9	(	(	PUNCT
ejpam-804	43	10	kf	kf	NOUN
ejpam-804	43	11	)	)	PUNCT
ejpam-804	43	12	processes	process	NOUN
ejpam-804	43	13	.	.	PUNCT
ejpam-804	44	1	kampé	kampé	PROPN
ejpam-804	44	2	de	de	PROPN
ejpam-804	44	3	fériet	fériet	NOUN
ejpam-804	44	4	processes	process	NOUN
ejpam-804	44	5	provide	provide	VERB
ejpam-804	44	6	a	a	DET
ejpam-804	44	7	natural	natural	ADJ
ejpam-804	44	8	extension	extension	NOUN
ejpam-804	44	9	to	to	ADP
ejpam-804	44	10	the	the	DET
ejpam-804	44	11	class	class	NOUN
ejpam-804	44	12	of	of	ADP
ejpam-804	44	13	stationary	stationary	ADJ
ejpam-804	44	14	processes	process	NOUN
ejpam-804	44	15	.	.	PUNCT
ejpam-804	45	1	the	the	DET
ejpam-804	45	2	(	(	PUNCT
ejpam-804	45	3	kf	kf	NOUN
ejpam-804	45	4	)	)	PUNCT
ejpam-804	45	5	class	class	NOUN
ejpam-804	45	6	includes	include	VERB
ejpam-804	45	7	modulated	modulate	VERB
ejpam-804	45	8	stationary	stationary	ADJ
ejpam-804	45	9	processes	process	NOUN
ejpam-804	45	10	,	,	PUNCT
ejpam-804	45	11	slowly	slowly	ADV
ejpam-804	45	12	changing	change	VERB
ejpam-804	45	13	processes	process	NOUN
ejpam-804	45	14	and	and	CCONJ
ejpam-804	45	15	periodic	periodic	ADJ
ejpam-804	45	16	stationary	stationary	ADJ
ejpam-804	45	17	processes	process	NOUN
ejpam-804	45	18	.	.	PUNCT
ejpam-804	46	1	they	they	PRON
ejpam-804	46	2	have	have	AUX
ejpam-804	46	3	been	be	AUX
ejpam-804	46	4	studied	study	VERB
ejpam-804	46	5	in	in	ADP
ejpam-804	46	6	engineering	engineering	NOUN
ejpam-804	46	7	and	and	CCONJ
ejpam-804	46	8	signal	signal	NOUN
ejpam-804	46	9	processing	processing	NOUN
ejpam-804	46	10	.	.	PUNCT
ejpam-804	47	1	their	their	PRON
ejpam-804	47	2	wavelet	wavelet	NOUN
ejpam-804	47	3	decomposition	decomposition	NOUN
ejpam-804	47	4	has	have	AUX
ejpam-804	47	5	also	also	ADV
ejpam-804	47	6	been	be	AUX
ejpam-804	47	7	investigated	investigate	VERB
ejpam-804	47	8	(	(	PUNCT
ejpam-804	47	9	[	[	X
ejpam-804	47	10	2	2	NUM
ejpam-804	47	11	,	,	PUNCT
ejpam-804	47	12	28	28	NUM
ejpam-804	47	13	]	]	PUNCT
ejpam-804	47	14	.	.	PUNCT
ejpam-804	48	1	in	in	ADP
ejpam-804	48	2	section	section	NOUN
ejpam-804	48	3	2	2	NUM
ejpam-804	48	4	we	we	PRON
ejpam-804	48	5	consider	consider	VERB
ejpam-804	48	6	the	the	DET
ejpam-804	48	7	class	class	NOUN
ejpam-804	48	8	(	(	PUNCT
ejpam-804	48	9	kf	kf	NOUN
ejpam-804	48	10	)	)	PUNCT
ejpam-804	48	11	studied	study	VERB
ejpam-804	48	12	by	by	ADP
ejpam-804	48	13	kampé	kampé	PROPN
ejpam-804	48	14	de	de	PROPN
ejpam-804	48	15	fériet	fériet	PROPN
ejpam-804	48	16	and	and	CCONJ
ejpam-804	48	17	frankel	frankel	NOUN
ejpam-804	48	18	[	[	X
ejpam-804	48	19	17	17	NUM
ejpam-804	48	20	]	]	PUNCT
ejpam-804	48	21	and	and	CCONJ
ejpam-804	48	22	independently	independently	ADV
ejpam-804	48	23	by	by	ADP
ejpam-804	48	24	parzen	parzen	NOUN
ejpam-804	48	25	[	[	X
ejpam-804	48	26	22	22	NUM
ejpam-804	48	27	]	]	PUNCT
ejpam-804	48	28	and	and	CCONJ
ejpam-804	48	29	rozanov	rozanov	VERB
ejpam-804	48	30	[	[	NOUN
ejpam-804	48	31	27	27	NUM
ejpam-804	48	32	]	]	PUNCT
ejpam-804	48	33	under	under	ADP
ejpam-804	48	34	the	the	DET
ejpam-804	48	35	name	name	NOUN
ejpam-804	48	36	of	of	ADP
ejpam-804	48	37	asymptotically	asymptotically	ADV
ejpam-804	48	38	stationary	stationary	ADJ
ejpam-804	48	39	processes	process	NOUN
ejpam-804	48	40	.	.	PUNCT
ejpam-804	49	1	we	we	PRON
ejpam-804	49	2	show	show	VERB
ejpam-804	49	3	that	that	SCONJ
ejpam-804	49	4	,	,	PUNCT
ejpam-804	49	5	for	for	ADP
ejpam-804	49	6	example	example	NOUN
ejpam-804	49	7	,	,	PUNCT
ejpam-804	49	8	the	the	DET
ejpam-804	49	9	non	non	ADJ
ejpam-804	49	10	linear	linear	PROPN
ejpam-804	49	11	processes	process	NOUN
ejpam-804	49	12	considered	consider	VERB
ejpam-804	49	13	by	by	ADP
ejpam-804	49	14	enders	ender	NOUN
ejpam-804	49	15	and	and	CCONJ
ejpam-804	49	16	ludlow	ludlow	NOUN
ejpam-804	49	17	[	[	X
ejpam-804	49	18	6	6	NUM
ejpam-804	49	19	]	]	PUNCT
ejpam-804	49	20	are	be	AUX
ejpam-804	49	21	of	of	ADP
ejpam-804	49	22	class	class	NOUN
ejpam-804	49	23	(	(	PUNCT
ejpam-804	49	24	kf	kf	NOUN
ejpam-804	49	25	)	)	PUNCT
ejpam-804	49	26	.	.	PUNCT
ejpam-804	50	1	in	in	ADP
ejpam-804	50	2	section	section	NOUN
ejpam-804	50	3	3	3	NUM
ejpam-804	50	4	we	we	PRON
ejpam-804	50	5	study	study	VERB
ejpam-804	50	6	the	the	DET
ejpam-804	50	7	properties	property	NOUN
ejpam-804	50	8	of	of	ADP
ejpam-804	50	9	a	a	DET
ejpam-804	50	10	subclass	subclass	NOUN
ejpam-804	50	11	of	of	ADP
ejpam-804	50	12	the	the	DET
ejpam-804	50	13	(	(	PUNCT
ejpam-804	50	14	kf	kf	NOUN
ejpam-804	50	15	)	)	PUNCT
ejpam-804	50	16	class	class	NOUN
ejpam-804	50	17	:	:	PUNCT
ejpam-804	50	18	strongly	strongly	ADV
ejpam-804	50	19	harmonizable	harmonizable	ADJ
ejpam-804	50	20	processes	process	NOUN
ejpam-804	50	21	.	.	PUNCT
ejpam-804	51	1	in	in	ADP
ejpam-804	51	2	section	section	NOUN
ejpam-804	51	3	4	4	NUM
ejpam-804	51	4	we	we	PRON
ejpam-804	51	5	investigate	investigate	VERB
ejpam-804	51	6	generalizations	generalization	NOUN
ejpam-804	51	7	of	of	ADP
ejpam-804	51	8	the	the	DET
ejpam-804	51	9	concept	concept	NOUN
ejpam-804	51	10	of	of	ADP
ejpam-804	51	11	cointegration	cointegration	NOUN
ejpam-804	51	12	to	to	ADP
ejpam-804	51	13	(	(	PUNCT
ejpam-804	51	14	kf	kf	NOUN
ejpam-804	51	15	)	)	PUNCT
ejpam-804	51	16	processes	process	NOUN
ejpam-804	51	17	and	and	CCONJ
ejpam-804	51	18	consider	consider	VERB
ejpam-804	51	19	the	the	DET
ejpam-804	51	20	special	special	ADJ
ejpam-804	51	21	case	case	NOUN
ejpam-804	51	22	of	of	ADP
ejpam-804	51	23	strongly	strongly	ADV
ejpam-804	51	24	harmonizable	harmonizable	ADJ
ejpam-804	51	25	processes	process	NOUN
ejpam-804	51	26	.	.	PUNCT
ejpam-804	52	1	we	we	PRON
ejpam-804	52	2	present	present	VERB
ejpam-804	52	3	two	two	NUM
ejpam-804	52	4	concepts	concept	NOUN
ejpam-804	52	5	of	of	ADP
ejpam-804	52	6	cointegration	cointegration	NOUN
ejpam-804	52	7	.	.	PUNCT
ejpam-804	53	1	the	the	DET
ejpam-804	53	2	first	first	ADJ
ejpam-804	53	3	one	one	NOUN
ejpam-804	53	4	is	be	AUX
ejpam-804	53	5	the	the	DET
ejpam-804	53	6	case	case	NOUN
ejpam-804	53	7	where	where	SCONJ
ejpam-804	53	8	there	there	PRON
ejpam-804	53	9	exists	exist	VERB
ejpam-804	53	10	a	a	DET
ejpam-804	53	11	stationary	stationary	ADJ
ejpam-804	53	12	linear	linear	ADJ
ejpam-804	53	13	combination	combination	NOUN
ejpam-804	53	14	of	of	ADP
ejpam-804	53	15	(	(	PUNCT
ejpam-804	53	16	kf	kf	NOUN
ejpam-804	53	17	)	)	PUNCT
ejpam-804	53	18	processes	process	NOUN
ejpam-804	53	19	.	.	PUNCT
ejpam-804	54	1	this	this	PRON
ejpam-804	54	2	would	would	AUX
ejpam-804	54	3	happen	happen	VERB
ejpam-804	54	4	,	,	PUNCT
ejpam-804	54	5	for	for	ADP
ejpam-804	54	6	example	example	NOUN
ejpam-804	54	7	,	,	PUNCT
ejpam-804	54	8	if	if	SCONJ
ejpam-804	54	9	two	two	NUM
ejpam-804	54	10	processes	process	NOUN
ejpam-804	54	11	were	be	AUX
ejpam-804	54	12	generated	generate	VERB
ejpam-804	54	13	by	by	ADP
ejpam-804	54	14	some	some	DET
ejpam-804	54	15	(	(	PUNCT
ejpam-804	54	16	kf	kf	NOUN
ejpam-804	54	17	)	)	PUNCT
ejpam-804	54	18	non	non	ADJ
ejpam-804	54	19	-	-	ADJ
ejpam-804	54	20	linear	linear	ADJ
ejpam-804	54	21	systems	system	NOUN
ejpam-804	54	22	but	but	CCONJ
ejpam-804	54	23	co	co	VERB
ejpam-804	54	24	-	-	VERB
ejpam-804	54	25	moved	moved	ADJ
ejpam-804	54	26	according	accord	VERB
ejpam-804	54	27	to	to	ADP
ejpam-804	54	28	a	a	DET
ejpam-804	54	29	stationary	stationary	ADJ
ejpam-804	54	30	linear	linear	NOUN
ejpam-804	54	31	adjustment	adjustment	NOUN
ejpam-804	54	32	process	process	NOUN
ejpam-804	54	33	.	.	PUNCT
ejpam-804	55	1	we	we	PRON
ejpam-804	55	2	also	also	ADV
ejpam-804	55	3	consider	consider	VERB
ejpam-804	55	4	the	the	DET
ejpam-804	55	5	case	case	NOUN
ejpam-804	55	6	where	where	SCONJ
ejpam-804	55	7	we	we	PRON
ejpam-804	55	8	have	have	VERB
ejpam-804	55	9	series	series	NOUN
ejpam-804	55	10	whose	whose	DET
ejpam-804	55	11	first	first	ADJ
ejpam-804	55	12	differences	difference	NOUN
ejpam-804	55	13	are	be	AUX
ejpam-804	55	14	of	of	ADP
ejpam-804	55	15	class	class	NOUN
ejpam-804	55	16	(	(	PUNCT
ejpam-804	55	17	kf	kf	NOUN
ejpam-804	55	18	)	)	PUNCT
ejpam-804	55	19	and	and	CCONJ
ejpam-804	55	20	for	for	ADP
ejpam-804	55	21	which	which	PRON
ejpam-804	55	22	there	there	PRON
ejpam-804	55	23	exists	exist	VERB
ejpam-804	55	24	a	a	DET
ejpam-804	55	25	linear	linear	ADJ
ejpam-804	55	26	combination	combination	NOUN
ejpam-804	55	27	of	of	ADP
ejpam-804	55	28	class	class	NOUN
ejpam-804	55	29	(	(	PUNCT
ejpam-804	55	30	kf	kf	PROPN
ejpam-804	55	31	)	)	PUNCT
ejpam-804	55	32	.	.	PUNCT
ejpam-804	56	1	thus	thus	ADV
ejpam-804	56	2	covering	cover	VERB
ejpam-804	56	3	the	the	DET
ejpam-804	56	4	case	case	NOUN
ejpam-804	56	5	∗[12	∗[12	NOUN
ejpam-804	56	6	]	]	PUNCT
ejpam-804	56	7	defines	define	VERB
ejpam-804	56	8	a	a	DET
ejpam-804	56	9	process	process	NOUN
ejpam-804	56	10	as	as	ADP
ejpam-804	56	11	mean	mean	ADV
ejpam-804	56	12	reverting	revert	VERB
ejpam-804	56	13	to	to	ADP
ejpam-804	56	14	zero	zero	NUM
ejpam-804	56	15	if	if	SCONJ
ejpam-804	56	16	e(x	e(x	NOUN
ejpam-804	56	17	t+s	t+s	PUNCT
ejpam-804	57	1	|	|	ADV
ejpam-804	57	2	x	x	SYM
ejpam-804	57	3	t	t	PROPN
ejpam-804	57	4	,	,	PUNCT
ejpam-804	57	5	...	...	PUNCT
ejpam-804	57	6	,	,	PUNCT
ejpam-804	57	7	x1	x1	PROPN
ejpam-804	57	8	,	,	PUNCT
ejpam-804	57	9	...	...	PUNCT
ejpam-804	57	10	)	)	PUNCT
ejpam-804	58	1	p	p	NOUN
ejpam-804	58	2	→0	→0	PUNCT
ejpam-804	58	3	as	as	ADP
ejpam-804	58	4	s→∞	s→∞	X
ejpam-804	58	5	.	.	PUNCT
ejpam-804	59	1	r.	r.	PROPN
ejpam-804	59	2	joyeux	joyeux	PROPN
ejpam-804	59	3	/	/	SYM
ejpam-804	59	4	eur	eur	PROPN
ejpam-804	59	5	.	.	PUNCT
ejpam-804	60	1	j.	j.	PROPN
ejpam-804	60	2	pure	pure	PROPN
ejpam-804	60	3	appl	appl	PROPN
ejpam-804	60	4	.	.	PROPN
ejpam-804	60	5	math	math	PROPN
ejpam-804	60	6	,	,	PUNCT
ejpam-804	60	7	3	3	NUM
ejpam-804	60	8	(	(	PUNCT
ejpam-804	60	9	2010	2010	NUM
ejpam-804	60	10	)	)	PUNCT
ejpam-804	60	11	,	,	PUNCT
ejpam-804	60	12	519	519	NUM
ejpam-804	60	13	-	-	SYM
ejpam-804	60	14	530	530	NUM
ejpam-804	60	15	521	521	NUM
ejpam-804	60	16	where	where	SCONJ
ejpam-804	60	17	we	we	PRON
ejpam-804	60	18	might	might	AUX
ejpam-804	60	19	have	have	VERB
ejpam-804	60	20	i(1	i(1	NOUN
ejpam-804	60	21	)	)	PUNCT
ejpam-804	60	22	processes	process	VERB
ejpam-804	60	23	co	co	ADJ
ejpam-804	60	24	-	-	VERB
ejpam-804	60	25	moving	move	VERB
ejpam-804	60	26	according	accord	VERB
ejpam-804	60	27	to	to	ADP
ejpam-804	60	28	a	a	DET
ejpam-804	60	29	nonlinear	nonlinear	ADJ
ejpam-804	60	30	adjustment	adjustment	NOUN
ejpam-804	60	31	process	process	NOUN
ejpam-804	60	32	or	or	CCONJ
ejpam-804	60	33	a	a	DET
ejpam-804	60	34	heteroskedastic	heteroskedastic	ADJ
ejpam-804	60	35	adjustment	adjustment	NOUN
ejpam-804	60	36	process	process	NOUN
ejpam-804	60	37	.	.	PUNCT
ejpam-804	61	1	section	section	NOUN
ejpam-804	61	2	5	5	NUM
ejpam-804	61	3	concludes	conclude	VERB
ejpam-804	61	4	.	.	PUNCT
ejpam-804	62	1	2	2	X
ejpam-804	62	2	.	.	X
ejpam-804	62	3	class	class	NOUN
ejpam-804	62	4	(	(	PUNCT
ejpam-804	62	5	kf	kf	NOUN
ejpam-804	62	6	)	)	PUNCT
ejpam-804	62	7	we	we	PRON
ejpam-804	62	8	assume	assume	VERB
ejpam-804	62	9	,	,	PUNCT
ejpam-804	62	10	without	without	ADP
ejpam-804	62	11	loss	loss	NOUN
ejpam-804	62	12	of	of	ADP
ejpam-804	62	13	generality	generality	NOUN
ejpam-804	62	14	,	,	PUNCT
ejpam-804	62	15	that	that	SCONJ
ejpam-804	62	16	the	the	DET
ejpam-804	62	17	processes	process	NOUN
ejpam-804	62	18	studied	study	VERB
ejpam-804	62	19	have	have	VERB
ejpam-804	62	20	zero	zero	NUM
ejpam-804	62	21	means	mean	NOUN
ejpam-804	62	22	.	.	PUNCT
ejpam-804	63	1	to	to	PART
ejpam-804	63	2	see	see	VERB
ejpam-804	63	3	that	that	SCONJ
ejpam-804	63	4	there	there	PRON
ejpam-804	63	5	is	be	VERB
ejpam-804	63	6	no	no	DET
ejpam-804	63	7	generality	generality	NOUN
ejpam-804	63	8	loss	loss	NOUN
ejpam-804	63	9	,	,	PUNCT
ejpam-804	63	10	let	let	VERB
ejpam-804	63	11	x	x	PROPN
ejpam-804	63	12	t	t	PROPN
ejpam-804	63	13	,	,	PUNCT
ejpam-804	63	14	t	t	PROPN
ejpam-804	63	15	real	real	ADJ
ejpam-804	63	16	or	or	CCONJ
ejpam-804	63	17	integer	integer	NOUN
ejpam-804	63	18	,	,	PUNCT
ejpam-804	63	19	be	be	AUX
ejpam-804	63	20	a	a	DET
ejpam-804	63	21	real	real	ADV
ejpam-804	63	22	random	random	ADJ
ejpam-804	63	23	process	process	NOUN
ejpam-804	63	24	,	,	PUNCT
ejpam-804	63	25	we	we	PRON
ejpam-804	63	26	can	can	AUX
ejpam-804	63	27	replace	replace	VERB
ejpam-804	63	28	x	x	PROPN
ejpam-804	63	29	t	t	NOUN
ejpam-804	63	30	by	by	ADP
ejpam-804	63	31	yt	yt	NOUN
ejpam-804	63	32	=	=	PUNCT
ejpam-804	63	33	ηx	ηx	PROPN
ejpam-804	63	34	t	t	PROPN
ejpam-804	63	35	,	,	PUNCT
ejpam-804	63	36	where	where	SCONJ
ejpam-804	63	37	η	η	PROPN
ejpam-804	63	38	is	be	AUX
ejpam-804	63	39	a	a	DET
ejpam-804	63	40	random	random	ADJ
ejpam-804	63	41	variable	variable	NOUN
ejpam-804	63	42	,	,	PUNCT
ejpam-804	63	43	independent	independent	ADJ
ejpam-804	63	44	of	of	ADP
ejpam-804	63	45	x	x	PROPN
ejpam-804	63	46	t	t	PROPN
ejpam-804	63	47	for	for	ADP
ejpam-804	63	48	any	any	DET
ejpam-804	63	49	t	t	NOUN
ejpam-804	63	50	,	,	PUNCT
ejpam-804	63	51	such	such	ADJ
ejpam-804	63	52	that	that	SCONJ
ejpam-804	63	53	:	:	PUNCT
ejpam-804	63	54	e(η2	e(η2	NOUN
ejpam-804	63	55	)	)	PUNCT
ejpam-804	63	56	=	=	SYM
ejpam-804	63	57	1	1	NUM
ejpam-804	63	58	ande(η	ande(η	VERB
ejpam-804	63	59	)	)	PUNCT
ejpam-804	63	60	=	=	SYM
ejpam-804	63	61	0	0	NUM
ejpam-804	64	1	this	this	PRON
ejpam-804	64	2	implies	imply	VERB
ejpam-804	64	3	that	that	SCONJ
ejpam-804	64	4	e(yt+syt	e(yt+syt	NOUN
ejpam-804	64	5	)	)	PUNCT
ejpam-804	64	6	=	=	PUNCT
ejpam-804	64	7	e(x	e(x	NUM
ejpam-804	64	8	t+sx	t+sx	NOUN
ejpam-804	64	9	t	t	PROPN
ejpam-804	64	10	)	)	PUNCT
ejpam-804	64	11	,	,	PUNCT
ejpam-804	64	12	for	for	ADP
ejpam-804	64	13	any	any	DET
ejpam-804	64	14	t	t	NOUN
ejpam-804	64	15	and	and	CCONJ
ejpam-804	64	16	s.	s.	PROPN
ejpam-804	64	17	e(x	e(x	PROPN
ejpam-804	64	18	t+sx	t+sx	NOUN
ejpam-804	64	19	t	t	PROPN
ejpam-804	64	20	)	)	PUNCT
ejpam-804	64	21	can	can	AUX
ejpam-804	64	22	be	be	AUX
ejpam-804	64	23	considered	consider	VERB
ejpam-804	64	24	as	as	ADP
ejpam-804	64	25	the	the	DET
ejpam-804	64	26	covariance	covariance	NOUN
ejpam-804	64	27	of	of	ADP
ejpam-804	64	28	a	a	DET
ejpam-804	64	29	process	process	NOUN
ejpam-804	64	30	with	with	ADP
ejpam-804	64	31	zero	zero	NUM
ejpam-804	64	32	mean	mean	NOUN
ejpam-804	64	33	:	:	PUNCT
ejpam-804	64	34	yt	yt	PROPN
ejpam-804	64	35	.	.	PUNCT
ejpam-804	65	1	in	in	ADP
ejpam-804	65	2	what	what	PRON
ejpam-804	65	3	follows	follow	VERB
ejpam-804	65	4	we	we	PRON
ejpam-804	65	5	assume	assume	VERB
ejpam-804	65	6	that	that	SCONJ
ejpam-804	65	7	t	t	PROPN
ejpam-804	65	8	is	be	AUX
ejpam-804	65	9	an	an	DET
ejpam-804	65	10	integer	integer	NOUN
ejpam-804	65	11	but	but	CCONJ
ejpam-804	65	12	the	the	DET
ejpam-804	65	13	definitions	definition	NOUN
ejpam-804	65	14	and	and	CCONJ
ejpam-804	65	15	results	result	NOUN
ejpam-804	65	16	presented	present	VERB
ejpam-804	65	17	generalize	generalize	VERB
ejpam-804	65	18	to	to	ADP
ejpam-804	65	19	the	the	DET
ejpam-804	65	20	case	case	NOUN
ejpam-804	65	21	where	where	SCONJ
ejpam-804	65	22	t	t	PROPN
ejpam-804	65	23	is	be	AUX
ejpam-804	65	24	real	real	ADJ
ejpam-804	65	25	.	.	PUNCT
ejpam-804	66	1	2.1	2.1	NUM
ejpam-804	66	2	.	.	PUNCT
ejpam-804	66	3	definition	definition	NOUN
ejpam-804	66	4	a	a	DET
ejpam-804	66	5	process	process	NOUN
ejpam-804	66	6	x	x	PUNCT
ejpam-804	66	7	t	t	NOUN
ejpam-804	66	8	t	t	NOUN
ejpam-804	66	9	integer	integer	NOUN
ejpam-804	66	10	,	,	PUNCT
ejpam-804	66	11	is	be	AUX
ejpam-804	66	12	of	of	ADP
ejpam-804	66	13	class	class	NOUN
ejpam-804	66	14	(	(	PUNCT
ejpam-804	66	15	kf	kf	NOUN
ejpam-804	66	16	)	)	PUNCT
ejpam-804	66	17	if	if	SCONJ
ejpam-804	66	18	for	for	SCONJ
ejpam-804	66	19	each	each	DET
ejpam-804	66	20	h	h	NOUN
ejpam-804	66	21	integer	integer	VERB
ejpam-804	66	22	the	the	DET
ejpam-804	66	23	following	follow	VERB
ejpam-804	66	24	limit	limit	NOUN
ejpam-804	66	25	exists	exist	VERB
ejpam-804	66	26	:	:	PUNCT
ejpam-804	66	27	r(h	r(h	NOUN
ejpam-804	66	28	)	)	PUNCT
ejpam-804	67	1	=	=	VERB
ejpam-804	67	2	lim	lim	PROPN
ejpam-804	67	3	t→∞	t→∞	X
ejpam-804	67	4	rt	rt	PROPN
ejpam-804	67	5	(	(	PUNCT
ejpam-804	67	6	h	h	NOUN
ejpam-804	67	7	)	)	PUNCT
ejpam-804	68	1	=	=	SYM
ejpam-804	68	2	lim	lim	PROPN
ejpam-804	68	3	t→∞	t→∞	ADP
ejpam-804	68	4	1	1	NUM
ejpam-804	68	5	t	t	NOUN
ejpam-804	68	6	t	t	PROPN
ejpam-804	68	7	∑	∑	PROPN
ejpam-804	68	8	s=0	s=0	PROPN
ejpam-804	68	9	b(s	b(s	PROPN
ejpam-804	68	10	,	,	PUNCT
ejpam-804	68	11	s	s	PART
ejpam-804	68	12	+	+	NOUN
ejpam-804	68	13	h	h	NOUN
ejpam-804	68	14	)	)	PUNCT
ejpam-804	68	15	(	(	PUNCT
ejpam-804	68	16	1	1	X
ejpam-804	68	17	)	)	PUNCT
ejpam-804	69	1	where	where	SCONJ
ejpam-804	69	2	rt	rt	PROPN
ejpam-804	69	3	(	(	PUNCT
ejpam-804	69	4	h	h	NOUN
ejpam-804	69	5	)	)	PUNCT
ejpam-804	69	6	=	=	SYM
ejpam-804	69	7	1	1	NUM
ejpam-804	69	8	t	t	X
ejpam-804	69	9	∑t	∑t	PROPN
ejpam-804	69	10	s=0	s=0	PROPN
ejpam-804	69	11	b(s	b(s	PROPN
ejpam-804	69	12	,	,	PUNCT
ejpam-804	69	13	s+	s+	PUNCT
ejpam-804	69	14	h	h	X
ejpam-804	69	15	)	)	PUNCT
ejpam-804	69	16	and	and	CCONJ
ejpam-804	69	17	b(s	b(s	PROPN
ejpam-804	69	18	,	,	PUNCT
ejpam-804	69	19	t	t	PROPN
ejpam-804	69	20	)	)	PUNCT
ejpam-804	69	21	=	=	PUNCT
ejpam-804	69	22	e(x	e(x	PROPN
ejpam-804	69	23	sx	sx	PROPN
ejpam-804	69	24	t	t	PROPN
ejpam-804	69	25	)	)	PUNCT
ejpam-804	69	26	is	be	AUX
ejpam-804	69	27	the	the	DET
ejpam-804	69	28	covariance	covariance	NOUN
ejpam-804	69	29	of	of	ADP
ejpam-804	69	30	x	x	PROPN
ejpam-804	69	31	t	t	NOUN
ejpam-804	69	32	.	.	PUNCT
ejpam-804	70	1	2.2	2.2	NUM
ejpam-804	70	2	.	.	PUNCT
ejpam-804	70	3	classification	classification	NOUN
ejpam-804	70	4	of	of	ADP
ejpam-804	70	5	class	class	NOUN
ejpam-804	70	6	(	(	PUNCT
ejpam-804	70	7	kf	kf	NOUN
ejpam-804	70	8	)	)	PUNCT
ejpam-804	70	9	processes	process	VERB
ejpam-804	70	10	2.2.1	2.2.1	NUM
ejpam-804	70	11	.	.	PUNCT
ejpam-804	71	1	stationary	stationary	ADJ
ejpam-804	71	2	processes	process	NOUN
ejpam-804	71	3	if	if	SCONJ
ejpam-804	71	4	x	x	PROPN
ejpam-804	71	5	t	t	PROPN
ejpam-804	71	6	is	be	AUX
ejpam-804	71	7	real	real	ADJ
ejpam-804	71	8	and	and	CCONJ
ejpam-804	71	9	stationary	stationary	ADJ
ejpam-804	71	10	,	,	PUNCT
ejpam-804	71	11	so	so	SCONJ
ejpam-804	71	12	that	that	SCONJ
ejpam-804	71	13	b(s	b(	NOUN
ejpam-804	71	14	,	,	PUNCT
ejpam-804	71	15	t	t	PROPN
ejpam-804	71	16	)	)	PUNCT
ejpam-804	71	17	=	=	SYM
ejpam-804	71	18	b(t	b(t	PROPN
ejpam-804	71	19	−	−	PROPN
ejpam-804	71	20	s	s	NOUN
ejpam-804	71	21	)	)	PUNCT
ejpam-804	71	22	,	,	PUNCT
ejpam-804	71	23	then	then	ADV
ejpam-804	71	24	r(h	r(h	NOUN
ejpam-804	71	25	)	)	PUNCT
ejpam-804	71	26	=	=	SYM
ejpam-804	71	27	b(h	b(h	PROPN
ejpam-804	71	28	)	)	PUNCT
ejpam-804	71	29	=	=	SYM
ejpam-804	71	30	b(|h|	b(|h|	PROPN
ejpam-804	71	31	)	)	PUNCT
ejpam-804	71	32	.	.	PUNCT
ejpam-804	72	1	this	this	PRON
ejpam-804	72	2	shows	show	VERB
ejpam-804	72	3	that	that	SCONJ
ejpam-804	72	4	every	every	DET
ejpam-804	72	5	stationary	stationary	ADJ
ejpam-804	72	6	process	process	NOUN
ejpam-804	72	7	is	be	AUX
ejpam-804	72	8	in	in	ADP
ejpam-804	72	9	(	(	PUNCT
ejpam-804	72	10	kf	kf	NOUN
ejpam-804	72	11	)	)	PUNCT
ejpam-804	72	12	.	.	PUNCT
ejpam-804	73	1	2.2.2	2.2.2	X
ejpam-804	73	2	.	.	PUNCT
ejpam-804	73	3	non	non	ADJ
ejpam-804	73	4	-	-	ADJ
ejpam-804	73	5	linear	linear	ADJ
ejpam-804	73	6	sequences	sequence	NOUN
ejpam-804	73	7	theorem	theorem	VERB
ejpam-804	73	8	1	1	X
ejpam-804	73	9	.	.	PUNCT
ejpam-804	74	1	let	let	VERB
ejpam-804	74	2	x	x	PRON
ejpam-804	74	3	t	t	PROPN
ejpam-804	74	4	=	=	PUNCT
ejpam-804	74	5	k	k	PROPN
ejpam-804	74	6	∑	∑	PUNCT
ejpam-804	74	7	i=1	i=1	PROPN
ejpam-804	74	8	αi(t)x	αi(t)x	PROPN
ejpam-804	74	9	t−i	t−i	NOUN
ejpam-804	74	10	+	+	CCONJ
ejpam-804	74	11	ǫt	ǫt	PROPN
ejpam-804	74	12	,	,	PUNCT
ejpam-804	74	13	t	t	PROPN
ejpam-804	74	14	≥	≥	NUM
ejpam-804	74	15	1	1	NUM
ejpam-804	74	16	integer	integer	NOUN
ejpam-804	74	17	(	(	PUNCT
ejpam-804	74	18	2	2	NUM
ejpam-804	74	19	)	)	PUNCT
ejpam-804	74	20	where	where	SCONJ
ejpam-804	74	21	the	the	DET
ejpam-804	74	22	αi(t	αi(t	NOUN
ejpam-804	74	23	)	)	PUNCT
ejpam-804	74	24	’s	’	VERB
ejpam-804	74	25	are	be	AUX
ejpam-804	74	26	non	non	X
ejpam-804	74	27	stochastic	stochastic	ADJ
ejpam-804	74	28	functions	function	NOUN
ejpam-804	74	29	of	of	ADP
ejpam-804	74	30	time	time	NOUN
ejpam-804	75	1	and	and	CCONJ
ejpam-804	75	2	εt	εt	PROPN
ejpam-804	75	3	is	be	AUX
ejpam-804	75	4	a	a	DET
ejpam-804	75	5	white	white	ADJ
ejpam-804	75	6	noise	noise	NOUN
ejpam-804	75	7	process	process	NOUN
ejpam-804	75	8	with	with	ADP
ejpam-804	75	9	variance	variance	NOUN
ejpam-804	75	10	σ2	σ2	PROPN
ejpam-804	75	11	.	.	PUNCT
ejpam-804	76	1	if	if	SCONJ
ejpam-804	76	2	ϕ(t	ϕ(t	PROPN
ejpam-804	76	3	,	,	PUNCT
ejpam-804	76	4	m	m	NOUN
ejpam-804	76	5	)	)	PUNCT
ejpam-804	76	6	=	=	SYM
ejpam-804	76	7	∑	∑	PUNCT
ejpam-804	76	8	k1+	k1+	PROPN
ejpam-804	76	9	...	...	PUNCT
ejpam-804	76	10	+ki	+ki	X
ejpam-804	76	11	=	=	NOUN
ejpam-804	76	12	m	m	VERB
ejpam-804	76	13	i	i	PRON
ejpam-804	76	14	∏	∏	NUM
ejpam-804	76	15	j=1	j=1	NOUN
ejpam-804	77	1	αk	αk	PRON
ejpam-804	77	2	j	j	PROPN
ejpam-804	77	3	(	(	PUNCT
ejpam-804	77	4	t	t	PROPN
ejpam-804	77	5	−	−	PROPN
ejpam-804	77	6	j−1	j−1	PROPN
ejpam-804	77	7	∑	∑	PUNCT
ejpam-804	77	8	r=0	r=0	PROPN
ejpam-804	77	9	kr	kr	PROPN
ejpam-804	77	10	)	)	PUNCT
ejpam-804	77	11	,	,	PUNCT
ejpam-804	77	12	0≤	0≤	NUM
ejpam-804	77	13	m	m	VERB
ejpam-804	77	14	≤	≤	NOUN
ejpam-804	77	15	t	t	PROPN
ejpam-804	77	16	,	,	PUNCT
ejpam-804	77	17	k0	k0	PROPN
ejpam-804	77	18	=	=	PROPN
ejpam-804	77	19	0	0	NUM
ejpam-804	77	20	(	(	PUNCT
ejpam-804	77	21	3	3	NUM
ejpam-804	77	22	)	)	PUNCT
ejpam-804	77	23	r.	r.	PROPN
ejpam-804	77	24	joyeux	joyeux	PROPN
ejpam-804	77	25	/	/	SYM
ejpam-804	77	26	eur	eur	PROPN
ejpam-804	77	27	.	.	PUNCT
ejpam-804	78	1	j.	j.	PROPN
ejpam-804	78	2	pure	pure	PROPN
ejpam-804	78	3	appl	appl	PROPN
ejpam-804	78	4	.	.	PROPN
ejpam-804	78	5	math	math	PROPN
ejpam-804	78	6	,	,	PUNCT
ejpam-804	78	7	3	3	NUM
ejpam-804	78	8	(	(	PUNCT
ejpam-804	78	9	2010	2010	NUM
ejpam-804	78	10	)	)	PUNCT
ejpam-804	78	11	,	,	PUNCT
ejpam-804	78	12	519	519	NUM
ejpam-804	78	13	-	-	SYM
ejpam-804	78	14	530	530	NUM
ejpam-804	78	15	522	522	NUM
ejpam-804	78	16	the	the	DET
ejpam-804	78	17	sum	sum	NOUN
ejpam-804	78	18	ranging	range	VERB
ejpam-804	78	19	over	over	ADP
ejpam-804	78	20	all	all	DET
ejpam-804	78	21	partitions	partition	NOUN
ejpam-804	78	22	of	of	ADP
ejpam-804	78	23	m	m	NOUN
ejpam-804	78	24	into	into	ADP
ejpam-804	78	25	integers	integer	NOUN
ejpam-804	78	26	ki	ki	PROPN
ejpam-804	78	27	,	,	PUNCT
ejpam-804	78	28	then	then	ADV
ejpam-804	78	29	x	x	PROPN
ejpam-804	78	30	t	t	PROPN
ejpam-804	78	31	belongs	belong	VERB
ejpam-804	78	32	to	to	ADP
ejpam-804	78	33	the	the	DET
ejpam-804	78	34	class	class	NOUN
ejpam-804	78	35	(	(	PUNCT
ejpam-804	78	36	kf	kf	PROPN
ejpam-804	78	37	)	)	PUNCT
ejpam-804	78	38	if	if	SCONJ
ejpam-804	78	39	the	the	DET
ejpam-804	78	40	αi	αi	NOUN
ejpam-804	78	41	(	(	PUNCT
ejpam-804	78	42	·	·	PUNCT
ejpam-804	78	43	)	)	PUNCT
ejpam-804	78	44	satisfy	satisfy	PROPN
ejpam-804	78	45	t	t	PROPN
ejpam-804	78	46	∑	∑	PROPN
ejpam-804	78	47	m=0	m=0	PROPN
ejpam-804	78	48	�	�	PROPN
ejpam-804	78	49	�	�	PROPN
ejpam-804	78	50	ϕ(t	ϕ(t	PROPN
ejpam-804	78	51	,	,	PUNCT
ejpam-804	78	52	m	m	NOUN
ejpam-804	78	53	)	)	PUNCT
ejpam-804	78	54	�	�	PROPN
ejpam-804	78	55	�	�	PROPN
ejpam-804	78	56	2	2	NUM
ejpam-804	78	57	≤	≤	NOUN
ejpam-804	78	58	m	m	NOUN
ejpam-804	78	59	<	<	X
ejpam-804	78	60	∞	∞	PROPN
ejpam-804	78	61	,	,	PUNCT
ejpam-804	78	62	t	t	PROPN
ejpam-804	78	63	≥	≥	NUM
ejpam-804	78	64	1	1	NUM
ejpam-804	78	65	(	(	PUNCT
ejpam-804	78	66	4	4	NUM
ejpam-804	78	67	)	)	PUNCT
ejpam-804	78	68	proof	proof	NOUN
ejpam-804	78	69	.	.	PUNCT
ejpam-804	79	1	the	the	DET
ejpam-804	79	2	solution	solution	NOUN
ejpam-804	79	3	to	to	ADP
ejpam-804	79	4	the	the	DET
ejpam-804	79	5	difference	difference	NOUN
ejpam-804	79	6	equation	equation	NOUN
ejpam-804	79	7	in	in	ADP
ejpam-804	79	8	(	(	PUNCT
ejpam-804	79	9	2	2	X
ejpam-804	79	10	)	)	PUNCT
ejpam-804	79	11	is	be	AUX
ejpam-804	79	12	given	give	VERB
ejpam-804	79	13	by	by	ADP
ejpam-804	79	14	:	:	PUNCT
ejpam-804	79	15	x	x	SYM
ejpam-804	79	16	t	t	NOUN
ejpam-804	79	17	=	=	SYM
ejpam-804	79	18	t−1	t−1	PROPN
ejpam-804	79	19	∑	∑	PUNCT
ejpam-804	79	20	i=0	i=0	PROPN
ejpam-804	79	21	ϕ(t	ϕ(t	PROPN
ejpam-804	79	22	,	,	PUNCT
ejpam-804	79	23	i)ǫt−i	i)ǫt−i	NOUN
ejpam-804	79	24	+	+	CCONJ
ejpam-804	79	25	t+k−1	t+k−1	VERB
ejpam-804	79	26	∑	∑	VERB
ejpam-804	79	27	i	i	PROPN
ejpam-804	79	28	=	=	PROPN
ejpam-804	79	29	t	t	PROPN
ejpam-804	79	30	ϕ(t	ϕ(t	NUM
ejpam-804	79	31	,	,	PUNCT
ejpam-804	79	32	i)ct−i	i)ct−i	NOUN
ejpam-804	79	33	,	,	PUNCT
ejpam-804	79	34	t	t	PROPN
ejpam-804	79	35	≥	≥	NUM
ejpam-804	79	36	1	1	NUM
ejpam-804	79	37	(	(	PUNCT
ejpam-804	79	38	5	5	NUM
ejpam-804	79	39	)	)	PUNCT
ejpam-804	79	40	where	where	SCONJ
ejpam-804	79	41	x	x	X
ejpam-804	79	42	i	i	NOUN
ejpam-804	79	43	=	=	PROPN
ejpam-804	79	44	ci	ci	PROPN
ejpam-804	79	45	,	,	PUNCT
ejpam-804	79	46	i	i	PRON
ejpam-804	79	47	=	=	PUNCT
ejpam-804	79	48	−k+	−k+	NOUN
ejpam-804	79	49	1	1	NUM
ejpam-804	79	50	,	,	PUNCT
ejpam-804	79	51	.	.	PUNCT
ejpam-804	79	52	.	.	PUNCT
ejpam-804	79	53	.	.	PUNCT
ejpam-804	80	1	,	,	PUNCT
ejpam-804	80	2	0	0	NUM
ejpam-804	80	3	are	be	AUX
ejpam-804	80	4	the	the	DET
ejpam-804	80	5	initial	initial	ADJ
ejpam-804	80	6	values	value	NOUN
ejpam-804	80	7	[	[	X
ejpam-804	80	8	see	see	VERB
ejpam-804	80	9	14	14	NUM
ejpam-804	80	10	,	,	PUNCT
ejpam-804	80	11	25	25	NUM
ejpam-804	80	12	]	]	PUNCT
ejpam-804	80	13	.	.	PUNCT
ejpam-804	81	1	without	without	ADP
ejpam-804	81	2	loss	loss	NOUN
ejpam-804	81	3	of	of	ADP
ejpam-804	81	4	generality	generality	NOUN
ejpam-804	81	5	the	the	DET
ejpam-804	81	6	starting	start	VERB
ejpam-804	81	7	values	value	NOUN
ejpam-804	81	8	can	can	AUX
ejpam-804	81	9	be	be	AUX
ejpam-804	81	10	assumed	assume	VERB
ejpam-804	81	11	to	to	PART
ejpam-804	81	12	be	be	AUX
ejpam-804	81	13	zero	zero	NUM
ejpam-804	81	14	.	.	PUNCT
ejpam-804	82	1	b(s	b(	NOUN
ejpam-804	82	2	,	,	PUNCT
ejpam-804	82	3	s	s	PART
ejpam-804	82	4	+	+	NOUN
ejpam-804	82	5	h	h	NOUN
ejpam-804	82	6	)	)	PUNCT
ejpam-804	82	7	=	=	PUNCT
ejpam-804	82	8	e(x	e(x	NUM
ejpam-804	82	9	sx	sx	PROPN
ejpam-804	82	10	s+h	s+h	NOUN
ejpam-804	82	11	)	)	PUNCT
ejpam-804	83	1	=	=	SYM
ejpam-804	83	2	σ	σ	NOUN
ejpam-804	83	3	2	2	NUM
ejpam-804	83	4	s−1	s−1	PROPN
ejpam-804	83	5	∑	∑	PROPN
ejpam-804	83	6	m=0	m=0	PROPN
ejpam-804	83	7	ϕ(s	ϕ(s	PROPN
ejpam-804	83	8	,	,	PUNCT
ejpam-804	83	9	m)ϕ(s+	m)ϕ(s+	PROPN
ejpam-804	83	10	h	h	NOUN
ejpam-804	83	11	,	,	PUNCT
ejpam-804	83	12	m+	m+	NOUN
ejpam-804	83	13	h	h	NOUN
ejpam-804	83	14	)	)	PUNCT
ejpam-804	83	15	,	,	PUNCT
ejpam-804	83	16	h≥	h≥	PROPN
ejpam-804	83	17	0	0	NUM
ejpam-804	83	18	,	,	PUNCT
ejpam-804	83	19	s	s	VERB
ejpam-804	83	20	≥	≥	NOUN
ejpam-804	83	21	1	1	NUM
ejpam-804	83	22	.	.	PUNCT
ejpam-804	83	23	(	(	PUNCT
ejpam-804	83	24	4	4	X
ejpam-804	83	25	)	)	PUNCT
ejpam-804	83	26	implies	imply	VERB
ejpam-804	83	27	that	that	SCONJ
ejpam-804	83	28	|b(s	|b(	NOUN
ejpam-804	83	29	,	,	PUNCT
ejpam-804	83	30	s+	s+	ADV
ejpam-804	83	31	h)|	h)|	VERB
ejpam-804	83	32	≤	≤	PROPN
ejpam-804	83	33	σ2	σ2	PROPN
ejpam-804	83	34	m	m	PROPN
ejpam-804	83	35	for	for	ADP
ejpam-804	83	36	all	all	DET
ejpam-804	83	37	h	h	NOUN
ejpam-804	83	38	by	by	ADP
ejpam-804	83	39	cauchy	cauchy	PROPN
ejpam-804	83	40	inequality	inequality	NOUN
ejpam-804	83	41	.	.	PUNCT
ejpam-804	84	1	this	this	PRON
ejpam-804	84	2	implies	imply	VERB
ejpam-804	84	3	that	that	SCONJ
ejpam-804	84	4	lim	lim	PROPN
ejpam-804	84	5	t→∞	t→∞	ADP
ejpam-804	84	6	1	1	NUM
ejpam-804	84	7	t	t	NOUN
ejpam-804	84	8	∑t	∑t	NOUN
ejpam-804	84	9	s=1	s=1	X
ejpam-804	84	10	b(s	b(	NOUN
ejpam-804	84	11	,	,	PUNCT
ejpam-804	84	12	s+	s+	PUNCT
ejpam-804	84	13	h	h	X
ejpam-804	84	14	)	)	PUNCT
ejpam-804	84	15	=	=	SYM
ejpam-804	84	16	r(h	r(h	NOUN
ejpam-804	84	17	)	)	PUNCT
ejpam-804	84	18	exists	exist	VERB
ejpam-804	84	19	.	.	PUNCT
ejpam-804	85	1	this	this	DET
ejpam-804	85	2	model	model	NOUN
ejpam-804	85	3	is	be	AUX
ejpam-804	85	4	a	a	DET
ejpam-804	85	5	more	more	ADV
ejpam-804	85	6	general	general	ADJ
ejpam-804	85	7	non	non	ADJ
ejpam-804	85	8	-	-	ADJ
ejpam-804	85	9	linear	linear	ADJ
ejpam-804	85	10	model	model	NOUN
ejpam-804	85	11	than	than	ADP
ejpam-804	85	12	the	the	DET
ejpam-804	85	13	one	one	NOUN
ejpam-804	85	14	considered	consider	VERB
ejpam-804	85	15	in	in	ADP
ejpam-804	85	16	[	[	X
ejpam-804	85	17	6	6	NUM
ejpam-804	85	18	]	]	PUNCT
ejpam-804	85	19	.	.	PUNCT
ejpam-804	86	1	consequently	consequently	ADV
ejpam-804	86	2	this	this	PRON
ejpam-804	86	3	implies	imply	VERB
ejpam-804	86	4	that	that	SCONJ
ejpam-804	86	5	the	the	DET
ejpam-804	86	6	non	non	ADJ
ejpam-804	86	7	linear	linear	PROPN
ejpam-804	86	8	processes	process	NOUN
ejpam-804	86	9	considered	consider	VERB
ejpam-804	86	10	in	in	ADP
ejpam-804	86	11	[	[	X
ejpam-804	86	12	6	6	NUM
ejpam-804	86	13	]	]	PUNCT
ejpam-804	86	14	are	be	AUX
ejpam-804	86	15	of	of	ADP
ejpam-804	86	16	class	class	NOUN
ejpam-804	86	17	(	(	PUNCT
ejpam-804	86	18	kf	kf	PROPN
ejpam-804	86	19	)	)	PUNCT
ejpam-804	86	20	.	.	PUNCT
ejpam-804	87	1	2.3	2.3	NUM
ejpam-804	87	2	.	.	PUNCT
ejpam-804	87	3	vector	vector	NOUN
ejpam-804	87	4	class	class	NOUN
ejpam-804	87	5	(	(	PUNCT
ejpam-804	87	6	kf	kf	NOUN
ejpam-804	87	7	)	)	PUNCT
ejpam-804	87	8	processes	process	VERB
ejpam-804	87	9	definition	definition	NOUN
ejpam-804	87	10	1	1	NUM
ejpam-804	87	11	.	.	PUNCT
ejpam-804	88	1	an	an	DET
ejpam-804	88	2	n	n	ADV
ejpam-804	88	3	-	-	PUNCT
ejpam-804	88	4	dimensional	dimensional	ADJ
ejpam-804	88	5	vector	vector	NOUN
ejpam-804	88	6	process	process	NOUN
ejpam-804	88	7	x	x	X
ejpam-804	88	8	t	t	NOUN
ejpam-804	88	9	=	=	SYM
ejpam-804	88	10	(	(	PUNCT
ejpam-804	88	11	x1	x1	PROPN
ejpam-804	88	12	t	t	PROPN
ejpam-804	88	13	,	,	PUNCT
ejpam-804	88	14	.	.	PUNCT
ejpam-804	88	15	.	.	PUNCT
ejpam-804	88	16	.	.	PUNCT
ejpam-804	89	1	,	,	PUNCT
ejpam-804	89	2	xnt	xnt	PROPN
ejpam-804	89	3	)	)	PUNCT
ejpam-804	89	4	′	′	NUM
ejpam-804	89	5	is	be	AUX
ejpam-804	89	6	an	an	DET
ejpam-804	89	7	n	n	ADV
ejpam-804	89	8	-	-	PUNCT
ejpam-804	89	9	dimensional	dimensional	ADJ
ejpam-804	89	10	class	class	NOUN
ejpam-804	89	11	(	(	PUNCT
ejpam-804	89	12	kf	kf	NOUN
ejpam-804	89	13	)	)	PUNCT
ejpam-804	89	14	process	process	NOUN
ejpam-804	89	15	if	if	SCONJ
ejpam-804	90	1	and	and	CCONJ
ejpam-804	90	2	only	only	ADV
ejpam-804	90	3	if	if	SCONJ
ejpam-804	90	4	for	for	ADP
ejpam-804	90	5	every	every	DET
ejpam-804	90	6	n×	n×	NUM
ejpam-804	90	7	1	1	NUM
ejpam-804	90	8	vector	vector	NOUN
ejpam-804	90	9	of	of	ADP
ejpam-804	90	10	real	real	ADJ
ejpam-804	90	11	numbers	number	NOUN
ejpam-804	90	12	,	,	PUNCT
ejpam-804	90	13	w	w	PROPN
ejpam-804	90	14	,	,	PUNCT
ejpam-804	90	15	the	the	DET
ejpam-804	90	16	process	process	NOUN
ejpam-804	90	17	w′x	w′x	PROPN
ejpam-804	90	18	t	t	PROPN
ejpam-804	90	19	is	be	AUX
ejpam-804	90	20	of	of	ADP
ejpam-804	90	21	class	class	NOUN
ejpam-804	90	22	(	(	PUNCT
ejpam-804	90	23	kf	kf	PROPN
ejpam-804	90	24	)	)	PUNCT
ejpam-804	90	25	.	.	PUNCT
ejpam-804	91	1	2.4	2.4	NUM
ejpam-804	91	2	.	.	PUNCT
ejpam-804	91	3	harmonizable	harmonizable	ADJ
ejpam-804	91	4	processes	process	NOUN
ejpam-804	91	5	:	:	PUNCT
ejpam-804	91	6	definitions	definition	NOUN
ejpam-804	91	7	and	and	CCONJ
ejpam-804	91	8	properties	property	NOUN
ejpam-804	91	9	in	in	ADP
ejpam-804	91	10	this	this	DET
ejpam-804	91	11	section	section	NOUN
ejpam-804	91	12	a	a	DET
ejpam-804	91	13	few	few	ADJ
ejpam-804	91	14	definitions	definition	NOUN
ejpam-804	91	15	and	and	CCONJ
ejpam-804	91	16	properties	property	NOUN
ejpam-804	91	17	of	of	ADP
ejpam-804	91	18	harmonizable	harmonizable	ADJ
ejpam-804	91	19	processes	process	NOUN
ejpam-804	91	20	are	be	AUX
ejpam-804	91	21	summarized	summarize	VERB
ejpam-804	91	22	.	.	PUNCT
ejpam-804	92	1	for	for	ADP
ejpam-804	92	2	more	more	ADJ
ejpam-804	92	3	details	detail	NOUN
ejpam-804	92	4	the	the	DET
ejpam-804	92	5	reader	reader	NOUN
ejpam-804	92	6	is	be	AUX
ejpam-804	92	7	referred	refer	VERB
ejpam-804	92	8	to	to	ADP
ejpam-804	92	9	[	[	X
ejpam-804	92	10	1	1	NUM
ejpam-804	92	11	,	,	PUNCT
ejpam-804	92	12	19	19	NUM
ejpam-804	92	13	,	,	PUNCT
ejpam-804	92	14	20	20	NUM
ejpam-804	92	15	,	,	PUNCT
ejpam-804	92	16	21	21	NUM
ejpam-804	92	17	,	,	PUNCT
ejpam-804	92	18	29	29	NUM
ejpam-804	92	19	]	]	PUNCT
ejpam-804	92	20	.	.	PUNCT
ejpam-804	93	1	2.5	2.5	NUM
ejpam-804	93	2	.	.	PUNCT
ejpam-804	94	1	strongly	strongly	ADV
ejpam-804	94	2	harmonizable	harmonizable	ADJ
ejpam-804	94	3	processes	process	NOUN
ejpam-804	94	4	a	a	DET
ejpam-804	94	5	second	second	ADJ
ejpam-804	94	6	order	order	NOUN
ejpam-804	94	7	process	process	NOUN
ejpam-804	94	8	x	x	PUNCT
ejpam-804	94	9	t	t	PROPN
ejpam-804	94	10	,	,	PUNCT
ejpam-804	94	11	t	t	PROPN
ejpam-804	94	12	integer	integer	NOUN
ejpam-804	94	13	,	,	PUNCT
ejpam-804	94	14	is	be	AUX
ejpam-804	94	15	strongly	strongly	ADV
ejpam-804	94	16	harmonizable	harmonizable	ADJ
ejpam-804	94	17	if	if	SCONJ
ejpam-804	95	1	and	and	CCONJ
ejpam-804	95	2	only	only	ADV
ejpam-804	95	3	if	if	SCONJ
ejpam-804	95	4	it	it	PRON
ejpam-804	95	5	has	have	VERB
ejpam-804	95	6	the	the	DET
ejpam-804	95	7	quadratic	quadratic	ADJ
ejpam-804	95	8	mean	mean	NOUN
ejpam-804	95	9	representation	representation	NOUN
ejpam-804	95	10	:	:	PUNCT
ejpam-804	96	1	x	x	SYM
ejpam-804	96	2	t	t	X
ejpam-804	96	3	=	=	SYM
ejpam-804	96	4	∫	∫	PROPN
ejpam-804	96	5	π	π	NOUN
ejpam-804	96	6	−π	−π	INTJ
ejpam-804	96	7	ei	ei	X
ejpam-804	96	8	tuz(du	tuz(du	NOUN
ejpam-804	96	9	)	)	PUNCT
ejpam-804	96	10	(	(	PUNCT
ejpam-804	96	11	6	6	NUM
ejpam-804	96	12	)	)	PUNCT
ejpam-804	96	13	where	where	SCONJ
ejpam-804	96	14	z	z	NOUN
ejpam-804	96	15	(	(	PUNCT
ejpam-804	96	16	·	·	PUNCT
ejpam-804	96	17	)	)	PUNCT
ejpam-804	96	18	is	be	AUX
ejpam-804	96	19	a	a	DET
ejpam-804	96	20	stochastic	stochastic	ADJ
ejpam-804	96	21	measure	measure	NOUN
ejpam-804	96	22	whose	whose	DET
ejpam-804	96	23	covariance	covariance	NOUN
ejpam-804	96	24	is	be	AUX
ejpam-804	96	25	of	of	ADP
ejpam-804	96	26	bounded	bounded	ADJ
ejpam-804	96	27	variation	variation	NOUN
ejpam-804	96	28	.	.	PUNCT
ejpam-804	97	1	assuming	assume	VERB
ejpam-804	97	2	that	that	SCONJ
ejpam-804	97	3	x	x	PROPN
ejpam-804	97	4	t	t	PROPN
ejpam-804	97	5	is	be	AUX
ejpam-804	97	6	a	a	DET
ejpam-804	97	7	strongly	strongly	ADV
ejpam-804	97	8	harmonizable	harmonizable	ADJ
ejpam-804	97	9	process	process	NOUN
ejpam-804	97	10	with	with	ADP
ejpam-804	97	11	zero	zero	NUM
ejpam-804	97	12	mean	mean	NOUN
ejpam-804	97	13	loéve	loéve	NOUN
ejpam-804	98	1	[	[	X
ejpam-804	98	2	19	19	NUM
ejpam-804	98	3	]	]	PUNCT
ejpam-804	98	4	showed	show	VERB
ejpam-804	98	5	that	that	SCONJ
ejpam-804	98	6	a	a	DET
ejpam-804	98	7	second	second	ADJ
ejpam-804	98	8	order	order	NOUN
ejpam-804	98	9	process	process	NOUN
ejpam-804	98	10	x	x	PUNCT
ejpam-804	98	11	t	t	PROPN
ejpam-804	98	12	is	be	AUX
ejpam-804	98	13	strongly	strongly	ADV
ejpam-804	98	14	harmonizable	harmonizable	ADJ
ejpam-804	98	15	if	if	SCONJ
ejpam-804	98	16	and	and	CCONJ
ejpam-804	98	17	only	only	ADV
ejpam-804	98	18	if	if	SCONJ
ejpam-804	98	19	its	its	PRON
ejpam-804	98	20	covariance	covariance	NOUN
ejpam-804	98	21	b(s	b(	NOUN
ejpam-804	98	22	,	,	PUNCT
ejpam-804	98	23	t	t	PROPN
ejpam-804	98	24	)	)	PUNCT
ejpam-804	98	25	=	=	PUNCT
ejpam-804	98	26	e(x	e(x	NUM
ejpam-804	98	27	sx	sx	PROPN
ejpam-804	98	28	t	t	PROPN
ejpam-804	98	29	has	have	VERB
ejpam-804	98	30	the	the	DET
ejpam-804	98	31	integral	integral	ADJ
ejpam-804	98	32	representation	representation	NOUN
ejpam-804	98	33	:	:	PUNCT
ejpam-804	98	34	b(s	b(	NOUN
ejpam-804	98	35	,	,	PUNCT
ejpam-804	98	36	t	t	PROPN
ejpam-804	98	37	)	)	PUNCT
ejpam-804	98	38	=	=	SYM
ejpam-804	99	1	∫	∫	PROPN
ejpam-804	100	1	π	π	NOUN
ejpam-804	100	2	−π	−π	X
ejpam-804	100	3	∫	∫	PROPN
ejpam-804	101	1	π	π	NOUN
ejpam-804	101	2	−π	−π	PRON
ejpam-804	101	3	ei(su−t	ei(su−t	PROPN
ejpam-804	101	4	v)f(du	v)f(du	NUM
ejpam-804	101	5	,	,	PUNCT
ejpam-804	101	6	dv	dv	PROPN
ejpam-804	101	7	)	)	PUNCT
ejpam-804	101	8	(	(	PUNCT
ejpam-804	101	9	7	7	X
ejpam-804	101	10	)	)	PUNCT
ejpam-804	101	11	r.	r.	PROPN
ejpam-804	101	12	joyeux	joyeux	PROPN
ejpam-804	101	13	/	/	SYM
ejpam-804	101	14	eur	eur	PROPN
ejpam-804	101	15	.	.	PUNCT
ejpam-804	102	1	j.	j.	PROPN
ejpam-804	102	2	pure	pure	PROPN
ejpam-804	102	3	appl	appl	PROPN
ejpam-804	102	4	.	.	PROPN
ejpam-804	102	5	math	math	PROPN
ejpam-804	102	6	,	,	PUNCT
ejpam-804	102	7	3	3	NUM
ejpam-804	102	8	(	(	PUNCT
ejpam-804	102	9	2010	2010	NUM
ejpam-804	102	10	)	)	PUNCT
ejpam-804	102	11	,	,	PUNCT
ejpam-804	102	12	519	519	NUM
ejpam-804	102	13	-	-	SYM
ejpam-804	102	14	530	530	NUM
ejpam-804	102	15	523	523	NUM
ejpam-804	102	16	for	for	ADP
ejpam-804	102	17	all	all	DET
ejpam-804	102	18	s	s	NOUN
ejpam-804	102	19	and	and	CCONJ
ejpam-804	102	20	t	t	NOUN
ejpam-804	102	21	integers	integer	NOUN
ejpam-804	102	22	,	,	PUNCT
ejpam-804	102	23	where	where	SCONJ
ejpam-804	102	24	f	f	PROPN
ejpam-804	102	25	is	be	AUX
ejpam-804	102	26	a	a	DET
ejpam-804	102	27	covariance	covariance	NOUN
ejpam-804	102	28	of	of	ADP
ejpam-804	102	29	bounded	bounded	ADJ
ejpam-804	102	30	variation	variation	NOUN
ejpam-804	103	1	(	(	PUNCT
ejpam-804	103	2	∫	∫	PROPN
ejpam-804	103	3	π	π	PROPN
ejpam-804	103	4	−π	−π	NUM
ejpam-804	104	1	∫	∫	PROPN
ejpam-804	105	1	π	π	PROPN
ejpam-804	105	2	−π	−π	PROPN
ejpam-804	105	3	|f(du	|f(du	PROPN
ejpam-804	105	4	,	,	PUNCT
ejpam-804	105	5	dv)|	dv)|	PROPN
ejpam-804	105	6	<	<	X
ejpam-804	105	7	∞	∞	PROPN
ejpam-804	105	8	)	)	PUNCT
ejpam-804	105	9	,	,	PUNCT
ejpam-804	105	10	so	so	SCONJ
ejpam-804	105	11	that	that	SCONJ
ejpam-804	105	12	the	the	DET
ejpam-804	105	13	integral	integral	ADJ
ejpam-804	105	14	in	in	ADP
ejpam-804	105	15	(	(	PUNCT
ejpam-804	105	16	7	7	NUM
ejpam-804	105	17	)	)	PUNCT
ejpam-804	105	18	exists	exist	VERB
ejpam-804	105	19	.	.	PUNCT
ejpam-804	106	1	blanc	blanc	NOUN
ejpam-804	106	2	-	-	PUNCT
ejpam-804	106	3	lapierre	lapierre	PROPN
ejpam-804	106	4	and	and	CCONJ
ejpam-804	106	5	fortet	fortet	NOUN
ejpam-804	107	1	[	[	X
ejpam-804	107	2	1	1	NUM
ejpam-804	107	3	,	,	PUNCT
ejpam-804	107	4	volume	volume	NOUN
ejpam-804	107	5	2	2	NUM
ejpam-804	107	6	]	]	PUNCT
ejpam-804	107	7	showed	show	VERB
ejpam-804	107	8	that	that	SCONJ
ejpam-804	107	9	a	a	DET
ejpam-804	107	10	strongly	strongly	ADV
ejpam-804	107	11	harmonizable	harmonizable	ADJ
ejpam-804	107	12	process	process	NOUN
ejpam-804	107	13	has	have	VERB
ejpam-804	107	14	a	a	DET
ejpam-804	107	15	unique	unique	ADJ
ejpam-804	107	16	quadratic	quadratic	ADJ
ejpam-804	107	17	mean	mean	NOUN
ejpam-804	107	18	representation	representation	NOUN
ejpam-804	107	19	such	such	ADJ
ejpam-804	107	20	as	as	ADP
ejpam-804	107	21	(	(	PUNCT
ejpam-804	107	22	6	6	NUM
ejpam-804	107	23	)	)	PUNCT
ejpam-804	107	24	.	.	PUNCT
ejpam-804	108	1	it	it	PRON
ejpam-804	108	2	is	be	AUX
ejpam-804	108	3	shown	show	VERB
ejpam-804	108	4	in	in	ADP
ejpam-804	108	5	[	[	X
ejpam-804	108	6	15	15	NUM
ejpam-804	108	7	]	]	PUNCT
ejpam-804	108	8	that	that	SCONJ
ejpam-804	108	9	oscillatory	oscillatory	ADJ
ejpam-804	108	10	sequences	sequence	NOUN
ejpam-804	108	11	are	be	AUX
ejpam-804	108	12	strongly	strongly	ADV
ejpam-804	108	13	harmonizable	harmonizable	ADJ
ejpam-804	108	14	and	and	CCONJ
ejpam-804	108	15	that	that	SCONJ
ejpam-804	108	16	slowly	slowly	ADV
ejpam-804	108	17	changing	change	VERB
ejpam-804	108	18	processes	process	NOUN
ejpam-804	108	19	in	in	ADP
ejpam-804	108	20	continuous	continuous	ADJ
ejpam-804	108	21	and	and	CCONJ
ejpam-804	108	22	discrete	discrete	ADJ
ejpam-804	108	23	time	time	NOUN
ejpam-804	108	24	are	be	AUX
ejpam-804	108	25	also	also	ADV
ejpam-804	108	26	strongly	strongly	ADV
ejpam-804	108	27	harmonizable	harmonizable	ADJ
ejpam-804	108	28	.	.	PUNCT
ejpam-804	109	1	gladyshev	gladyshev	PROPN
ejpam-804	109	2	[	[	X
ejpam-804	109	3	8	8	NUM
ejpam-804	109	4	]	]	PUNCT
ejpam-804	109	5	proved	prove	VERB
ejpam-804	109	6	that	that	SCONJ
ejpam-804	109	7	periodic	periodic	ADJ
ejpam-804	109	8	stationary	stationary	ADJ
ejpam-804	109	9	sequences	sequence	NOUN
ejpam-804	109	10	are	be	AUX
ejpam-804	109	11	strongly	strongly	ADV
ejpam-804	109	12	harmonizable	harmonizable	ADJ
ejpam-804	109	13	.	.	PUNCT
ejpam-804	110	1	he	he	PRON
ejpam-804	110	2	also	also	ADV
ejpam-804	110	3	showed	show	VERB
ejpam-804	110	4	that	that	SCONJ
ejpam-804	110	5	periodic	periodic	ADJ
ejpam-804	110	6	stationary	stationary	ADJ
ejpam-804	110	7	processes	process	NOUN
ejpam-804	110	8	with	with	ADP
ejpam-804	110	9	continuous	continuous	ADJ
ejpam-804	110	10	time	time	NOUN
ejpam-804	110	11	are	be	AUX
ejpam-804	110	12	not	not	PART
ejpam-804	110	13	necessarily	necessarily	ADV
ejpam-804	110	14	strongly	strongly	ADV
ejpam-804	110	15	harmonizable	harmonizable	ADJ
ejpam-804	110	16	.	.	PUNCT
ejpam-804	111	1	2.6	2.6	NUM
ejpam-804	111	2	.	.	PUNCT
ejpam-804	112	1	weakly	weakly	ADJ
ejpam-804	112	2	harmonizable	harmonizable	ADJ
ejpam-804	112	3	processes	process	NOUN
ejpam-804	112	4	a	a	DET
ejpam-804	112	5	second	second	ADJ
ejpam-804	112	6	order	order	NOUN
ejpam-804	112	7	process	process	NOUN
ejpam-804	112	8	x	x	PUNCT
ejpam-804	112	9	t	t	PROPN
ejpam-804	112	10	is	be	AUX
ejpam-804	112	11	weakly	weakly	ADV
ejpam-804	112	12	harmonizable	harmonizable	ADJ
ejpam-804	112	13	if	if	SCONJ
ejpam-804	112	14	and	and	CCONJ
ejpam-804	112	15	only	only	ADV
ejpam-804	112	16	if	if	SCONJ
ejpam-804	112	17	its	its	PRON
ejpam-804	112	18	covariance	covariance	NOUN
ejpam-804	112	19	function	function	NOUN
ejpam-804	112	20	has	have	VERB
ejpam-804	112	21	the	the	DET
ejpam-804	112	22	integral	integral	ADJ
ejpam-804	112	23	representation	representation	NOUN
ejpam-804	112	24	:	:	PUNCT
ejpam-804	112	25	b(s	b(	NOUN
ejpam-804	112	26	,	,	PUNCT
ejpam-804	112	27	t	t	PROPN
ejpam-804	112	28	)	)	PUNCT
ejpam-804	112	29	=	=	SYM
ejpam-804	113	1	∫	∫	PROPN
ejpam-804	114	1	π	π	NOUN
ejpam-804	114	2	−π	−π	X
ejpam-804	114	3	∫	∫	PROPN
ejpam-804	115	1	π	π	NOUN
ejpam-804	115	2	−π	−π	PRON
ejpam-804	115	3	ei(su−t	ei(su−t	PROPN
ejpam-804	115	4	v)f(du	v)f(du	NUM
ejpam-804	115	5	,	,	PUNCT
ejpam-804	115	6	dv	dv	PROPN
ejpam-804	115	7	)	)	PUNCT
ejpam-804	115	8	(	(	PUNCT
ejpam-804	115	9	8)	8)	NUM
ejpam-804	115	10	for	for	ADP
ejpam-804	115	11	all	all	DET
ejpam-804	115	12	s	s	NOUN
ejpam-804	115	13	and	and	CCONJ
ejpam-804	115	14	t	t	NOUN
ejpam-804	115	15	integers	integer	NOUN
ejpam-804	115	16	,	,	PUNCT
ejpam-804	115	17	where	where	SCONJ
ejpam-804	115	18	f	f	PROPN
ejpam-804	115	19	is	be	AUX
ejpam-804	115	20	a	a	DET
ejpam-804	115	21	positive	positive	ADJ
ejpam-804	115	22	definite	definite	ADJ
ejpam-804	115	23	and	and	CCONJ
ejpam-804	115	24	σ	σ	VERB
ejpam-804	115	25	-	-	PUNCT
ejpam-804	115	26	additive	additive	ADJ
ejpam-804	115	27	bimeasure	bimeasure	NOUN
ejpam-804	115	28	i.e.	i.e.	X
ejpam-804	115	29	sup	sup	NOUN
ejpam-804	115	30	n∑∑	n∑∑	PROPN
ejpam-804	115	31	ai	ai	VERB
ejpam-804	115	32	ā	ā	PROPN
ejpam-804	115	33	j	j	PROPN
ejpam-804	115	34	f(ai	f(ai	PROPN
ejpam-804	115	35	,	,	PUNCT
ejpam-804	115	36	a	a	DET
ejpam-804	115	37	j)/ai	j)/ai	PROPN
ejpam-804	115	38	∈	∈	PROPN
ejpam-804	115	39	b	b	PROPN
ejpam-804	115	40	disjoint	disjoint	PROPN
ejpam-804	115	41	,	,	PUNCT
ejpam-804	115	42	�	�	PROPN
ejpam-804	115	43	�	�	PROPN
ejpam-804	115	44	ai	ai	PROPN
ejpam-804	115	45	�	�	PROPN
ejpam-804	115	46	�	�	PROPN
ejpam-804	115	47	≤	≤	NOUN
ejpam-804	115	48	1	1	NUM
ejpam-804	115	49	o	o	NOUN
ejpam-804	115	50	<	<	X
ejpam-804	115	51	∞	∞	PROPN
ejpam-804	115	52	(	(	PUNCT
ejpam-804	115	53	9	9	NUM
ejpam-804	115	54	)	)	PUNCT
ejpam-804	115	55	where	where	SCONJ
ejpam-804	115	56	b	b	NOUN
ejpam-804	115	57	is	be	AUX
ejpam-804	115	58	the	the	DET
ejpam-804	115	59	borel	borel	PROPN
ejpam-804	115	60	σ	σ	PROPN
ejpam-804	115	61	-	-	PROPN
ejpam-804	115	62	algebra	algebra	NOUN
ejpam-804	115	63	of	of	ADP
ejpam-804	115	64	[	[	X
ejpam-804	115	65	−π	−π	PROPN
ejpam-804	115	66	,	,	PUNCT
ejpam-804	115	67	π	π	X
ejpam-804	115	68	]	]	X
ejpam-804	115	69	and	and	CCONJ
ejpam-804	115	70	f	f	X
ejpam-804	115	71	(	(	PUNCT
ejpam-804	115	72	·	·	PUNCT
ejpam-804	115	73	,	,	PUNCT
ejpam-804	115	74	c	c	NOUN
ejpam-804	115	75	)	)	PUNCT
ejpam-804	115	76	,	,	PUNCT
ejpam-804	115	77	f(a	f(a	NOUN
ejpam-804	115	78	,	,	PUNCT
ejpam-804	115	79	·	·	PUNCT
ejpam-804	115	80	)	)	PUNCT
ejpam-804	115	81	are	be	AUX
ejpam-804	115	82	complex	complex	ADJ
ejpam-804	115	83	measures	measure	NOUN
ejpam-804	115	84	on	on	ADP
ejpam-804	115	85	b.	b.	PROPN
ejpam-804	115	86	in	in	ADP
ejpam-804	115	87	that	that	DET
ejpam-804	115	88	case	case	NOUN
ejpam-804	115	89	,	,	PUNCT
ejpam-804	115	90	integrals	integral	NOUN
ejpam-804	115	91	relative	relative	ADJ
ejpam-804	115	92	to	to	ADP
ejpam-804	115	93	f	f	PROPN
ejpam-804	115	94	can	can	AUX
ejpam-804	115	95	not	not	PART
ejpam-804	115	96	generally	generally	ADV
ejpam-804	115	97	be	be	AUX
ejpam-804	115	98	lebesgue	lebesgue	ADJ
ejpam-804	115	99	-	-	PUNCT
ejpam-804	115	100	stieltjes	stieltjes	NOUN
ejpam-804	115	101	integrals	integral	NOUN
ejpam-804	115	102	,	,	PUNCT
ejpam-804	115	103	but	but	CCONJ
ejpam-804	115	104	one	one	PRON
ejpam-804	115	105	can	can	AUX
ejpam-804	115	106	define	define	VERB
ejpam-804	115	107	a	a	DET
ejpam-804	115	108	morse	morse	NOUN
ejpam-804	115	109	-	-	PUNCT
ejpam-804	115	110	transue	transue	NOUN
ejpam-804	115	111	integral	integral	ADJ
ejpam-804	115	112	[	[	X
ejpam-804	115	113	26	26	NUM
ejpam-804	115	114	]	]	PUNCT
ejpam-804	115	115	.	.	PUNCT
ejpam-804	116	1	rozanov	rozanov	VERB
ejpam-804	117	1	[	[	X
ejpam-804	117	2	27	27	NUM
ejpam-804	117	3	]	]	PUNCT
ejpam-804	117	4	proved	prove	VERB
ejpam-804	117	5	that	that	SCONJ
ejpam-804	117	6	strongly	strongly	ADV
ejpam-804	117	7	harmonizable	harmonizable	ADJ
ejpam-804	117	8	processes	process	NOUN
ejpam-804	117	9	belong	belong	VERB
ejpam-804	117	10	to	to	ADP
ejpam-804	117	11	the	the	DET
ejpam-804	117	12	class	class	NOUN
ejpam-804	117	13	(	(	PUNCT
ejpam-804	117	14	kf	kf	PROPN
ejpam-804	117	15	)	)	PUNCT
ejpam-804	117	16	and	and	CCONJ
ejpam-804	117	17	rao	rao	NOUN
ejpam-804	118	1	[	[	X
ejpam-804	118	2	26	26	NUM
ejpam-804	118	3	]	]	PUNCT
ejpam-804	118	4	showed	show	VERB
ejpam-804	118	5	that	that	SCONJ
ejpam-804	118	6	many	many	ADJ
ejpam-804	118	7	weakly	weakly	ADJ
ejpam-804	118	8	harmonizable	harmonizable	ADJ
ejpam-804	118	9	processes	process	NOUN
ejpam-804	118	10	also	also	ADV
ejpam-804	118	11	belong	belong	VERB
ejpam-804	118	12	to	to	ADP
ejpam-804	118	13	the	the	DET
ejpam-804	118	14	class	class	NOUN
ejpam-804	118	15	(	(	PUNCT
ejpam-804	118	16	kf	kf	PROPN
ejpam-804	118	17	)	)	PUNCT
ejpam-804	118	18	.	.	PUNCT
ejpam-804	119	1	however	however	ADV
ejpam-804	119	2	not	not	PART
ejpam-804	119	3	all	all	DET
ejpam-804	119	4	weakly	weakly	ADJ
ejpam-804	119	5	harmonizable	harmonizable	ADJ
ejpam-804	119	6	processes	process	NOUN
ejpam-804	119	7	are	be	AUX
ejpam-804	119	8	of	of	ADP
ejpam-804	119	9	class	class	NOUN
ejpam-804	119	10	(	(	PUNCT
ejpam-804	119	11	kf	kf	NOUN
ejpam-804	119	12	)	)	PUNCT
ejpam-804	119	13	and	and	CCONJ
ejpam-804	119	14	inversely	inversely	ADV
ejpam-804	119	15	not	not	PART
ejpam-804	119	16	all	all	DET
ejpam-804	119	17	class	class	NOUN
ejpam-804	119	18	(	(	PUNCT
ejpam-804	119	19	kf	kf	NOUN
ejpam-804	119	20	)	)	PUNCT
ejpam-804	119	21	processes	process	NOUN
ejpam-804	119	22	belong	belong	VERB
ejpam-804	119	23	to	to	ADP
ejpam-804	119	24	the	the	DET
ejpam-804	119	25	weakly	weakly	ADJ
ejpam-804	119	26	harmonizable	harmonizable	ADJ
ejpam-804	119	27	class	class	NOUN
ejpam-804	119	28	.	.	PUNCT
ejpam-804	120	1	note	note	VERB
ejpam-804	120	2	that	that	SCONJ
ejpam-804	120	3	the	the	DET
ejpam-804	120	4	brownian	brownian	ADJ
ejpam-804	120	5	motion	motion	NOUN
ejpam-804	120	6	is	be	AUX
ejpam-804	120	7	not	not	PART
ejpam-804	120	8	harmonizable	harmonizable	ADJ
ejpam-804	120	9	but	but	CCONJ
ejpam-804	120	10	is	be	AUX
ejpam-804	120	11	of	of	ADP
ejpam-804	120	12	class	class	NOUN
ejpam-804	120	13	(	(	PUNCT
ejpam-804	120	14	kf	kf	NOUN
ejpam-804	120	15	)	)	PUNCT
ejpam-804	121	1	see	see	VERB
ejpam-804	121	2	figure	figure	NOUN
ejpam-804	121	3	1	1	NUM
ejpam-804	121	4	.	.	PUNCT
ejpam-804	121	5	figure	figure	NOUN
ejpam-804	121	6	1	1	NUM
ejpam-804	121	7	:	:	PUNCT
ejpam-804	121	8	demonstrating	demonstrate	VERB
ejpam-804	121	9	nested	nested	ADJ
ejpam-804	121	10	stru	stru	PROPN
ejpam-804	121	11	ture	ture	PROPN
ejpam-804	121	12	of	of	ADP
ejpam-804	121	13	classes	class	NOUN
ejpam-804	121	14	.	.	PUNCT
ejpam-804	122	1	r.	r.	PROPN
ejpam-804	122	2	joyeux	joyeux	PROPN
ejpam-804	122	3	/	/	SYM
ejpam-804	122	4	eur	eur	PROPN
ejpam-804	122	5	.	.	PUNCT
ejpam-804	123	1	j.	j.	PROPN
ejpam-804	123	2	pure	pure	PROPN
ejpam-804	123	3	appl	appl	PROPN
ejpam-804	123	4	.	.	PROPN
ejpam-804	123	5	math	math	PROPN
ejpam-804	123	6	,	,	PUNCT
ejpam-804	123	7	3	3	NUM
ejpam-804	123	8	(	(	PUNCT
ejpam-804	123	9	2010	2010	NUM
ejpam-804	123	10	)	)	PUNCT
ejpam-804	123	11	,	,	PUNCT
ejpam-804	123	12	519	519	NUM
ejpam-804	123	13	-	-	SYM
ejpam-804	123	14	530	530	NUM
ejpam-804	123	15	524	524	NUM
ejpam-804	123	16	2.7	2.7	NUM
ejpam-804	123	17	.	.	PUNCT
ejpam-804	124	1	spectral	spectral	ADJ
ejpam-804	124	2	properties	property	NOUN
ejpam-804	124	3	of	of	ADP
ejpam-804	124	4	harmonizable	harmonizable	ADJ
ejpam-804	124	5	processes	process	NOUN
ejpam-804	124	6	2.7.1	2.7.1	NUM
ejpam-804	124	7	.	.	PUNCT
ejpam-804	125	1	asymptotic	asymptotic	ADJ
ejpam-804	125	2	stationarity	stationarity	NOUN
ejpam-804	125	3	rozanov	rozanov	NOUN
ejpam-804	126	1	[	[	X
ejpam-804	126	2	27	27	NUM
ejpam-804	126	3	]	]	PUNCT
ejpam-804	126	4	proved	prove	VERB
ejpam-804	126	5	that	that	SCONJ
ejpam-804	126	6	every	every	DET
ejpam-804	126	7	strongly	strongly	ADV
ejpam-804	126	8	harmonizable	harmonizable	ADJ
ejpam-804	126	9	process	process	NOUN
ejpam-804	126	10	is	be	AUX
ejpam-804	126	11	of	of	ADP
ejpam-804	126	12	class	class	NOUN
ejpam-804	126	13	(	(	PUNCT
ejpam-804	126	14	kf	kf	NOUN
ejpam-804	126	15	)	)	PUNCT
ejpam-804	126	16	(	(	PUNCT
ejpam-804	126	17	or	or	CCONJ
ejpam-804	126	18	asymptotically	asymptotically	ADV
ejpam-804	126	19	stationary	stationary	NOUN
ejpam-804	126	20	)	)	PUNCT
ejpam-804	126	21	and	and	CCONJ
ejpam-804	126	22	more	more	ADV
ejpam-804	126	23	precisely	precisely	ADV
ejpam-804	126	24	that	that	SCONJ
ejpam-804	126	25	the	the	DET
ejpam-804	126	26	following	follow	VERB
ejpam-804	126	27	theorem	theorem	ADJ
ejpam-804	126	28	holds	hold	NOUN
ejpam-804	126	29	.	.	PUNCT
ejpam-804	127	1	theorem	theorem	NOUN
ejpam-804	127	2	2	2	NUM
ejpam-804	127	3	.	.	PUNCT
ejpam-804	128	1	let	let	VERB
ejpam-804	128	2	x	x	SYM
ejpam-804	128	3	t	t	PROPN
ejpam-804	128	4	be	be	AUX
ejpam-804	128	5	a	a	DET
ejpam-804	128	6	strongly	strongly	ADV
ejpam-804	128	7	harmonizable	harmonizable	ADJ
ejpam-804	128	8	process	process	NOUN
ejpam-804	128	9	with	with	ADP
ejpam-804	128	10	spectral	spectral	ADJ
ejpam-804	128	11	measure	measure	NOUN
ejpam-804	128	12	f	f	X
ejpam-804	128	13	,	,	PUNCT
ejpam-804	128	14	and	and	CCONJ
ejpam-804	128	15	let	let	VERB
ejpam-804	128	16	∆	∆	PROPN
ejpam-804	128	17	=	=	PRON
ejpam-804	128	18	{	{	PUNCT
ejpam-804	128	19	(	(	PUNCT
ejpam-804	128	20	u	u	NOUN
ejpam-804	128	21	,	,	PUNCT
ejpam-804	128	22	v	v	NOUN
ejpam-804	128	23	)	)	PUNCT
ejpam-804	129	1	|	|	ADV
ejpam-804	129	2	u=	u=	NOUN
ejpam-804	129	3	v	v	NOUN
ejpam-804	129	4	}	}	PUNCT
ejpam-804	129	5	be	be	AUX
ejpam-804	129	6	the	the	DET
ejpam-804	129	7	diagonal	diagonal	ADJ
ejpam-804	129	8	axis	axis	NOUN
ejpam-804	129	9	of	of	ADP
ejpam-804	129	10	[	[	X
ejpam-804	129	11	−π	−π	ADJ
ejpam-804	129	12	,	,	PUNCT
ejpam-804	129	13	π]×	π]×	NOUN
ejpam-804	129	14	[	[	X
ejpam-804	129	15	−π	−π	PROPN
ejpam-804	129	16	,	,	PUNCT
ejpam-804	129	17	π	π	PROPN
ejpam-804	129	18	]	]	X
ejpam-804	129	19	.	.	PUNCT
ejpam-804	130	1	then	then	ADV
ejpam-804	130	2	for	for	ADP
ejpam-804	130	3	all	all	DET
ejpam-804	130	4	integer	integer	NOUN
ejpam-804	130	5	h	h	NOUN
ejpam-804	130	6	we	we	PRON
ejpam-804	130	7	have	have	VERB
ejpam-804	130	8	:	:	PUNCT
ejpam-804	130	9	lim	lim	PROPN
ejpam-804	130	10	t→∞	t→∞	ADP
ejpam-804	130	11	1	1	NUM
ejpam-804	130	12	t	t	NOUN
ejpam-804	130	13	t	t	PROPN
ejpam-804	130	14	∑	∑	PROPN
ejpam-804	130	15	s=0	s=0	PROPN
ejpam-804	130	16	b(s	b(s	PROPN
ejpam-804	130	17	,	,	PUNCT
ejpam-804	130	18	s+	s+	PUNCT
ejpam-804	130	19	h	h	X
ejpam-804	130	20	)	)	PUNCT
ejpam-804	130	21	=	=	PUNCT
ejpam-804	131	1	∫∫	∫∫	ADV
ejpam-804	131	2	∆	∆	PROPN
ejpam-804	131	3	eihv	eihv	VERB
ejpam-804	131	4	f(du	f(du	PROPN
ejpam-804	131	5	,	,	PUNCT
ejpam-804	131	6	dv	dv	PROPN
ejpam-804	131	7	)	)	PUNCT
ejpam-804	131	8	(	(	PUNCT
ejpam-804	131	9	10	10	NUM
ejpam-804	131	10	)	)	PUNCT
ejpam-804	131	11	2.7.2	2.7.2	NUM
ejpam-804	131	12	.	.	PUNCT
ejpam-804	132	1	energy	energy	NOUN
ejpam-804	132	2	properties	property	NOUN
ejpam-804	132	3	of	of	ADP
ejpam-804	132	4	harmonizable	harmonizable	ADJ
ejpam-804	132	5	processes	process	NOUN
ejpam-804	132	6	let	let	VERB
ejpam-804	132	7	x	x	PART
ejpam-804	132	8	t	t	PROPN
ejpam-804	132	9	be	be	AUX
ejpam-804	132	10	a	a	DET
ejpam-804	132	11	strongly	strongly	ADV
ejpam-804	132	12	harmonizable	harmonizable	ADJ
ejpam-804	132	13	process	process	NOUN
ejpam-804	132	14	with	with	ADP
ejpam-804	132	15	spectral	spectral	ADJ
ejpam-804	132	16	measure	measure	NOUN
ejpam-804	132	17	f	f	PROPN
ejpam-804	132	18	,	,	PUNCT
ejpam-804	132	19	then	then	ADV
ejpam-804	132	20	f	f	PROPN
ejpam-804	132	21	can	can	AUX
ejpam-804	132	22	be	be	AUX
ejpam-804	132	23	decomposed	decompose	VERB
ejpam-804	132	24	into	into	ADP
ejpam-804	132	25	f1	f1	NOUN
ejpam-804	132	26	,	,	PUNCT
ejpam-804	132	27	f2	f2	PROPN
ejpam-804	132	28	,	,	PUNCT
ejpam-804	132	29	f3	f3	PROPN
ejpam-804	133	1	where	where	SCONJ
ejpam-804	133	2	:	:	PUNCT
ejpam-804	133	3	f(du	f(du	NOUN
ejpam-804	133	4	,	,	PUNCT
ejpam-804	133	5	dv	dv	PROPN
ejpam-804	133	6	)	)	PUNCT
ejpam-804	133	7	=	=	SYM
ejpam-804	133	8	f1(du	f1(du	PROPN
ejpam-804	133	9	,	,	PUNCT
ejpam-804	133	10	dv)+	dv)+	NOUN
ejpam-804	133	11	f2(du	f2(du	PROPN
ejpam-804	133	12	,	,	PUNCT
ejpam-804	133	13	dv)+	dv)+	VERB
ejpam-804	133	14	f3(du	f3(du	PROPN
ejpam-804	133	15	,	,	PUNCT
ejpam-804	133	16	dv	dv	PROPN
ejpam-804	133	17	)	)	PUNCT
ejpam-804	133	18	(	(	PUNCT
ejpam-804	133	19	11	11	NUM
ejpam-804	133	20	)	)	PUNCT
ejpam-804	133	21	f1	f1	NOUN
ejpam-804	133	22	is	be	AUX
ejpam-804	133	23	absolutely	absolutely	ADV
ejpam-804	133	24	continuous	continuous	ADJ
ejpam-804	133	25	with	with	ADP
ejpam-804	133	26	spectral	spectral	ADJ
ejpam-804	133	27	density	density	NOUN
ejpam-804	133	28	f1	f1	NOUN
ejpam-804	133	29	.	.	PUNCT
ejpam-804	134	1	f2	f2	PROPN
ejpam-804	134	2	is	be	AUX
ejpam-804	134	3	a	a	DET
ejpam-804	134	4	distribution	distribution	NOUN
ejpam-804	134	5	,	,	PUNCT
ejpam-804	134	6	which	which	PRON
ejpam-804	134	7	has	have	VERB
ejpam-804	134	8	its	its	PRON
ejpam-804	134	9	mass	mass	NOUN
ejpam-804	134	10	concentrated	concentrate	VERB
ejpam-804	134	11	on	on	ADP
ejpam-804	134	12	a	a	DET
ejpam-804	134	13	set	set	NOUN
ejpam-804	134	14	at	at	ADP
ejpam-804	134	15	most	most	ADV
ejpam-804	134	16	denumerable	denumerable	ADJ
ejpam-804	134	17	,	,	PUNCT
ejpam-804	134	18	and	and	CCONJ
ejpam-804	134	19	each	each	DET
ejpam-804	134	20	point	point	NOUN
ejpam-804	134	21	carries	carry	VERB
ejpam-804	134	22	a	a	DET
ejpam-804	134	23	mass	mass	NOUN
ejpam-804	134	24	different	different	ADJ
ejpam-804	134	25	from	from	ADP
ejpam-804	134	26	zero	zero	NUM
ejpam-804	134	27	.	.	PUNCT
ejpam-804	135	1	f3	f3	PROPN
ejpam-804	135	2	has	have	VERB
ejpam-804	135	3	its	its	PRON
ejpam-804	135	4	mass	mass	NOUN
ejpam-804	135	5	concentrated	concentrate	VERB
ejpam-804	135	6	on	on	ADP
ejpam-804	135	7	a	a	DET
ejpam-804	135	8	set	set	ADJ
ejpam-804	135	9	non	non	ADJ
ejpam-804	135	10	-	-	ADJ
ejpam-804	135	11	denumerable	denumerable	ADJ
ejpam-804	135	12	,	,	PUNCT
ejpam-804	135	13	and	and	CCONJ
ejpam-804	135	14	each	each	DET
ejpam-804	135	15	single	single	ADJ
ejpam-804	135	16	point	point	NOUN
ejpam-804	135	17	carries	carry	VERB
ejpam-804	135	18	the	the	DET
ejpam-804	135	19	mass	mass	NOUN
ejpam-804	135	20	zero	zero	NUM
ejpam-804	135	21	.	.	PUNCT
ejpam-804	136	1	note	note	VERB
ejpam-804	136	2	that	that	SCONJ
ejpam-804	136	3	in	in	ADP
ejpam-804	136	4	the	the	DET
ejpam-804	136	5	stationary	stationary	ADJ
ejpam-804	136	6	case	case	NOUN
ejpam-804	136	7	f1	f1	NOUN
ejpam-804	136	8	,	,	PUNCT
ejpam-804	136	9	f2	f2	PROPN
ejpam-804	136	10	and	and	CCONJ
ejpam-804	136	11	f3	f3	PROPN
ejpam-804	136	12	have	have	VERB
ejpam-804	136	13	their	their	PRON
ejpam-804	136	14	total	total	ADJ
ejpam-804	136	15	masses	masse	NOUN
ejpam-804	136	16	located	locate	VERB
ejpam-804	136	17	on	on	ADP
ejpam-804	136	18	the	the	DET
ejpam-804	136	19	bisector	bisector	NOUN
ejpam-804	136	20	.	.	PUNCT
ejpam-804	137	1	lii	lii	NOUN
ejpam-804	137	2	and	and	CCONJ
ejpam-804	137	3	rosenblatt	rosenblatt	PROPN
ejpam-804	138	1	[	[	X
ejpam-804	138	2	18	18	NUM
ejpam-804	138	3	]	]	PUNCT
ejpam-804	138	4	derive	derive	ADJ
ejpam-804	138	5	consistent	consistent	ADJ
ejpam-804	138	6	estimators	estimator	NOUN
ejpam-804	138	7	for	for	ADP
ejpam-804	138	8	the	the	DET
ejpam-804	138	9	spectral	spectral	ADJ
ejpam-804	138	10	distribution	distribution	NOUN
ejpam-804	138	11	of	of	ADP
ejpam-804	138	12	harmonizable	harmonizable	ADJ
ejpam-804	138	13	processes	process	NOUN
ejpam-804	138	14	when	when	SCONJ
ejpam-804	138	15	the	the	DET
ejpam-804	138	16	spectral	spectral	ADJ
ejpam-804	138	17	support	support	NOUN
ejpam-804	138	18	of	of	ADP
ejpam-804	138	19	the	the	DET
ejpam-804	138	20	process	process	NOUN
ejpam-804	138	21	consists	consist	VERB
ejpam-804	138	22	of	of	ADP
ejpam-804	138	23	lines	line	NOUN
ejpam-804	138	24	.	.	PUNCT
ejpam-804	139	1	2.8	2.8	NUM
ejpam-804	139	2	.	.	X
ejpam-804	140	1	vector	vector	NOUN
ejpam-804	140	2	harmonizable	harmonizable	ADJ
ejpam-804	140	3	processes	process	NOUN
ejpam-804	140	4	definition	definition	NOUN
ejpam-804	140	5	2	2	NUM
ejpam-804	140	6	.	.	PUNCT
ejpam-804	141	1	an	an	DET
ejpam-804	141	2	n	n	ADV
ejpam-804	141	3	-	-	PUNCT
ejpam-804	141	4	dimensional	dimensional	ADJ
ejpam-804	141	5	vector	vector	NOUN
ejpam-804	141	6	process	process	NOUN
ejpam-804	141	7	x	x	X
ejpam-804	141	8	t	t	NOUN
ejpam-804	141	9	=	=	SYM
ejpam-804	141	10	(	(	PUNCT
ejpam-804	141	11	x1	x1	PROPN
ejpam-804	141	12	t	t	PROPN
ejpam-804	141	13	,	,	PUNCT
ejpam-804	141	14	.	.	PUNCT
ejpam-804	141	15	.	.	PUNCT
ejpam-804	141	16	.	.	PUNCT
ejpam-804	142	1	,	,	PUNCT
ejpam-804	142	2	xnt	xnt	PROPN
ejpam-804	142	3	)	)	PUNCT
ejpam-804	142	4	′	′	NUM
ejpam-804	142	5	is	be	AUX
ejpam-804	142	6	an	an	DET
ejpam-804	142	7	n	n	ADV
ejpam-804	142	8	-	-	PUNCT
ejpam-804	142	9	dimensional	dimensional	ADJ
ejpam-804	142	10	strongly	strongly	ADV
ejpam-804	142	11	harmonizable	harmonizable	ADJ
ejpam-804	142	12	process	process	NOUN
ejpam-804	142	13	if	if	SCONJ
ejpam-804	143	1	and	and	CCONJ
ejpam-804	143	2	only	only	ADV
ejpam-804	143	3	if	if	SCONJ
ejpam-804	143	4	for	for	ADP
ejpam-804	143	5	every	every	DET
ejpam-804	143	6	n×	n×	NUM
ejpam-804	143	7	1	1	NUM
ejpam-804	143	8	vector	vector	NOUN
ejpam-804	143	9	of	of	ADP
ejpam-804	143	10	real	real	ADJ
ejpam-804	143	11	numbers	number	NOUN
ejpam-804	143	12	,	,	PUNCT
ejpam-804	143	13	w	w	PROPN
ejpam-804	143	14	,	,	PUNCT
ejpam-804	143	15	the	the	DET
ejpam-804	143	16	process	process	NOUN
ejpam-804	143	17	w′x	w′x	PROPN
ejpam-804	143	18	t	t	PROPN
ejpam-804	143	19	is	be	AUX
ejpam-804	143	20	strongly	strongly	ADV
ejpam-804	143	21	harmonizable	harmonizable	ADJ
ejpam-804	143	22	.	.	PUNCT
ejpam-804	144	1	the	the	DET
ejpam-804	144	2	above	above	ADJ
ejpam-804	144	3	definition	definition	NOUN
ejpam-804	144	4	is	be	AUX
ejpam-804	144	5	equivalent	equivalent	ADJ
ejpam-804	144	6	to	to	ADP
ejpam-804	144	7	requiring	require	VERB
ejpam-804	144	8	that	that	SCONJ
ejpam-804	144	9	the	the	DET
ejpam-804	144	10	covariance	covariance	NOUN
ejpam-804	144	11	function	function	NOUN
ejpam-804	144	12	of	of	ADP
ejpam-804	144	13	x	x	SYM
ejpam-804	144	14	t	t	PROPN
ejpam-804	144	15	be	be	AUX
ejpam-804	144	16	represented	represent	VERB
ejpam-804	144	17	as	as	ADP
ejpam-804	144	18	b(s	b(	NOUN
ejpam-804	144	19	,	,	PUNCT
ejpam-804	144	20	t	t	PROPN
ejpam-804	144	21	)	)	PUNCT
ejpam-804	144	22	=	=	SYM
ejpam-804	145	1	∫	∫	PROPN
ejpam-804	146	1	π	π	NOUN
ejpam-804	146	2	−π	−π	X
ejpam-804	146	3	∫	∫	PROPN
ejpam-804	147	1	π	π	NOUN
ejpam-804	147	2	−π	−π	PRON
ejpam-804	147	3	ei(su−t	ei(su−t	PROPN
ejpam-804	147	4	v)f(du	v)f(du	NUM
ejpam-804	147	5	,	,	PUNCT
ejpam-804	147	6	dv	dv	PROPN
ejpam-804	147	7	)	)	PUNCT
ejpam-804	147	8	(	(	PUNCT
ejpam-804	147	9	12	12	NUM
ejpam-804	147	10	)	)	PUNCT
ejpam-804	147	11	where	where	SCONJ
ejpam-804	147	12	f(du	f(du	NOUN
ejpam-804	147	13	,	,	PUNCT
ejpam-804	147	14	dv	dv	PROPN
ejpam-804	147	15	)	)	PUNCT
ejpam-804	147	16	is	be	AUX
ejpam-804	147	17	an	an	DET
ejpam-804	147	18	n×	n×	PROPN
ejpam-804	147	19	n	n	NOUN
ejpam-804	147	20	matrix	matrix	NOUN
ejpam-804	147	21	array	array	NOUN
ejpam-804	147	22	of	of	ADP
ejpam-804	147	23	covariance	covariance	NOUN
ejpam-804	147	24	functions	function	NOUN
ejpam-804	147	25	of	of	ADP
ejpam-804	147	26	bounded	bounded	ADJ
ejpam-804	147	27	variation	variation	NOUN
ejpam-804	147	28	.	.	PUNCT
ejpam-804	148	1	equation	equation	NOUN
ejpam-804	148	2	(	(	PUNCT
ejpam-804	148	3	6	6	NUM
ejpam-804	148	4	)	)	PUNCT
ejpam-804	148	5	holds	hold	VERB
ejpam-804	148	6	with	with	ADP
ejpam-804	148	7	z	z	PROPN
ejpam-804	148	8	(	(	PUNCT
ejpam-804	148	9	·	·	PUNCT
ejpam-804	148	10	)	)	PUNCT
ejpam-804	148	11	an	an	DET
ejpam-804	148	12	n	n	NUM
ejpam-804	148	13	×	×	NOUN
ejpam-804	148	14	1	1	NUM
ejpam-804	148	15	vector	vector	NOUN
ejpam-804	148	16	of	of	ADP
ejpam-804	148	17	stochastic	stochastic	ADJ
ejpam-804	148	18	measures	measure	NOUN
ejpam-804	148	19	with	with	ADP
ejpam-804	148	20	covariance	covariance	NOUN
ejpam-804	148	21	of	of	ADP
ejpam-804	148	22	bounded	bounded	ADJ
ejpam-804	148	23	variation	variation	NOUN
ejpam-804	148	24	.	.	PUNCT
ejpam-804	149	1	the	the	DET
ejpam-804	149	2	matrix	matrix	NOUN
ejpam-804	149	3	spectral	spectral	ADJ
ejpam-804	149	4	function	function	NOUN
ejpam-804	149	5	f	f	PROPN
ejpam-804	149	6	:	:	PUNCT
ejpam-804	149	7	(	(	PUNCT
ejpam-804	149	8	a	a	PRON
ejpam-804	149	9	,	,	PUNCT
ejpam-804	149	10	b)→	b)→	ADJ
ejpam-804	149	11	e(z(a)z(b)′	e(z(a)z(b)′	PROPN
ejpam-804	149	12	=	=	SYM
ejpam-804	149	13	(	(	PUNCT
ejpam-804	149	14	fi	fi	NOUN
ejpam-804	149	15	j(a	j(a	PROPN
ejpam-804	149	16	,	,	PUNCT
ejpam-804	149	17	b	b	NOUN
ejpam-804	149	18	)	)	PUNCT
ejpam-804	149	19	)	)	PUNCT
ejpam-804	149	20	,	,	PUNCT
ejpam-804	149	21	a	a	DET
ejpam-804	149	22	and	and	CCONJ
ejpam-804	149	23	b	b	PROPN
ejpam-804	149	24	borel	borel	NOUN
ejpam-804	149	25	sets	set	NOUN
ejpam-804	149	26	of	of	ADP
ejpam-804	149	27	[	[	X
ejpam-804	149	28	−π	−π	X
ejpam-804	149	29	,	,	PUNCT
ejpam-804	149	30	π	π	PROPN
ejpam-804	149	31	]	]	X
ejpam-804	149	32	,	,	PUNCT
ejpam-804	149	33	has	have	VERB
ejpam-804	149	34	fii	fii	PROPN
ejpam-804	149	35	positive	positive	ADJ
ejpam-804	149	36	definite	definite	ADJ
ejpam-804	149	37	,	,	PUNCT
ejpam-804	149	38	fi	fi	NOUN
ejpam-804	149	39	j(a	j(a	PROPN
ejpam-804	149	40	,	,	PUNCT
ejpam-804	149	41	b	b	X
ejpam-804	149	42	)	)	PUNCT
ejpam-804	150	1	=	=	SYM
ejpam-804	150	2	f	f	PROPN
ejpam-804	150	3	ji(b	ji(b	PROPN
ejpam-804	150	4	,	,	PUNCT
ejpam-804	150	5	a	a	PRON
ejpam-804	150	6	)	)	PUNCT
ejpam-804	150	7	,	,	PUNCT
ejpam-804	150	8	i	i	PROPN
ejpam-804	150	9	6=	6=	PROPN
ejpam-804	150	10	j	j	PROPN
ejpam-804	150	11	and	and	CCONJ
ejpam-804	150	12	in	in	ADP
ejpam-804	150	13	the	the	DET
ejpam-804	150	14	stationary	stationary	ADJ
ejpam-804	150	15	case	case	NOUN
ejpam-804	150	16	f	f	PROPN
ejpam-804	150	17	itself	itself	PRON
ejpam-804	150	18	is	be	AUX
ejpam-804	150	19	positive	positive	ADJ
ejpam-804	150	20	hermitian	hermitian	NOUN
ejpam-804	150	21	.	.	PUNCT
ejpam-804	151	1	in	in	ADP
ejpam-804	151	2	the	the	DET
ejpam-804	151	3	strongly	strongly	ADV
ejpam-804	151	4	harmonizable	harmonizable	ADJ
ejpam-804	151	5	case	case	NOUN
ejpam-804	151	6	each	each	DET
ejpam-804	151	7	fi	fi	NOUN
ejpam-804	151	8	j	j	PROPN
ejpam-804	151	9	determines	determine	VERB
ejpam-804	151	10	a	a	DET
ejpam-804	151	11	radon	radon	ADJ
ejpam-804	151	12	measure	measure	NOUN
ejpam-804	151	13	on	on	ADP
ejpam-804	151	14	[	[	X
ejpam-804	151	15	−π	−π	ADJ
ejpam-804	151	16	,	,	PUNCT
ejpam-804	151	17	π]×	π]×	NOUN
ejpam-804	151	18	[	[	X
ejpam-804	151	19	−π	−π	PROPN
ejpam-804	151	20	,	,	PUNCT
ejpam-804	151	21	π	π	PROPN
ejpam-804	151	22	]	]	X
ejpam-804	151	23	.	.	PUNCT
ejpam-804	152	1	r.	r.	PROPN
ejpam-804	152	2	joyeux	joyeux	PROPN
ejpam-804	152	3	/	/	SYM
ejpam-804	152	4	eur	eur	PROPN
ejpam-804	152	5	.	.	PUNCT
ejpam-804	153	1	j.	j.	PROPN
ejpam-804	153	2	pure	pure	PROPN
ejpam-804	153	3	appl	appl	PROPN
ejpam-804	153	4	.	.	PROPN
ejpam-804	153	5	math	math	PROPN
ejpam-804	153	6	,	,	PUNCT
ejpam-804	153	7	3	3	NUM
ejpam-804	153	8	(	(	PUNCT
ejpam-804	153	9	2010	2010	NUM
ejpam-804	153	10	)	)	PUNCT
ejpam-804	153	11	,	,	PUNCT
ejpam-804	153	12	519	519	NUM
ejpam-804	153	13	-	-	SYM
ejpam-804	153	14	530	530	NUM
ejpam-804	153	15	525	525	NUM
ejpam-804	153	16	3	3	NUM
ejpam-804	153	17	.	.	PUNCT
ejpam-804	153	18	generalization	generalization	NOUN
ejpam-804	153	19	of	of	ADP
ejpam-804	153	20	the	the	DET
ejpam-804	153	21	concept	concept	NOUN
ejpam-804	153	22	of	of	ADP
ejpam-804	153	23	cointegration	cointegration	NOUN
ejpam-804	153	24	to	to	ADP
ejpam-804	153	25	class	class	NOUN
ejpam-804	153	26	(	(	PUNCT
ejpam-804	153	27	kf	kf	NOUN
ejpam-804	153	28	)	)	PUNCT
ejpam-804	153	29	and	and	CCONJ
ejpam-804	153	30	strongly	strongly	ADV
ejpam-804	153	31	harmonizable	harmonizable	ADJ
ejpam-804	153	32	processes	process	NOUN
ejpam-804	153	33	3.1	3.1	NUM
ejpam-804	153	34	.	.	PUNCT
ejpam-804	154	1	generalization	generalization	NOUN
ejpam-804	154	2	1	1	NUM
ejpam-804	154	3	in	in	ADP
ejpam-804	154	4	this	this	DET
ejpam-804	154	5	section	section	NOUN
ejpam-804	154	6	we	we	PRON
ejpam-804	154	7	consider	consider	VERB
ejpam-804	154	8	the	the	DET
ejpam-804	154	9	case	case	NOUN
ejpam-804	154	10	where	where	SCONJ
ejpam-804	154	11	there	there	PRON
ejpam-804	154	12	exists	exist	VERB
ejpam-804	154	13	a	a	DET
ejpam-804	154	14	stationary	stationary	ADJ
ejpam-804	154	15	linear	linear	ADJ
ejpam-804	154	16	combination	combination	NOUN
ejpam-804	154	17	of	of	ADP
ejpam-804	154	18	class	class	NOUN
ejpam-804	154	19	(	(	PUNCT
ejpam-804	154	20	kf	kf	NOUN
ejpam-804	154	21	)	)	PUNCT
ejpam-804	154	22	processes	process	NOUN
ejpam-804	154	23	.	.	PUNCT
ejpam-804	155	1	this	this	PRON
ejpam-804	155	2	would	would	AUX
ejpam-804	155	3	be	be	AUX
ejpam-804	155	4	the	the	DET
ejpam-804	155	5	case	case	NOUN
ejpam-804	155	6	,	,	PUNCT
ejpam-804	155	7	for	for	ADP
ejpam-804	155	8	example	example	NOUN
ejpam-804	155	9	,	,	PUNCT
ejpam-804	155	10	of	of	ADP
ejpam-804	155	11	non	non	ADJ
ejpam-804	155	12	-	-	ADJ
ejpam-804	155	13	stationary	stationary	ADJ
ejpam-804	155	14	processes	process	NOUN
ejpam-804	155	15	generated	generate	VERB
ejpam-804	155	16	by	by	ADP
ejpam-804	155	17	nonlinear	nonlinear	ADJ
ejpam-804	155	18	systems	system	NOUN
ejpam-804	155	19	which	which	PRON
ejpam-804	155	20	co	co	VERB
ejpam-804	155	21	-	-	NOUN
ejpam-804	155	22	move	move	NOUN
ejpam-804	155	23	according	accord	VERB
ejpam-804	155	24	to	to	ADP
ejpam-804	155	25	a	a	DET
ejpam-804	155	26	linear	linear	ADJ
ejpam-804	155	27	adjustment	adjustment	NOUN
ejpam-804	155	28	process	process	NOUN
ejpam-804	155	29	.	.	PUNCT
ejpam-804	156	1	definition	definition	NOUN
ejpam-804	156	2	3	3	NUM
ejpam-804	156	3	.	.	PUNCT
ejpam-804	157	1	an	an	DET
ejpam-804	157	2	n	n	CCONJ
ejpam-804	157	3	-	-	PUNCT
ejpam-804	157	4	vector	vector	NOUN
ejpam-804	157	5	process	process	NOUN
ejpam-804	157	6	x	x	PUNCT
ejpam-804	157	7	t	t	NOUN
ejpam-804	157	8	of	of	ADP
ejpam-804	157	9	class	class	NOUN
ejpam-804	157	10	(	(	PUNCT
ejpam-804	157	11	kf	kf	PROPN
ejpam-804	157	12	)	)	PUNCT
ejpam-804	157	13	is	be	AUX
ejpam-804	157	14	said	say	VERB
ejpam-804	157	15	to	to	PART
ejpam-804	157	16	be	be	AUX
ejpam-804	157	17	cointegrated	cointegrate	VERB
ejpam-804	157	18	if	if	SCONJ
ejpam-804	157	19	there	there	PRON
ejpam-804	157	20	exists	exist	VERB
ejpam-804	157	21	a	a	DET
ejpam-804	157	22	linear	linear	ADJ
ejpam-804	157	23	combination	combination	NOUN
ejpam-804	157	24	of	of	ADP
ejpam-804	157	25	the	the	DET
ejpam-804	157	26	series	series	NOUN
ejpam-804	157	27	which	which	PRON
ejpam-804	157	28	is	be	AUX
ejpam-804	157	29	stationary	stationary	ADJ
ejpam-804	157	30	.	.	PUNCT
ejpam-804	158	1	this	this	PRON
ejpam-804	158	2	means	mean	VERB
ejpam-804	158	3	that	that	SCONJ
ejpam-804	158	4	there	there	PRON
ejpam-804	158	5	exists	exist	VERB
ejpam-804	158	6	β	β	NOUN
ejpam-804	158	7	6=	6=	ADP
ejpam-804	158	8	0	0	NUM
ejpam-804	158	9	such	such	ADJ
ejpam-804	158	10	that	that	SCONJ
ejpam-804	158	11	β	β	PROPN
ejpam-804	158	12	′x	′x	PROPN
ejpam-804	158	13	t	t	PROPN
ejpam-804	158	14	=	=	SYM
ejpam-804	158	15	ǫt	ǫt	PROPN
ejpam-804	158	16	where	where	SCONJ
ejpam-804	158	17	εt	εt	PROPN
ejpam-804	158	18	is	be	AUX
ejpam-804	158	19	stationary	stationary	ADJ
ejpam-804	158	20	.	.	PUNCT
ejpam-804	159	1	application	application	NOUN
ejpam-804	159	2	:	:	PUNCT
ejpam-804	159	3	slowly	slowly	ADV
ejpam-804	159	4	changing	change	VERB
ejpam-804	159	5	processes	process	NOUN
ejpam-804	159	6	let	let	VERB
ejpam-804	159	7	x	x	PROPN
ejpam-804	159	8	t	t	PROPN
ejpam-804	159	9	,	,	PUNCT
ejpam-804	159	10	t	t	PROPN
ejpam-804	159	11	integer	integer	NOUN
ejpam-804	159	12	,	,	PUNCT
ejpam-804	159	13	be	be	AUX
ejpam-804	159	14	a	a	DET
ejpam-804	159	15	second	second	ADJ
ejpam-804	159	16	order	order	NOUN
ejpam-804	159	17	n	n	CCONJ
ejpam-804	159	18	-	-	PUNCT
ejpam-804	159	19	vector	vector	NOUN
ejpam-804	159	20	process	process	NOUN
ejpam-804	159	21	such	such	ADJ
ejpam-804	159	22	that	that	SCONJ
ejpam-804	159	23	e(x	e(x	PROPN
ejpam-804	159	24	t	t	PROPN
ejpam-804	159	25	)	)	PUNCT
ejpam-804	159	26	=	=	SYM
ejpam-804	160	1	0	0	X
ejpam-804	160	2	.	.	PUNCT
ejpam-804	160	3	assume	assume	VERB
ejpam-804	160	4	that	that	SCONJ
ejpam-804	160	5	x	x	PRON
ejpam-804	160	6	j	j	PROPN
ejpam-804	160	7	t	t	PROPN
ejpam-804	160	8	,	,	PUNCT
ejpam-804	160	9	j	j	PROPN
ejpam-804	160	10	=	=	SYM
ejpam-804	160	11	1	1	NUM
ejpam-804	160	12	,	,	PUNCT
ejpam-804	160	13	.	.	PUNCT
ejpam-804	160	14	.	.	PUNCT
ejpam-804	161	1	.	.	PUNCT
ejpam-804	162	1	,	,	PUNCT
ejpam-804	162	2	n	n	CCONJ
ejpam-804	162	3	,	,	PUNCT
ejpam-804	162	4	can	can	AUX
ejpam-804	162	5	be	be	AUX
ejpam-804	162	6	represented	represent	VERB
ejpam-804	162	7	as	as	ADP
ejpam-804	162	8	:	:	PUNCT
ejpam-804	162	9	x	x	X
ejpam-804	162	10	j	j	PROPN
ejpam-804	162	11	t	t	PROPN
ejpam-804	163	1	=	=	SYM
ejpam-804	163	2	∫	∫	PROPN
ejpam-804	164	1	π	π	PROPN
ejpam-804	164	2	−π	−π	PROPN
ejpam-804	164	3	a	a	DET
ejpam-804	164	4	j	j	PROPN
ejpam-804	164	5	t(u)e	t(u)e	PROPN
ejpam-804	164	6	i	i	PRON
ejpam-804	164	7	tuz	tuz	PROPN
ejpam-804	164	8	j(du	j(du	PROPN
ejpam-804	164	9	)	)	PUNCT
ejpam-804	164	10	(	(	PUNCT
ejpam-804	164	11	13	13	NUM
ejpam-804	164	12	)	)	PUNCT
ejpam-804	164	13	where	where	SCONJ
ejpam-804	164	14	z	z	PROPN
ejpam-804	164	15	j	j	PROPN
ejpam-804	164	16	(	(	PUNCT
ejpam-804	164	17	·	·	PUNCT
ejpam-804	164	18	)	)	PUNCT
ejpam-804	164	19	is	be	AUX
ejpam-804	164	20	a	a	DET
ejpam-804	164	21	stochastic	stochastic	ADJ
ejpam-804	164	22	measure	measure	NOUN
ejpam-804	164	23	with	with	ADP
ejpam-804	164	24	orthogonal	orthogonal	ADJ
ejpam-804	164	25	increments	increment	NOUN
ejpam-804	164	26	:	:	PUNCT
ejpam-804	164	27	e	e	PROPN
ejpam-804	164	28	�	�	PROPN
ejpam-804	164	29	�	�	PROPN
ejpam-804	164	30	z	z	PROPN
ejpam-804	164	31	j(du	j(du	PROPN
ejpam-804	164	32	)	)	PUNCT
ejpam-804	164	33	�	�	PROPN
ejpam-804	164	34	�	�	PROPN
ejpam-804	164	35	2	2	NUM
ejpam-804	164	36	=	=	SYM
ejpam-804	164	37	µ	µ	PRON
ejpam-804	164	38	j(du	j(du	PROPN
ejpam-804	164	39	)	)	PUNCT
ejpam-804	164	40	,	,	PUNCT
ejpam-804	164	41	µ	µ	PROPN
ejpam-804	164	42	j	j	PROPN
ejpam-804	164	43	a	a	DET
ejpam-804	164	44	finite	finite	ADJ
ejpam-804	164	45	positive	positive	ADJ
ejpam-804	164	46	measure	measure	NOUN
ejpam-804	164	47	,	,	PUNCT
ejpam-804	164	48	e(zi(du)z̄	e(zi(du)z̄	NOUN
ejpam-804	164	49	j(dv	j(dv	NOUN
ejpam-804	164	50	)	)	PUNCT
ejpam-804	164	51	)	)	PUNCT
ejpam-804	165	1	=	=	SYM
ejpam-804	165	2	0	0	NUM
ejpam-804	165	3	,	,	PUNCT
ejpam-804	165	4	u	u	PROPN
ejpam-804	165	5	6=	6=	PROPN
ejpam-804	165	6	v	v	NOUN
ejpam-804	165	7	,	,	PUNCT
ejpam-804	165	8	e	e	PROPN
ejpam-804	165	9	�	�	PROPN
ejpam-804	165	10	zi(du)z̄	zi(du)z̄	PART
ejpam-804	165	11	j(du	j(du	PROPN
ejpam-804	165	12	)	)	PUNCT
ejpam-804	165	13	�	�	PROPN
ejpam-804	165	14	=	=	PUNCT
ejpam-804	165	15	µi	µi	PROPN
ejpam-804	165	16	j(du	j(du	PROPN
ejpam-804	165	17	)	)	PUNCT
ejpam-804	165	18	and	and	CCONJ
ejpam-804	165	19	a	a	DET
ejpam-804	165	20	j	j	NOUN
ejpam-804	165	21	t(u	t(u	NUM
ejpam-804	165	22	)	)	PUNCT
ejpam-804	165	23	=	=	SYM
ejpam-804	166	1	∫	∫	PROPN
ejpam-804	166	2	π	π	NOUN
ejpam-804	166	3	−π	−π	INTJ
ejpam-804	166	4	ei	ei	X
ejpam-804	166	5	t	t	PROPN
ejpam-804	166	6	x	x	PROPN
ejpam-804	166	7	h	h	PROPN
ejpam-804	166	8	j(u	j(u	PROPN
ejpam-804	166	9	,	,	PUNCT
ejpam-804	166	10	d	d	NOUN
ejpam-804	166	11	x	x	X
ejpam-804	166	12	)	)	PUNCT
ejpam-804	166	13	(	(	PUNCT
ejpam-804	166	14	14	14	NUM
ejpam-804	166	15	)	)	PUNCT
ejpam-804	166	16	finally	finally	ADV
ejpam-804	166	17	,	,	PUNCT
ejpam-804	166	18	it	it	PRON
ejpam-804	166	19	is	be	AUX
ejpam-804	166	20	assumed	assume	VERB
ejpam-804	166	21	that	that	SCONJ
ejpam-804	166	22	the	the	DET
ejpam-804	166	23	generalised	generalise	VERB
ejpam-804	166	24	fourier	fourier	NOUN
ejpam-804	166	25	transform	transform	NOUN
ejpam-804	166	26	of	of	ADP
ejpam-804	166	27	a	a	DET
ejpam-804	166	28	j	j	NOUN
ejpam-804	166	29	t(u	t(u	NUM
ejpam-804	166	30	)	)	PUNCT
ejpam-804	166	31	has	have	VERB
ejpam-804	166	32	an	an	DET
ejpam-804	166	33	absolute	absolute	ADJ
ejpam-804	166	34	maximum	maximum	NOUN
ejpam-804	166	35	at	at	ADP
ejpam-804	166	36	x	x	X
ejpam-804	166	37	=	=	SYM
ejpam-804	166	38	0	0	NUM
ejpam-804	166	39	independently	independently	ADV
ejpam-804	166	40	of	of	ADP
ejpam-804	166	41	u	u	NOUN
ejpam-804	166	42	,	,	PUNCT
ejpam-804	166	43	that	that	SCONJ
ejpam-804	166	44	h	h	NOUN
ejpam-804	166	45	j(·,a	j(·,a	NOUN
ejpam-804	166	46	)	)	PUNCT
ejpam-804	166	47	is	be	AUX
ejpam-804	166	48	a	a	DET
ejpam-804	166	49	borel	borel	NOUN
ejpam-804	166	50	function	function	NOUN
ejpam-804	166	51	and	and	CCONJ
ejpam-804	166	52	that	that	SCONJ
ejpam-804	166	53	h	h	PROPN
ejpam-804	166	54	j(u	j(u	PROPN
ejpam-804	166	55	,	,	PUNCT
ejpam-804	166	56	·	·	PUNCT
ejpam-804	166	57	)	)	PUNCT
ejpam-804	166	58	is	be	AUX
ejpam-804	166	59	a	a	DET
ejpam-804	166	60	signed	sign	VERB
ejpam-804	166	61	measure	measure	NOUN
ejpam-804	166	62	on	on	ADP
ejpam-804	166	63	the	the	DET
ejpam-804	166	64	borel	borel	NOUN
ejpam-804	166	65	sets	set	NOUN
ejpam-804	166	66	of	of	ADP
ejpam-804	166	67	[	[	X
ejpam-804	166	68	−π	−π	PROPN
ejpam-804	166	69	,	,	PUNCT
ejpam-804	166	70	π	π	NOUN
ejpam-804	166	71	]	]	X
ejpam-804	166	72	.	.	PUNCT
ejpam-804	167	1	then	then	ADV
ejpam-804	167	2	x	x	X
ejpam-804	167	3	j	j	PROPN
ejpam-804	167	4	t	t	PROPN
ejpam-804	167	5	is	be	AUX
ejpam-804	167	6	said	say	VERB
ejpam-804	167	7	to	to	PART
ejpam-804	167	8	be	be	AUX
ejpam-804	167	9	an	an	DET
ejpam-804	167	10	oscillatory	oscillatory	ADJ
ejpam-804	167	11	process	process	NOUN
ejpam-804	167	12	.	.	PUNCT
ejpam-804	168	1	thus	thus	ADV
ejpam-804	168	2	an	an	DET
ejpam-804	168	3	oscillatory	oscillatory	ADJ
ejpam-804	168	4	process	process	NOUN
ejpam-804	168	5	x	x	PUNCT
ejpam-804	168	6	j	j	PROPN
ejpam-804	168	7	t	t	PROPN
ejpam-804	168	8	is	be	AUX
ejpam-804	168	9	defined	define	VERB
ejpam-804	168	10	as	as	ADP
ejpam-804	168	11	the	the	DET
ejpam-804	168	12	output	output	NOUN
ejpam-804	168	13	of	of	ADP
ejpam-804	168	14	a	a	DET
ejpam-804	168	15	system	system	NOUN
ejpam-804	168	16	with	with	ADP
ejpam-804	168	17	stationary	stationary	ADJ
ejpam-804	168	18	input	input	NOUN
ejpam-804	168	19	process	process	NOUN
ejpam-804	168	20	v	v	ADP
ejpam-804	168	21	j	j	PROPN
ejpam-804	168	22	t	t	PROPN
ejpam-804	169	1	=	=	SYM
ejpam-804	169	2	∫	∫	PROPN
ejpam-804	170	1	π	π	NOUN
ejpam-804	170	2	−π	−π	INTJ
ejpam-804	170	3	ei	ei	PROPN
ejpam-804	170	4	tuz	tuz	PROPN
ejpam-804	170	5	j(du	j(du	PROPN
ejpam-804	170	6	)	)	PUNCT
ejpam-804	170	7	(	(	PUNCT
ejpam-804	170	8	15	15	NUM
ejpam-804	170	9	)	)	PUNCT
ejpam-804	170	10	and	and	CCONJ
ejpam-804	170	11	impulse	impulse	ADJ
ejpam-804	170	12	response	response	NOUN
ejpam-804	170	13	a	a	DET
ejpam-804	170	14	j	j	NOUN
ejpam-804	170	15	t(u	t(u	NUM
ejpam-804	170	16	)	)	PUNCT
ejpam-804	170	17	.	.	PUNCT
ejpam-804	171	1	this	this	PRON
ejpam-804	171	2	includes	include	VERB
ejpam-804	171	3	the	the	DET
ejpam-804	171	4	case	case	NOUN
ejpam-804	171	5	where	where	SCONJ
ejpam-804	171	6	the	the	DET
ejpam-804	171	7	amplitudes	amplitude	NOUN
ejpam-804	171	8	of	of	ADP
ejpam-804	171	9	different	different	ADJ
ejpam-804	171	10	frequency	frequency	NOUN
ejpam-804	171	11	bands	band	NOUN
ejpam-804	171	12	do	do	AUX
ejpam-804	171	13	not	not	PART
ejpam-804	171	14	change	change	VERB
ejpam-804	171	15	at	at	ADP
ejpam-804	171	16	the	the	DET
ejpam-804	171	17	same	same	ADJ
ejpam-804	171	18	rate	rate	NOUN
ejpam-804	171	19	.	.	PUNCT
ejpam-804	172	1	if	if	SCONJ
ejpam-804	172	2	we	we	PRON
ejpam-804	172	3	want	want	VERB
ejpam-804	172	4	a	a	DET
ejpam-804	172	5	j	j	NOUN
ejpam-804	172	6	t(u	t(u	PROPN
ejpam-804	172	7	)	)	PUNCT
ejpam-804	172	8	to	to	PART
ejpam-804	172	9	be	be	AUX
ejpam-804	172	10	slowly	slowly	ADV
ejpam-804	172	11	changing	change	VERB
ejpam-804	172	12	with	with	ADP
ejpam-804	172	13	time	time	NOUN
ejpam-804	172	14	the	the	DET
ejpam-804	172	15	fourier	fourier	ADJ
ejpam-804	172	16	-	-	PUNCT
ejpam-804	172	17	stieltjes	stieltjes	NOUN
ejpam-804	172	18	transform	transform	NOUN
ejpam-804	172	19	of	of	ADP
ejpam-804	172	20	a	a	DET
ejpam-804	172	21	j	j	NOUN
ejpam-804	172	22	t(u	t(u	NUM
ejpam-804	172	23	)	)	PUNCT
ejpam-804	172	24	has	have	VERB
ejpam-804	172	25	to	to	PART
ejpam-804	172	26	be	be	AUX
ejpam-804	172	27	highly	highly	ADV
ejpam-804	172	28	concentrated	concentrate	VERB
ejpam-804	172	29	around	around	ADP
ejpam-804	172	30	zero	zero	NUM
ejpam-804	172	31	,	,	PUNCT
ejpam-804	172	32	and	and	CCONJ
ejpam-804	172	33	the	the	DET
ejpam-804	172	34	measure	measure	NOUN
ejpam-804	172	35	of	of	ADP
ejpam-804	172	36	the	the	DET
ejpam-804	172	37	concentration	concentration	NOUN
ejpam-804	172	38	should	should	AUX
ejpam-804	172	39	be	be	AUX
ejpam-804	172	40	small	small	ADJ
ejpam-804	172	41	.	.	PUNCT
ejpam-804	173	1	if	if	SCONJ
ejpam-804	173	2	,	,	PUNCT
ejpam-804	173	3	moreover	moreover	ADV
ejpam-804	173	4	,	,	PUNCT
ejpam-804	173	5	b	b	PROPN
ejpam-804	173	6	j(u	j(u	PROPN
ejpam-804	173	7	)	)	PUNCT
ejpam-804	173	8	=	=	PUNCT
ejpam-804	174	1	∫	∫	PROPN
ejpam-804	174	2	π	π	PROPN
ejpam-804	174	3	−π	−π	PROPN
ejpam-804	174	4	|x	|x	PROPN
ejpam-804	174	5	|	|	PROPN
ejpam-804	174	6	�	�	PROPN
ejpam-804	174	7	�	�	PROPN
ejpam-804	174	8	h	h	PROPN
ejpam-804	174	9	j(u	j(u	PROPN
ejpam-804	174	10	,	,	PUNCT
ejpam-804	174	11	d	d	NOUN
ejpam-804	174	12	x	x	X
ejpam-804	174	13	)	)	PUNCT
ejpam-804	174	14	�	�	PROPN
ejpam-804	174	15	�	�	PROPN
ejpam-804	174	16	≤	≤	PROPN
ejpam-804	174	17	ǫ	ǫ	NOUN
ejpam-804	174	18	,	,	PUNCT
ejpam-804	174	19	∀u	∀u	NOUN
ejpam-804	174	20	∈	∈	NOUN
ejpam-804	174	21	[	[	X
ejpam-804	174	22	−π	−π	PROPN
ejpam-804	174	23	,	,	PUNCT
ejpam-804	174	24	π	π	X
ejpam-804	174	25	]	]	X
ejpam-804	174	26	(	(	PUNCT
ejpam-804	174	27	16	16	NUM
ejpam-804	174	28	)	)	PUNCT
ejpam-804	174	29	r.	r.	PROPN
ejpam-804	174	30	joyeux	joyeux	PROPN
ejpam-804	174	31	/	/	SYM
ejpam-804	174	32	eur	eur	PROPN
ejpam-804	174	33	.	.	PUNCT
ejpam-804	175	1	j.	j.	PROPN
ejpam-804	175	2	pure	pure	PROPN
ejpam-804	175	3	appl	appl	PROPN
ejpam-804	175	4	.	.	PROPN
ejpam-804	175	5	math	math	PROPN
ejpam-804	175	6	,	,	PUNCT
ejpam-804	175	7	3	3	NUM
ejpam-804	175	8	(	(	PUNCT
ejpam-804	175	9	2010	2010	NUM
ejpam-804	175	10	)	)	PUNCT
ejpam-804	175	11	,	,	PUNCT
ejpam-804	175	12	519	519	NUM
ejpam-804	175	13	-	-	SYM
ejpam-804	175	14	530	530	NUM
ejpam-804	175	15	526	526	NUM
ejpam-804	175	16	a	a	DET
ejpam-804	175	17	j	j	NOUN
ejpam-804	175	18	t(u	t(u	NUM
ejpam-804	175	19	)	)	PUNCT
ejpam-804	175	20	is	be	AUX
ejpam-804	175	21	said	say	VERB
ejpam-804	175	22	to	to	PART
ejpam-804	175	23	be	be	AUX
ejpam-804	175	24	ε	ε	PROPN
ejpam-804	175	25	-	-	PUNCT
ejpam-804	175	26	slowly	slowly	ADV
ejpam-804	175	27	changing	change	VERB
ejpam-804	175	28	.	.	PUNCT
ejpam-804	176	1	a	a	DET
ejpam-804	176	2	slowly	slowly	ADV
ejpam-804	176	3	changing	change	VERB
ejpam-804	176	4	process	process	NOUN
ejpam-804	176	5	x	x	PUNCT
ejpam-804	176	6	j	j	PROPN
ejpam-804	176	7	t	t	PROPN
ejpam-804	176	8	is	be	AUX
ejpam-804	176	9	non	non	ADJ
ejpam-804	176	10	-	-	ADJ
ejpam-804	176	11	stationary	stationary	ADJ
ejpam-804	176	12	,	,	PUNCT
ejpam-804	176	13	and	and	CCONJ
ejpam-804	176	14	we	we	PRON
ejpam-804	176	15	can	can	AUX
ejpam-804	176	16	think	think	VERB
ejpam-804	176	17	of	of	ADP
ejpam-804	176	18	its	its	PRON
ejpam-804	176	19	spectrum	spectrum	NOUN
ejpam-804	176	20	as	as	ADP
ejpam-804	176	21	continuously	continuously	ADV
ejpam-804	176	22	changing	change	VERB
ejpam-804	176	23	.	.	PUNCT
ejpam-804	177	1	its	its	PRON
ejpam-804	177	2	spectrum	spectrum	NOUN
ejpam-804	177	3	,	,	PUNCT
ejpam-804	177	4	however	however	ADV
ejpam-804	177	5	,	,	PUNCT
ejpam-804	177	6	is	be	AUX
ejpam-804	177	7	changing	change	VERB
ejpam-804	177	8	slowly	slowly	ADV
ejpam-804	177	9	over	over	ADP
ejpam-804	177	10	time	time	NOUN
ejpam-804	177	11	.	.	PUNCT
ejpam-804	178	1	priestley	priestley	NOUN
ejpam-804	178	2	[	[	X
ejpam-804	178	3	23	23	NUM
ejpam-804	178	4	]	]	PUNCT
ejpam-804	178	5	shows	show	VERB
ejpam-804	178	6	that	that	SCONJ
ejpam-804	178	7	it	it	PRON
ejpam-804	178	8	is	be	AUX
ejpam-804	178	9	possible	possible	ADJ
ejpam-804	178	10	to	to	PART
ejpam-804	178	11	define	define	VERB
ejpam-804	178	12	a	a	DET
ejpam-804	178	13	spectral	spectral	ADJ
ejpam-804	178	14	measure	measure	NOUN
ejpam-804	178	15	for	for	ADP
ejpam-804	178	16	such	such	DET
ejpam-804	178	17	a	a	DET
ejpam-804	178	18	process	process	NOUN
ejpam-804	178	19	,	,	PUNCT
ejpam-804	178	20	which	which	PRON
ejpam-804	178	21	he	he	PRON
ejpam-804	178	22	calls	call	VERB
ejpam-804	178	23	the	the	DET
ejpam-804	178	24	evolutionary	evolutionary	ADJ
ejpam-804	178	25	spectrum	spectrum	NOUN
ejpam-804	178	26	.	.	PUNCT
ejpam-804	179	1	let	let	VERB
ejpam-804	179	2	f	f	PROPN
ejpam-804	179	3	j(du	j(du	PROPN
ejpam-804	179	4	)	)	PUNCT
ejpam-804	180	1	=	=	SYM
ejpam-804	180	2	e	e	PROPN
ejpam-804	180	3	�	�	PROPN
ejpam-804	180	4	�	�	PROPN
ejpam-804	180	5	z	z	PROPN
ejpam-804	180	6	j(du	j(du	PROPN
ejpam-804	180	7	)	)	PUNCT
ejpam-804	180	8	�	�	PROPN
ejpam-804	180	9	�	�	PROPN
ejpam-804	180	10	2	2	NUM
ejpam-804	180	11	,	,	PUNCT
ejpam-804	180	12	the	the	DET
ejpam-804	180	13	evolutionary	evolutionary	ADJ
ejpam-804	180	14	power	power	NOUN
ejpam-804	180	15	spectrum	spectrum	NOUN
ejpam-804	180	16	is	be	AUX
ejpam-804	180	17	:	:	PUNCT
ejpam-804	180	18	f	f	PROPN
ejpam-804	180	19	j	j	PROPN
ejpam-804	180	20	t(du	t(du	PROPN
ejpam-804	180	21	)	)	PUNCT
ejpam-804	180	22	=	=	SYM
ejpam-804	180	23	�	�	PROPN
ejpam-804	180	24	�	�	PROPN
ejpam-804	180	25	a	a	DET
ejpam-804	180	26	j	j	NOUN
ejpam-804	180	27	t(u	t(u	PROPN
ejpam-804	180	28	)	)	PUNCT
ejpam-804	180	29	�	�	PROPN
ejpam-804	180	30	�	�	PROPN
ejpam-804	180	31	2	2	NUM
ejpam-804	180	32	f	f	PROPN
ejpam-804	180	33	j(du	j(du	PROPN
ejpam-804	180	34	)	)	PUNCT
ejpam-804	180	35	(	(	PUNCT
ejpam-804	180	36	17	17	NUM
ejpam-804	180	37	)	)	PUNCT
ejpam-804	180	38	note	note	NOUN
ejpam-804	180	39	that	that	SCONJ
ejpam-804	180	40	e(x	e(x	NUM
ejpam-804	180	41	2	2	NUM
ejpam-804	180	42	j	j	PROPN
ejpam-804	180	43	t	t	PROPN
ejpam-804	180	44	)	)	PUNCT
ejpam-804	180	45	=	=	SYM
ejpam-804	181	1	∫	∫	PROPN
ejpam-804	182	1	π	π	NOUN
ejpam-804	182	2	−π	−π	PROPN
ejpam-804	182	3	f	f	PROPN
ejpam-804	182	4	j	j	PROPN
ejpam-804	182	5	t	t	PROPN
ejpam-804	182	6	(	(	PUNCT
ejpam-804	182	7	du	du	PROPN
ejpam-804	182	8	)	)	PUNCT
ejpam-804	182	9	,	,	PUNCT
ejpam-804	182	10	which	which	PRON
ejpam-804	182	11	implies	imply	VERB
ejpam-804	182	12	that	that	SCONJ
ejpam-804	182	13	f	f	PROPN
ejpam-804	182	14	j	j	PROPN
ejpam-804	182	15	t	t	PROPN
ejpam-804	182	16	(	(	PUNCT
ejpam-804	182	17	du	du	PROPN
ejpam-804	182	18	)	)	PUNCT
ejpam-804	182	19	describes	describe	VERB
ejpam-804	182	20	a	a	DET
ejpam-804	182	21	frequency	frequency	NOUN
ejpam-804	182	22	decomposition	decomposition	NOUN
ejpam-804	182	23	of	of	ADP
ejpam-804	182	24	the	the	DET
ejpam-804	182	25	“	"	PUNCT
ejpam-804	182	26	total	total	ADJ
ejpam-804	182	27	energy	energy	NOUN
ejpam-804	182	28	”	"	PUNCT
ejpam-804	182	29	of	of	ADP
ejpam-804	182	30	the	the	DET
ejpam-804	182	31	process	process	NOUN
ejpam-804	182	32	.	.	PUNCT
ejpam-804	183	1	when	when	SCONJ
ejpam-804	183	2	f	f	PROPN
ejpam-804	183	3	j(u	j(u	PROPN
ejpam-804	183	4	)	)	PUNCT
ejpam-804	183	5	is	be	AUX
ejpam-804	183	6	differentiable	differentiable	ADJ
ejpam-804	183	7	,	,	PUNCT
ejpam-804	183	8	f	f	PROPN
ejpam-804	183	9	j(u	j(u	PROPN
ejpam-804	183	10	)	)	PUNCT
ejpam-804	184	1	=	=	SYM
ejpam-804	184	2	f	f	PROPN
ejpam-804	184	3	′j	′j	NOUN
ejpam-804	184	4	(	(	PUNCT
ejpam-804	184	5	u	u	NOUN
ejpam-804	184	6	)	)	PUNCT
ejpam-804	184	7	is	be	AUX
ejpam-804	184	8	the	the	DET
ejpam-804	184	9	spectral	spectral	ADJ
ejpam-804	184	10	density	density	NOUN
ejpam-804	184	11	function	function	NOUN
ejpam-804	184	12	of	of	ADP
ejpam-804	184	13	v	v	PROPN
ejpam-804	184	14	j	j	PROPN
ejpam-804	184	15	t	t	PROPN
ejpam-804	185	1	and	and	CCONJ
ejpam-804	185	2	we	we	PRON
ejpam-804	185	3	define	define	VERB
ejpam-804	185	4	the	the	DET
ejpam-804	185	5	evolutionary	evolutionary	ADJ
ejpam-804	185	6	spectral	spectral	ADJ
ejpam-804	185	7	density	density	NOUN
ejpam-804	185	8	function	function	NOUN
ejpam-804	185	9	as	as	ADP
ejpam-804	185	10	:	:	PUNCT
ejpam-804	185	11	f	f	PROPN
ejpam-804	185	12	j	j	PROPN
ejpam-804	185	13	t(u	t(u	PROPN
ejpam-804	185	14	)	)	PUNCT
ejpam-804	186	1	=	=	SYM
ejpam-804	186	2	�	�	PROPN
ejpam-804	186	3	�	�	PROPN
ejpam-804	186	4	a	a	DET
ejpam-804	186	5	j	j	NOUN
ejpam-804	186	6	t(u	t(u	PROPN
ejpam-804	186	7	)	)	PUNCT
ejpam-804	186	8	�	�	PROPN
ejpam-804	186	9	�	�	PROPN
ejpam-804	186	10	2	2	NUM
ejpam-804	186	11	f	f	PROPN
ejpam-804	186	12	j(u	j(u	PROPN
ejpam-804	186	13	)	)	PUNCT
ejpam-804	186	14	.	.	PUNCT
ejpam-804	187	1	b	b	X
ejpam-804	187	2	j(u	j(u	PROPN
ejpam-804	187	3	)	)	PUNCT
ejpam-804	187	4	is	be	AUX
ejpam-804	187	5	a	a	DET
ejpam-804	187	6	measure	measure	NOUN
ejpam-804	187	7	of	of	ADP
ejpam-804	187	8	the	the	DET
ejpam-804	187	9	concentration	concentration	NOUN
ejpam-804	187	10	of	of	ADP
ejpam-804	187	11	h	h	PROPN
ejpam-804	187	12	j(u	j(u	PROPN
ejpam-804	187	13	,	,	PUNCT
ejpam-804	187	14	d	d	NOUN
ejpam-804	187	15	x	x	NOUN
ejpam-804	187	16	)	)	PUNCT
ejpam-804	187	17	about	about	ADP
ejpam-804	187	18	zero	zero	NUM
ejpam-804	187	19	and	and	CCONJ
ejpam-804	187	20	thus	thus	ADV
ejpam-804	187	21	is	be	AUX
ejpam-804	187	22	also	also	ADV
ejpam-804	187	23	a	a	DET
ejpam-804	187	24	measure	measure	NOUN
ejpam-804	187	25	of	of	ADP
ejpam-804	187	26	the	the	DET
ejpam-804	187	27	rate	rate	NOUN
ejpam-804	187	28	at	at	ADP
ejpam-804	187	29	which	which	PRON
ejpam-804	187	30	a	a	DET
ejpam-804	187	31	j	j	NOUN
ejpam-804	187	32	t(u	t(u	NUM
ejpam-804	187	33	)	)	PUNCT
ejpam-804	187	34	is	be	AUX
ejpam-804	187	35	changing	change	VERB
ejpam-804	187	36	.	.	PUNCT
ejpam-804	188	1	it	it	PRON
ejpam-804	188	2	is	be	AUX
ejpam-804	188	3	shown	show	VERB
ejpam-804	188	4	in	in	ADP
ejpam-804	188	5	[	[	X
ejpam-804	188	6	15	15	NUM
ejpam-804	188	7	]	]	PUNCT
ejpam-804	188	8	that	that	SCONJ
ejpam-804	188	9	oscillatory	oscillatory	ADJ
ejpam-804	188	10	sequences	sequence	NOUN
ejpam-804	188	11	are	be	AUX
ejpam-804	188	12	strongly	strongly	ADV
ejpam-804	188	13	harmonizable	harmonizable	ADJ
ejpam-804	188	14	.	.	PUNCT
ejpam-804	189	1	it	it	PRON
ejpam-804	189	2	is	be	AUX
ejpam-804	189	3	also	also	ADV
ejpam-804	189	4	shown	show	VERB
ejpam-804	189	5	that	that	SCONJ
ejpam-804	189	6	the	the	DET
ejpam-804	189	7	distribution	distribution	NOUN
ejpam-804	189	8	of	of	ADP
ejpam-804	189	9	masses	masse	NOUN
ejpam-804	189	10	f(du	f(du	NOUN
ejpam-804	189	11	,	,	PUNCT
ejpam-804	189	12	dv	dv	PROPN
ejpam-804	189	13	)	)	PUNCT
ejpam-804	189	14	for	for	ADP
ejpam-804	189	15	an	an	DET
ejpam-804	189	16	ε	ε	VERB
ejpam-804	189	17	-	-	PUNCT
ejpam-804	189	18	slowly	slowly	ADV
ejpam-804	189	19	changing	change	VERB
ejpam-804	189	20	process	process	NOUN
ejpam-804	189	21	has	have	VERB
ejpam-804	189	22	to	to	PART
ejpam-804	189	23	be	be	AUX
ejpam-804	189	24	concentrated	concentrate	VERB
ejpam-804	189	25	on	on	ADP
ejpam-804	189	26	a	a	DET
ejpam-804	189	27	band	band	NOUN
ejpam-804	189	28	along	along	ADP
ejpam-804	189	29	the	the	DET
ejpam-804	189	30	bisector	bisector	NOUN
ejpam-804	189	31	whose	whose	DET
ejpam-804	189	32	width	width	NOUN
ejpam-804	189	33	is	be	AUX
ejpam-804	189	34	determined	determine	VERB
ejpam-804	189	35	by	by	ADP
ejpam-804	189	36	ε	ε	PROPN
ejpam-804	189	37	.	.	PUNCT
ejpam-804	189	38	long	long	ADJ
ejpam-804	189	39	run	run	NOUN
ejpam-804	189	40	relationships	relationship	NOUN
ejpam-804	189	41	between	between	ADP
ejpam-804	189	42	slowly	slowly	ADV
ejpam-804	189	43	changing	change	VERB
ejpam-804	189	44	processes	process	NOUN
ejpam-804	189	45	:	:	PUNCT
ejpam-804	189	46	priestley	priestley	NOUN
ejpam-804	189	47	and	and	CCONJ
ejpam-804	189	48	tong	tong	PROPN
ejpam-804	189	49	[	[	X
ejpam-804	189	50	24	24	NUM
ejpam-804	189	51	]	]	PUNCT
ejpam-804	189	52	consider	consider	VERB
ejpam-804	189	53	the	the	DET
ejpam-804	189	54	cross	cross	NOUN
ejpam-804	189	55	-	-	NOUN
ejpam-804	189	56	spectrum	spectrum	NOUN
ejpam-804	189	57	between	between	ADP
ejpam-804	189	58	slowly	slowly	ADV
ejpam-804	189	59	changing	change	VERB
ejpam-804	189	60	processes	process	NOUN
ejpam-804	189	61	.	.	PUNCT
ejpam-804	190	1	in	in	ADP
ejpam-804	190	2	the	the	DET
ejpam-804	190	3	case	case	NOUN
ejpam-804	190	4	where	where	SCONJ
ejpam-804	190	5	n=	n=	ADJ
ejpam-804	190	6	2	2	NUM
ejpam-804	190	7	they	they	PRON
ejpam-804	190	8	define	define	VERB
ejpam-804	190	9	the	the	DET
ejpam-804	190	10	evolutionary	evolutionary	ADJ
ejpam-804	190	11	power	power	PROPN
ejpam-804	190	12	cross	cross	PROPN
ejpam-804	190	13	spectrum	spectrum	NOUN
ejpam-804	190	14	at	at	ADP
ejpam-804	190	15	time	time	NOUN
ejpam-804	190	16	t	t	PROPN
ejpam-804	190	17	by	by	ADP
ejpam-804	190	18	:	:	PUNCT
ejpam-804	190	19	f12,t	f12,t	X
ejpam-804	190	20	(	(	PUNCT
ejpam-804	190	21	du=	du=	PROPN
ejpam-804	190	22	a1t(u)ā2t(u)e	a1t(u)ā2t(u)e	NUM
ejpam-804	190	23	�	�	PROPN
ejpam-804	190	24	z1(du)z̄2(du	z1(du)z̄2(du	NOUN
ejpam-804	190	25	)	)	PUNCT
ejpam-804	190	26	�	�	PROPN
ejpam-804	190	27	=	=	SYM
ejpam-804	190	28	a1t(u)ā2t(u)µ12(du	a1t(u)ā2t(u)µ12(du	NOUN
ejpam-804	190	29	)	)	PUNCT
ejpam-804	190	30	(	(	PUNCT
ejpam-804	190	31	18	18	NUM
ejpam-804	190	32	)	)	PUNCT
ejpam-804	190	33	f12,t	f12,t	X
ejpam-804	190	34	(	(	PUNCT
ejpam-804	190	35	du	du	NOUN
ejpam-804	190	36	)	)	PUNCT
ejpam-804	190	37	can	can	AUX
ejpam-804	190	38	be	be	AUX
ejpam-804	190	39	given	give	VERB
ejpam-804	190	40	a	a	DET
ejpam-804	190	41	physical	physical	ADJ
ejpam-804	190	42	interpretation	interpretation	NOUN
ejpam-804	190	43	similar	similar	ADJ
ejpam-804	190	44	to	to	ADP
ejpam-804	190	45	that	that	PRON
ejpam-804	190	46	of	of	ADP
ejpam-804	190	47	the	the	DET
ejpam-804	190	48	cross	cross	NOUN
ejpam-804	190	49	-	-	NOUN
ejpam-804	190	50	spectrum	spectrum	NOUN
ejpam-804	190	51	of	of	ADP
ejpam-804	190	52	a	a	DET
ejpam-804	190	53	bivariate	bivariate	ADJ
ejpam-804	190	54	stationary	stationary	ADJ
ejpam-804	190	55	process	process	NOUN
ejpam-804	190	56	:	:	PUNCT
ejpam-804	190	57	it	it	PRON
ejpam-804	190	58	represents	represent	VERB
ejpam-804	190	59	the	the	DET
ejpam-804	190	60	average	average	ADJ
ejpam-804	190	61	value	value	NOUN
ejpam-804	190	62	of	of	ADP
ejpam-804	190	63	the	the	DET
ejpam-804	190	64	product	product	NOUN
ejpam-804	190	65	of	of	ADP
ejpam-804	190	66	the	the	DET
ejpam-804	190	67	amplitudes	amplitude	NOUN
ejpam-804	190	68	of	of	ADP
ejpam-804	190	69	the	the	DET
ejpam-804	190	70	corresponding	corresponding	ADJ
ejpam-804	190	71	frequency	frequency	NOUN
ejpam-804	190	72	component	component	NOUN
ejpam-804	190	73	in	in	ADP
ejpam-804	190	74	the	the	DET
ejpam-804	190	75	two	two	NUM
ejpam-804	190	76	processes	process	NOUN
ejpam-804	190	77	x1	x1	PROPN
ejpam-804	190	78	t	t	NOUN
ejpam-804	190	79	and	and	CCONJ
ejpam-804	190	80	x2	x2	PROPN
ejpam-804	190	81	t	t	PROPN
ejpam-804	190	82	.	.	PUNCT
ejpam-804	191	1	since	since	SCONJ
ejpam-804	191	2	those	those	DET
ejpam-804	191	3	processes	process	NOUN
ejpam-804	191	4	are	be	AUX
ejpam-804	191	5	nonstationary	nonstationary	ADJ
ejpam-804	191	6	the	the	DET
ejpam-804	191	7	cross	cross	NOUN
ejpam-804	191	8	-	-	ADJ
ejpam-804	191	9	spectrum	spectrum	NOUN
ejpam-804	191	10	is	be	AUX
ejpam-804	191	11	time	time	NOUN
ejpam-804	191	12	dependent	dependent	ADJ
ejpam-804	191	13	.	.	PUNCT
ejpam-804	192	1	if	if	SCONJ
ejpam-804	192	2	the	the	DET
ejpam-804	192	3	measure	measure	NOUN
ejpam-804	192	4	µ12(du	µ12(du	NOUN
ejpam-804	192	5	)	)	PUNCT
ejpam-804	192	6	is	be	AUX
ejpam-804	192	7	absolutely	absolutely	ADV
ejpam-804	192	8	continuous	continuous	ADJ
ejpam-804	192	9	with	with	ADP
ejpam-804	192	10	respect	respect	NOUN
ejpam-804	192	11	to	to	ADP
ejpam-804	192	12	the	the	DET
ejpam-804	192	13	lebesgue	lebesgue	ADJ
ejpam-804	192	14	measure	measure	NOUN
ejpam-804	192	15	we	we	PRON
ejpam-804	192	16	have	have	VERB
ejpam-804	192	17	:	:	PUNCT
ejpam-804	192	18	f12,t	f12,t	X
ejpam-804	192	19	(	(	PUNCT
ejpam-804	192	20	du	du	X
ejpam-804	192	21	)	)	PUNCT
ejpam-804	192	22	=	=	SYM
ejpam-804	192	23	f12,t	f12,t	X
ejpam-804	192	24	(	(	PUNCT
ejpam-804	192	25	u)du	u)du	PROPN
ejpam-804	192	26	(	(	PUNCT
ejpam-804	192	27	19	19	NUM
ejpam-804	192	28	)	)	PUNCT
ejpam-804	192	29	where	where	SCONJ
ejpam-804	192	30	f12,t	f12,t	X
ejpam-804	192	31	(	(	PUNCT
ejpam-804	192	32	u	u	NOUN
ejpam-804	192	33	)	)	PUNCT
ejpam-804	192	34	is	be	AUX
ejpam-804	192	35	the	the	DET
ejpam-804	192	36	evolutionary	evolutionary	ADJ
ejpam-804	192	37	cross	cross	ADJ
ejpam-804	192	38	-	-	ADJ
ejpam-804	192	39	spectral	spectral	ADJ
ejpam-804	192	40	density	density	NOUN
ejpam-804	192	41	function	function	NOUN
ejpam-804	192	42	.	.	PUNCT
ejpam-804	193	1	if	if	SCONJ
ejpam-804	193	2	µ1(du	µ1(du	NOUN
ejpam-804	193	3	)	)	PUNCT
ejpam-804	193	4	and	and	CCONJ
ejpam-804	193	5	µ2(du	µ2(du	NUM
ejpam-804	193	6	)	)	PUNCT
ejpam-804	193	7	are	be	AUX
ejpam-804	193	8	absolutely	absolutely	ADV
ejpam-804	193	9	continuous	continuous	ADJ
ejpam-804	193	10	the	the	DET
ejpam-804	193	11	coherency	coherency	NOUN
ejpam-804	193	12	between	between	ADP
ejpam-804	193	13	x1	x1	PROPN
ejpam-804	193	14	t	t	PROPN
ejpam-804	193	15	and	and	CCONJ
ejpam-804	193	16	x2	x2	PROPN
ejpam-804	193	17	t	t	PROPN
ejpam-804	193	18	can	can	AUX
ejpam-804	193	19	be	be	AUX
ejpam-804	193	20	defined	define	VERB
ejpam-804	193	21	as	as	ADP
ejpam-804	193	22	:	:	PUNCT
ejpam-804	193	23	w12(u	w12(u	X
ejpam-804	193	24	)	)	PUNCT
ejpam-804	194	1	=	=	SYM
ejpam-804	194	2	�	�	PROPN
ejpam-804	194	3	�	�	PROPN
ejpam-804	194	4	f12,t(u	f12,t(u	PROPN
ejpam-804	194	5	)	)	PUNCT
ejpam-804	194	6	�	�	PROPN
ejpam-804	194	7	�	�	PROPN
ejpam-804	194	8	¦	¦	PROPN
ejpam-804	194	9	f1,t(u	f1,t(u	PROPN
ejpam-804	194	10	)	)	PUNCT
ejpam-804	194	11	f2,t(u	f2,t(u	CCONJ
ejpam-804	194	12	)	)	PUNCT
ejpam-804	194	13	©	©	PROPN
ejpam-804	194	14	1/2	1/2	NUM
ejpam-804	194	15	=	=	SYM
ejpam-804	194	16	�	�	PROPN
ejpam-804	194	17	�	�	PROPN
ejpam-804	194	18	e	e	PROPN
ejpam-804	194	19	�	�	PROPN
ejpam-804	194	20	z1(du)z̄2(du	z1(du)z̄2(du	NOUN
ejpam-804	194	21	)	)	PUNCT
ejpam-804	194	22	�	�	PROPN
ejpam-804	194	23	�	�	PROPN
ejpam-804	194	24	�	�	PROPN
ejpam-804	194	25	n	n	CCONJ
ejpam-804	194	26	e	e	PROPN
ejpam-804	194	27	�	�	PROPN
ejpam-804	194	28	�	�	PROPN
ejpam-804	194	29	z1(du	z1(du	NUM
ejpam-804	194	30	)	)	PUNCT
ejpam-804	194	31	�	�	PROPN
ejpam-804	194	32	�	�	PROPN
ejpam-804	194	33	2	2	NUM
ejpam-804	194	34	e	e	PROPN
ejpam-804	194	35	�	�	PROPN
ejpam-804	194	36	�	�	PROPN
ejpam-804	194	37	z2(du	z2(du	PROPN
ejpam-804	194	38	)	)	PUNCT
ejpam-804	194	39	�	�	PROPN
ejpam-804	194	40	�	�	PROPN
ejpam-804	194	41	2	2	NUM
ejpam-804	194	42	o1/2	o1/2	ADJ
ejpam-804	194	43	(	(	PUNCT
ejpam-804	194	44	20	20	NUM
ejpam-804	194	45	)	)	PUNCT
ejpam-804	194	46	w12(u	w12(u	NUM
ejpam-804	194	47	)	)	PUNCT
ejpam-804	194	48	is	be	AUX
ejpam-804	194	49	independent	independent	ADJ
ejpam-804	194	50	of	of	ADP
ejpam-804	194	51	time	time	NOUN
ejpam-804	194	52	and	and	CCONJ
ejpam-804	194	53	can	can	AUX
ejpam-804	194	54	be	be	AUX
ejpam-804	194	55	interpreted	interpret	VERB
ejpam-804	194	56	as	as	ADP
ejpam-804	194	57	the	the	DET
ejpam-804	194	58	modulus	modulus	NOUN
ejpam-804	194	59	of	of	ADP
ejpam-804	194	60	the	the	DET
ejpam-804	194	61	correlation	correlation	NOUN
ejpam-804	194	62	coefficient	coefficient	NOUN
ejpam-804	194	63	between	between	ADP
ejpam-804	194	64	z1(du	z1(du	NUM
ejpam-804	194	65	)	)	PUNCT
ejpam-804	194	66	and	and	CCONJ
ejpam-804	194	67	z2(du	z2(du	NOUN
ejpam-804	194	68	)	)	PUNCT
ejpam-804	194	69	.	.	PUNCT
ejpam-804	195	1	w12(u	w12(u	X
ejpam-804	195	2	)	)	PUNCT
ejpam-804	195	3	can	can	AUX
ejpam-804	195	4	also	also	ADV
ejpam-804	195	5	be	be	AUX
ejpam-804	195	6	interpreted	interpret	VERB
ejpam-804	195	7	as	as	ADP
ejpam-804	195	8	a	a	DET
ejpam-804	195	9	measure	measure	NOUN
ejpam-804	195	10	of	of	ADP
ejpam-804	195	11	the	the	DET
ejpam-804	195	12	linear	linear	ADJ
ejpam-804	195	13	relationship	relationship	NOUN
ejpam-804	195	14	between	between	ADP
ejpam-804	195	15	the	the	DET
ejpam-804	195	16	corresponding	correspond	VERB
ejpam-804	195	17	components	component	NOUN
ejpam-804	195	18	of	of	ADP
ejpam-804	195	19	x1	x1	PROPN
ejpam-804	195	20	t	t	PROPN
ejpam-804	195	21	and	and	CCONJ
ejpam-804	195	22	x2	x2	PROPN
ejpam-804	195	23	t	t	PROPN
ejpam-804	195	24	at	at	ADP
ejpam-804	195	25	frequency	frequency	NOUN
ejpam-804	195	26	u.	u.	NOUN
ejpam-804	196	1	this	this	DET
ejpam-804	196	2	result	result	NOUN
ejpam-804	196	3	generalises	generalise	VERB
ejpam-804	196	4	to	to	ADP
ejpam-804	196	5	more	more	ADJ
ejpam-804	196	6	than	than	ADP
ejpam-804	196	7	two	two	NUM
ejpam-804	196	8	series	series	NOUN
ejpam-804	196	9	using	use	VERB
ejpam-804	196	10	the	the	DET
ejpam-804	196	11	multiple	multiple	ADJ
ejpam-804	196	12	coherence	coherence	NOUN
ejpam-804	196	13	.	.	PUNCT
ejpam-804	197	1	if	if	SCONJ
ejpam-804	197	2	we	we	PRON
ejpam-804	197	3	are	be	AUX
ejpam-804	197	4	interested	interested	ADJ
ejpam-804	197	5	in	in	ADP
ejpam-804	197	6	long	long	ADJ
ejpam-804	197	7	run	run	NOUN
ejpam-804	197	8	relationships	relationship	NOUN
ejpam-804	197	9	between	between	ADP
ejpam-804	197	10	processes	process	NOUN
ejpam-804	197	11	we	we	PRON
ejpam-804	197	12	need	need	VERB
ejpam-804	197	13	to	to	PART
ejpam-804	197	14	estimate	estimate	VERB
ejpam-804	197	15	the	the	DET
ejpam-804	197	16	multiple	multiple	ADJ
ejpam-804	197	17	coherence	coherence	NOUN
ejpam-804	197	18	in	in	ADP
ejpam-804	197	19	a	a	DET
ejpam-804	197	20	frequency	frequency	NOUN
ejpam-804	197	21	band	band	NOUN
ejpam-804	197	22	around	around	ADP
ejpam-804	197	23	u	u	NOUN
ejpam-804	197	24	=	=	NOUN
ejpam-804	197	25	0	0	NUM
ejpam-804	197	26	.	.	PUNCT
ejpam-804	198	1	different	different	ADJ
ejpam-804	198	2	techniques	technique	NOUN
ejpam-804	198	3	to	to	PART
ejpam-804	198	4	estimate	estimate	VERB
ejpam-804	198	5	the	the	DET
ejpam-804	198	6	evolutionary	evolutionary	ADJ
ejpam-804	198	7	spectra	spectra	NOUN
ejpam-804	198	8	are	be	AUX
ejpam-804	198	9	available	available	ADJ
ejpam-804	198	10	in	in	ADP
ejpam-804	198	11	the	the	DET
ejpam-804	198	12	engineering	engineering	NOUN
ejpam-804	198	13	and	and	CCONJ
ejpam-804	198	14	statistical	statistical	ADJ
ejpam-804	198	15	literature	literature	NOUN
ejpam-804	198	16	.	.	PUNCT
ejpam-804	199	1	priestley	priestley	NOUN
ejpam-804	199	2	and	and	CCONJ
ejpam-804	199	3	tong	tong	PROPN
ejpam-804	200	1	[	[	X
ejpam-804	200	2	24	24	NUM
ejpam-804	200	3	]	]	PUNCT
ejpam-804	200	4	generalise	generalise	VERB
ejpam-804	200	5	priestley	priestley	NOUN
ejpam-804	200	6	[	[	X
ejpam-804	200	7	23	23	NUM
ejpam-804	200	8	]	]	PUNCT
ejpam-804	200	9	to	to	ADP
ejpam-804	200	10	the	the	DET
ejpam-804	200	11	multivariate	multivariate	NOUN
ejpam-804	200	12	case	case	NOUN
ejpam-804	200	13	whereas	whereas	SCONJ
ejpam-804	200	14	dalhaus	dalhaus	X
ejpam-804	200	15	[	[	X
ejpam-804	200	16	4	4	NUM
ejpam-804	200	17	]	]	PUNCT
ejpam-804	200	18	uses	use	VERB
ejpam-804	200	19	a	a	DET
ejpam-804	200	20	different	different	ADJ
ejpam-804	200	21	estimation	estimation	NOUN
ejpam-804	200	22	technique	technique	NOUN
ejpam-804	200	23	.	.	PUNCT
ejpam-804	201	1	r.	r.	PROPN
ejpam-804	201	2	joyeux	joyeux	PROPN
ejpam-804	201	3	/	/	SYM
ejpam-804	201	4	eur	eur	PROPN
ejpam-804	201	5	.	.	PUNCT
ejpam-804	202	1	j.	j.	PROPN
ejpam-804	202	2	pure	pure	PROPN
ejpam-804	202	3	appl	appl	PROPN
ejpam-804	202	4	.	.	PROPN
ejpam-804	202	5	math	math	PROPN
ejpam-804	202	6	,	,	PUNCT
ejpam-804	202	7	3	3	NUM
ejpam-804	202	8	(	(	PUNCT
ejpam-804	202	9	2010	2010	NUM
ejpam-804	202	10	)	)	PUNCT
ejpam-804	202	11	,	,	PUNCT
ejpam-804	202	12	519	519	NUM
ejpam-804	202	13	-	-	SYM
ejpam-804	202	14	530	530	NUM
ejpam-804	202	15	527	527	NUM
ejpam-804	202	16	3.2	3.2	NUM
ejpam-804	202	17	.	.	PUNCT
ejpam-804	203	1	generalization	generalization	NOUN
ejpam-804	203	2	2	2	NUM
ejpam-804	203	3	we	we	PRON
ejpam-804	203	4	also	also	ADV
ejpam-804	203	5	consider	consider	VERB
ejpam-804	203	6	the	the	DET
ejpam-804	203	7	case	case	NOUN
ejpam-804	203	8	where	where	SCONJ
ejpam-804	203	9	we	we	PRON
ejpam-804	203	10	have	have	VERB
ejpam-804	203	11	n	n	NUM
ejpam-804	203	12	series	series	NOUN
ejpam-804	203	13	whose	whose	DET
ejpam-804	203	14	first	first	ADJ
ejpam-804	203	15	differences	difference	NOUN
ejpam-804	203	16	are	be	AUX
ejpam-804	203	17	of	of	ADP
ejpam-804	203	18	class	class	NOUN
ejpam-804	203	19	(	(	PUNCT
ejpam-804	203	20	kf	kf	NOUN
ejpam-804	203	21	)	)	PUNCT
ejpam-804	203	22	and	and	CCONJ
ejpam-804	203	23	for	for	ADP
ejpam-804	203	24	which	which	PRON
ejpam-804	203	25	there	there	PRON
ejpam-804	203	26	exists	exist	VERB
ejpam-804	203	27	a	a	DET
ejpam-804	203	28	linear	linear	ADJ
ejpam-804	203	29	combination	combination	NOUN
ejpam-804	203	30	which	which	PRON
ejpam-804	203	31	is	be	AUX
ejpam-804	203	32	of	of	ADP
ejpam-804	203	33	class	class	NOUN
ejpam-804	203	34	(	(	PUNCT
ejpam-804	203	35	kf	kf	NOUN
ejpam-804	203	36	)	)	PUNCT
ejpam-804	203	37	.	.	PUNCT
ejpam-804	204	1	thus	thus	ADV
ejpam-804	204	2	covering	cover	VERB
ejpam-804	204	3	the	the	DET
ejpam-804	204	4	case	case	NOUN
ejpam-804	204	5	where	where	SCONJ
ejpam-804	204	6	we	we	PRON
ejpam-804	204	7	might	might	AUX
ejpam-804	204	8	have	have	VERB
ejpam-804	204	9	two	two	NUM
ejpam-804	204	10	i(1	i(1	NOUN
ejpam-804	204	11	)	)	PUNCT
ejpam-804	204	12	processes	process	VERB
ejpam-804	204	13	co	co	ADJ
ejpam-804	204	14	-	-	VERB
ejpam-804	204	15	moving	move	VERB
ejpam-804	204	16	according	accord	VERB
ejpam-804	204	17	to	to	ADP
ejpam-804	204	18	a	a	DET
ejpam-804	204	19	nonlinear	nonlinear	NOUN
ejpam-804	204	20	or	or	CCONJ
ejpam-804	204	21	a	a	DET
ejpam-804	204	22	heteroskedastic	heteroskedastic	ADJ
ejpam-804	204	23	adjustment	adjustment	NOUN
ejpam-804	204	24	process	process	NOUN
ejpam-804	204	25	.	.	PUNCT
ejpam-804	205	1	definition	definition	NOUN
ejpam-804	205	2	4	4	NUM
ejpam-804	205	3	(	(	PUNCT
ejpam-804	205	4	class	class	NOUN
ejpam-804	205	5	(	(	PUNCT
ejpam-804	205	6	kf)-integration	kf)-integration	NOUN
ejpam-804	205	7	)	)	PUNCT
ejpam-804	205	8	.	.	PUNCT
ejpam-804	206	1	an	an	DET
ejpam-804	206	2	n	n	CCONJ
ejpam-804	206	3	-	-	PUNCT
ejpam-804	206	4	vector	vector	NOUN
ejpam-804	206	5	process	process	NOUN
ejpam-804	206	6	x	x	PROPN
ejpam-804	206	7	t	t	PROPN
ejpam-804	206	8	is	be	AUX
ejpam-804	206	9	class	class	NOUN
ejpam-804	206	10	(	(	PUNCT
ejpam-804	206	11	kf)-integrated	kf)-integrate	VERB
ejpam-804	206	12	of	of	ADP
ejpam-804	206	13	order	order	NOUN
ejpam-804	206	14	d	d	NOUN
ejpam-804	206	15	,	,	PUNCT
ejpam-804	206	16	denoted	denote	VERB
ejpam-804	206	17	by	by	ADP
ejpam-804	206	18	kf	kf	PROPN
ejpam-804	206	19	i(d	i(d	NOUN
ejpam-804	206	20	)	)	PUNCT
ejpam-804	206	21	,	,	PUNCT
ejpam-804	206	22	if	if	SCONJ
ejpam-804	206	23	there	there	PRON
ejpam-804	206	24	exists	exist	VERB
ejpam-804	206	25	an	an	DET
ejpam-804	206	26	n	n	CCONJ
ejpam-804	206	27	-	-	PUNCT
ejpam-804	206	28	vector	vector	NOUN
ejpam-804	206	29	process	process	NOUN
ejpam-804	206	30	wt	wt	INTJ
ejpam-804	206	31	,	,	PUNCT
ejpam-804	206	32	which	which	PRON
ejpam-804	206	33	is	be	AUX
ejpam-804	206	34	of	of	ADP
ejpam-804	206	35	class	class	NOUN
ejpam-804	206	36	(	(	PUNCT
ejpam-804	206	37	kf	kf	PROPN
ejpam-804	206	38	)	)	PUNCT
ejpam-804	206	39	,	,	PUNCT
ejpam-804	206	40	such	such	ADJ
ejpam-804	206	41	that	that	SCONJ
ejpam-804	206	42	(	(	PUNCT
ejpam-804	206	43	1−	1−	NUM
ejpam-804	206	44	l)d	l)d	X
ejpam-804	206	45	x	x	X
ejpam-804	206	46	t	t	NOUN
ejpam-804	206	47	=	=	SYM
ejpam-804	206	48	wt	wt	NOUN
ejpam-804	206	49	definition	definition	NOUN
ejpam-804	206	50	5	5	NUM
ejpam-804	206	51	(	(	PUNCT
ejpam-804	206	52	class	class	NOUN
ejpam-804	206	53	(	(	PUNCT
ejpam-804	206	54	kf)-cointegration	kf)-cointegration	PROPN
ejpam-804	206	55	)	)	PUNCT
ejpam-804	206	56	.	.	PUNCT
ejpam-804	207	1	an	an	DET
ejpam-804	207	2	n	n	CCONJ
ejpam-804	207	3	-	-	PUNCT
ejpam-804	207	4	vector	vector	NOUN
ejpam-804	207	5	process	process	NOUN
ejpam-804	207	6	x	x	SYM
ejpam-804	207	7	t	t	NOUN
ejpam-804	207	8	class	class	NOUN
ejpam-804	207	9	(	(	PUNCT
ejpam-804	207	10	kf)-integrated	kf)-integrate	VERB
ejpam-804	207	11	of	of	ADP
ejpam-804	207	12	order	order	NOUN
ejpam-804	207	13	1	1	NUM
ejpam-804	207	14	is	be	AUX
ejpam-804	207	15	said	say	VERB
ejpam-804	207	16	to	to	PART
ejpam-804	207	17	be	be	AUX
ejpam-804	207	18	class	class	NOUN
ejpam-804	207	19	(	(	PUNCT
ejpam-804	207	20	kf)-cointegrated	kf)-cointegrate	VERB
ejpam-804	207	21	if	if	SCONJ
ejpam-804	207	22	there	there	PRON
ejpam-804	207	23	exists	exist	VERB
ejpam-804	207	24	a	a	DET
ejpam-804	207	25	linear	linear	ADJ
ejpam-804	207	26	combination	combination	NOUN
ejpam-804	207	27	of	of	ADP
ejpam-804	207	28	the	the	DET
ejpam-804	207	29	series	series	NOUN
ejpam-804	207	30	which	which	PRON
ejpam-804	207	31	is	be	AUX
ejpam-804	207	32	kf	kf	PROPN
ejpam-804	207	33	i(0	i(0	PROPN
ejpam-804	207	34	)	)	PUNCT
ejpam-804	207	35	.	.	PUNCT
ejpam-804	208	1	this	this	PRON
ejpam-804	208	2	means	mean	VERB
ejpam-804	208	3	that	that	SCONJ
ejpam-804	208	4	there	there	PRON
ejpam-804	208	5	exists	exist	VERB
ejpam-804	208	6	β	β	NOUN
ejpam-804	208	7	6=	6=	ADP
ejpam-804	208	8	0	0	NUM
ejpam-804	208	9	such	such	ADJ
ejpam-804	208	10	that	that	SCONJ
ejpam-804	208	11	β	β	PROPN
ejpam-804	208	12	′x	′x	PROPN
ejpam-804	208	13	t	t	PROPN
ejpam-804	208	14	=	=	SYM
ejpam-804	208	15	ǫt	ǫt	PROPN
ejpam-804	208	16	where	where	SCONJ
ejpam-804	208	17	εt	εt	PROPN
ejpam-804	208	18	is	be	AUX
ejpam-804	208	19	of	of	ADP
ejpam-804	208	20	class	class	NOUN
ejpam-804	208	21	(	(	PUNCT
ejpam-804	208	22	kf	kf	PROPN
ejpam-804	208	23	)	)	PUNCT
ejpam-804	208	24	.	.	PUNCT
ejpam-804	209	1	3.3	3.3	NUM
ejpam-804	209	2	.	.	PUNCT
ejpam-804	210	1	the	the	DET
ejpam-804	210	2	special	special	ADJ
ejpam-804	210	3	case	case	NOUN
ejpam-804	210	4	of	of	ADP
ejpam-804	210	5	harmonizable	harmonizable	ADJ
ejpam-804	210	6	cointegration	cointegration	NOUN
ejpam-804	210	7	the	the	DET
ejpam-804	210	8	usual	usual	ADJ
ejpam-804	210	9	concept	concept	NOUN
ejpam-804	210	10	of	of	ADP
ejpam-804	210	11	cointegration	cointegration	NOUN
ejpam-804	210	12	among	among	ADP
ejpam-804	210	13	integrated	integrated	ADJ
ejpam-804	210	14	variables	variable	NOUN
ejpam-804	210	15	refers	refer	VERB
ejpam-804	210	16	to	to	ADP
ejpam-804	210	17	cointegration	cointegration	NOUN
ejpam-804	210	18	at	at	ADP
ejpam-804	210	19	frequency	frequency	NOUN
ejpam-804	210	20	zero	zero	NUM
ejpam-804	210	21	.	.	PUNCT
ejpam-804	211	1	the	the	DET
ejpam-804	211	2	concept	concept	NOUN
ejpam-804	211	3	has	have	AUX
ejpam-804	211	4	been	be	AUX
ejpam-804	211	5	generalized	generalize	VERB
ejpam-804	211	6	to	to	ADP
ejpam-804	211	7	cointegration	cointegration	NOUN
ejpam-804	211	8	at	at	ADP
ejpam-804	211	9	different	different	ADJ
ejpam-804	211	10	frequencies	frequency	NOUN
ejpam-804	211	11	allowing	allow	VERB
ejpam-804	211	12	for	for	SCONJ
ejpam-804	211	13	the	the	DET
ejpam-804	211	14	cointegrating	cointegrate	VERB
ejpam-804	211	15	vectors	vector	NOUN
ejpam-804	211	16	to	to	PART
ejpam-804	211	17	be	be	AUX
ejpam-804	211	18	different	different	ADJ
ejpam-804	211	19	at	at	ADP
ejpam-804	211	20	different	different	ADJ
ejpam-804	211	21	frequencies	frequency	NOUN
ejpam-804	211	22	[	[	X
ejpam-804	211	23	3	3	NUM
ejpam-804	211	24	,	,	PUNCT
ejpam-804	211	25	16	16	NUM
ejpam-804	211	26	]	]	PUNCT
ejpam-804	211	27	.	.	PUNCT
ejpam-804	212	1	in	in	ADP
ejpam-804	212	2	this	this	DET
ejpam-804	212	3	section	section	NOUN
ejpam-804	212	4	we	we	PRON
ejpam-804	212	5	use	use	VERB
ejpam-804	212	6	the	the	DET
ejpam-804	212	7	more	more	ADV
ejpam-804	212	8	general	general	ADJ
ejpam-804	212	9	definition	definition	NOUN
ejpam-804	212	10	of	of	ADP
ejpam-804	212	11	cointegration	cointegration	NOUN
ejpam-804	212	12	at	at	ADP
ejpam-804	212	13	a	a	DET
ejpam-804	212	14	specific	specific	ADJ
ejpam-804	212	15	frequency	frequency	NOUN
ejpam-804	212	16	,	,	PUNCT
ejpam-804	212	17	not	not	PART
ejpam-804	212	18	necessarily	necessarily	ADV
ejpam-804	212	19	zero	zero	NUM
ejpam-804	212	20	.	.	PUNCT
ejpam-804	213	1	definition	definition	NOUN
ejpam-804	213	2	6	6	NUM
ejpam-804	213	3	.	.	PUNCT
ejpam-804	214	1	let	let	VERB
ejpam-804	214	2	x	x	SYM
ejpam-804	214	3	t	t	PROPN
ejpam-804	214	4	be	be	AUX
ejpam-804	214	5	a	a	DET
ejpam-804	214	6	strongly	strongly	ADV
ejpam-804	214	7	harmonizable	harmonizable	ADJ
ejpam-804	214	8	n	n	CCONJ
ejpam-804	214	9	-	-	PUNCT
ejpam-804	214	10	dimensional	dimensional	ADJ
ejpam-804	214	11	vector	vector	NOUN
ejpam-804	214	12	process	process	NOUN
ejpam-804	214	13	with	with	ADP
ejpam-804	214	14	matrix	matrix	NOUN
ejpam-804	214	15	spectral	spectral	ADJ
ejpam-804	214	16	function	function	NOUN
ejpam-804	214	17	f(a	f(a	PROPN
ejpam-804	214	18	,	,	PUNCT
ejpam-804	214	19	b	b	NOUN
ejpam-804	214	20	)	)	PUNCT
ejpam-804	214	21	.	.	PUNCT
ejpam-804	215	1	we	we	PRON
ejpam-804	215	2	will	will	AUX
ejpam-804	215	3	say	say	VERB
ejpam-804	215	4	that	that	SCONJ
ejpam-804	215	5	x	x	PROPN
ejpam-804	215	6	t	t	PROPN
ejpam-804	215	7	is	be	AUX
ejpam-804	215	8	cointegrated	cointegrate	VERB
ejpam-804	215	9	at	at	ADP
ejpam-804	215	10	frequencyω	frequencyω	NOUN
ejpam-804	215	11	with	with	ADP
ejpam-804	215	12	cointegrating	cointegrate	VERB
ejpam-804	215	13	vector	vector	NOUN
ejpam-804	215	14	βω	βω	INTJ
ejpam-804	216	1	if	if	SCONJ
ejpam-804	216	2	ǫt	ǫt	PROPN
ejpam-804	216	3	,	,	PUNCT
ejpam-804	216	4	ω	ω	PROPN
ejpam-804	216	5	=	=	PUNCT
ejpam-804	216	6	β	β	NOUN
ejpam-804	216	7	′	′	NUM
ejpam-804	216	8	ωx	ωx	VERB
ejpam-804	216	9	t	t	NOUN
ejpam-804	216	10	is	be	AUX
ejpam-804	216	11	such	such	ADJ
ejpam-804	216	12	that	that	SCONJ
ejpam-804	216	13	its	its	PRON
ejpam-804	216	14	matrix	matrix	NOUN
ejpam-804	216	15	spectral	spectral	ADJ
ejpam-804	216	16	function	function	NOUN
ejpam-804	216	17	fε	fε	NOUN
ejpam-804	216	18	,	,	PUNCT
ejpam-804	216	19	ω(a	ω(a	PROPN
ejpam-804	216	20	,	,	PUNCT
ejpam-804	216	21	b	b	NOUN
ejpam-804	216	22	)	)	PUNCT
ejpam-804	216	23	=	=	PUNCT
ejpam-804	216	24	β	β	X
ejpam-804	216	25	′ωf(a	′ωf(a	PROPN
ejpam-804	216	26	,	,	PUNCT
ejpam-804	216	27	b)βω	b)βω	PROPN
ejpam-804	216	28	=	=	SYM
ejpam-804	216	29	0n	0n	NOUN
ejpam-804	216	30	(	(	PUNCT
ejpam-804	216	31	21	21	NUM
ejpam-804	216	32	)	)	PUNCT
ejpam-804	216	33	for	for	ADP
ejpam-804	216	34	all	all	DET
ejpam-804	216	35	borel	borel	NOUN
ejpam-804	216	36	sets	set	VERB
ejpam-804	216	37	a=	a=	VERB
ejpam-804	217	1	[	[	X
ejpam-804	217	2	ω−	ω−	PROPN
ejpam-804	217	3	δ	δ	PROPN
ejpam-804	217	4	,	,	PUNCT
ejpam-804	217	5	ω+	ω+	NUM
ejpam-804	217	6	δ	δ	PROPN
ejpam-804	217	7	]	]	PUNCT
ejpam-804	217	8	and	and	CCONJ
ejpam-804	217	9	b	b	X
ejpam-804	217	10	such	such	ADJ
ejpam-804	217	11	that	that	SCONJ
ejpam-804	217	12	a	a	DET
ejpam-804	217	13	⋂	⋂	PROPN
ejpam-804	217	14	b	b	PROPN
ejpam-804	217	15	=	=	PUNCT
ejpam-804	217	16	;	;	PUNCT
ejpam-804	217	17	.	.	PUNCT
ejpam-804	217	18	let	let	VERB
ejpam-804	217	19	ǫt	ǫt	PRON
ejpam-804	217	20	,	,	PUNCT
ejpam-804	217	21	ω	ω	PROPN
ejpam-804	217	22	=	=	PUNCT
ejpam-804	217	23	β	β	NOUN
ejpam-804	217	24	′	′	NUM
ejpam-804	218	1	ωx	ωx	VERB
ejpam-804	218	2	t	t	NOUN
ejpam-804	218	3	=	=	SYM
ejpam-804	218	4	∫	∫	PROPN
ejpam-804	219	1	π	π	NOUN
ejpam-804	219	2	−π	−π	INTJ
ejpam-804	219	3	ei	ei	X
ejpam-804	219	4	tuzǫ	tuzǫ	PROPN
ejpam-804	219	5	,	,	PUNCT
ejpam-804	219	6	ω(du	ω(du	NOUN
ejpam-804	219	7	)	)	PUNCT
ejpam-804	219	8	then	then	ADV
ejpam-804	219	9	this	this	DET
ejpam-804	219	10	definition	definition	NOUN
ejpam-804	219	11	implies	imply	VERB
ejpam-804	219	12	that	that	SCONJ
ejpam-804	219	13	in	in	ADP
ejpam-804	219	14	the	the	DET
ejpam-804	219	15	spectral	spectral	ADJ
ejpam-804	219	16	decomposition	decomposition	NOUN
ejpam-804	219	17	of	of	ADP
ejpam-804	219	18	ǫt	ǫt	PROPN
ejpam-804	219	19	,	,	PUNCT
ejpam-804	219	20	ω	ω	PROPN
ejpam-804	219	21	the	the	DET
ejpam-804	219	22	frequency	frequency	NOUN
ejpam-804	219	23	ω	ω	PROPN
ejpam-804	219	24	is	be	AUX
ejpam-804	219	25	“	"	PUNCT
ejpam-804	219	26	independent	independent	ADJ
ejpam-804	219	27	”	"	PUNCT
ejpam-804	219	28	from	from	ADP
ejpam-804	219	29	the	the	DET
ejpam-804	219	30	other	other	ADJ
ejpam-804	219	31	frequencies	frequency	NOUN
ejpam-804	219	32	.	.	PUNCT
ejpam-804	220	1	this	this	DET
ejpam-804	220	2	definition	definition	NOUN
ejpam-804	220	3	also	also	ADV
ejpam-804	220	4	implies	imply	VERB
ejpam-804	220	5	that	that	SCONJ
ejpam-804	220	6	f(a	f(a	NOUN
ejpam-804	220	7	,	,	PUNCT
ejpam-804	220	8	b	b	NOUN
ejpam-804	220	9	)	)	PUNCT
ejpam-804	220	10	is	be	AUX
ejpam-804	220	11	singular	singular	ADJ
ejpam-804	220	12	and	and	CCONJ
ejpam-804	220	13	βω	βω	PROPN
ejpam-804	220	14	lies	lie	VERB
ejpam-804	220	15	in	in	ADP
ejpam-804	220	16	its	its	PRON
ejpam-804	220	17	null	null	ADJ
ejpam-804	220	18	space	space	NOUN
ejpam-804	220	19	for	for	ADP
ejpam-804	220	20	all	all	DET
ejpam-804	220	21	borel	borel	NOUN
ejpam-804	220	22	sets	set	VERB
ejpam-804	220	23	a	a	DET
ejpam-804	220	24	=	=	SYM
ejpam-804	220	25	[	[	X
ejpam-804	220	26	ω−	ω−	PROPN
ejpam-804	220	27	δ	δ	PROPN
ejpam-804	220	28	,	,	PUNCT
ejpam-804	220	29	ω+	ω+	NUM
ejpam-804	220	30	δ	δ	PROPN
ejpam-804	220	31	]	]	PUNCT
ejpam-804	220	32	and	and	CCONJ
ejpam-804	220	33	b	b	X
ejpam-804	220	34	such	such	ADJ
ejpam-804	220	35	that	that	SCONJ
ejpam-804	220	36	a	a	DET
ejpam-804	220	37	⋂	⋂	PROPN
ejpam-804	220	38	b	b	PROPN
ejpam-804	220	39	=	=	PUNCT
ejpam-804	220	40	;	;	PUNCT
ejpam-804	220	41	.	.	PUNCT
ejpam-804	221	1	if	if	SCONJ
ejpam-804	221	2	there	there	PRON
ejpam-804	221	3	are	be	VERB
ejpam-804	221	4	k	k	PROPN
ejpam-804	221	5	distinct	distinct	ADJ
ejpam-804	221	6	cointegrating	cointegrate	VERB
ejpam-804	221	7	vectors	vector	NOUN
ejpam-804	221	8	then	then	ADV
ejpam-804	221	9	f(a	f(a	PROPN
ejpam-804	221	10	,	,	PUNCT
ejpam-804	221	11	b	b	NOUN
ejpam-804	221	12	)	)	PUNCT
ejpam-804	221	13	has	have	AUX
ejpam-804	221	14	k	k	PROPN
ejpam-804	221	15	zero	zero	NUM
ejpam-804	221	16	eigenvalues	eigenvalue	NOUN
ejpam-804	221	17	.	.	PUNCT
ejpam-804	222	1	if	if	SCONJ
ejpam-804	222	2	the	the	DET
ejpam-804	222	3	vectors	vector	NOUN
ejpam-804	222	4	βω	βω	PRON
ejpam-804	222	5	are	be	AUX
ejpam-804	222	6	equal	equal	ADJ
ejpam-804	222	7	for	for	ADP
ejpam-804	222	8	all	all	DET
ejpam-804	222	9	frequencies	frequency	NOUN
ejpam-804	222	10	then	then	ADV
ejpam-804	222	11	ǫt	ǫt	PROPN
ejpam-804	222	12	,	,	PUNCT
ejpam-804	222	13	ω	ω	PROPN
ejpam-804	222	14	is	be	AUX
ejpam-804	222	15	a	a	DET
ejpam-804	222	16	stationary	stationary	ADJ
ejpam-804	222	17	process	process	NOUN
ejpam-804	222	18	.	.	PUNCT
ejpam-804	223	1	a	a	DET
ejpam-804	223	2	sufficient	sufficient	ADJ
ejpam-804	223	3	condition	condition	NOUN
ejpam-804	223	4	for	for	SCONJ
ejpam-804	223	5	x	x	PROPN
ejpam-804	223	6	t	t	PROPN
ejpam-804	223	7	to	to	PART
ejpam-804	223	8	be	be	AUX
ejpam-804	223	9	cointegrated	cointegrate	VERB
ejpam-804	223	10	at	at	ADP
ejpam-804	223	11	frequency	frequency	PROPN
ejpam-804	223	12	ω	ω	PROPN
ejpam-804	223	13	is	be	AUX
ejpam-804	223	14	that	that	SCONJ
ejpam-804	223	15	there	there	PRON
ejpam-804	223	16	exists	exist	VERB
ejpam-804	223	17	εt	εt	PROPN
ejpam-804	223	18	,	,	PUNCT
ejpam-804	223	19	ω	ω	PROPN
ejpam-804	223	20	for	for	ADP
ejpam-804	223	21	which	which	PRON
ejpam-804	223	22	the	the	DET
ejpam-804	223	23	ω	ω	PROPN
ejpam-804	223	24	frequency	frequency	NOUN
ejpam-804	223	25	be	be	AUX
ejpam-804	223	26	independent	independent	ADJ
ejpam-804	223	27	from	from	ADP
ejpam-804	223	28	the	the	DET
ejpam-804	223	29	other	other	ADJ
ejpam-804	223	30	frequencies	frequency	NOUN
ejpam-804	223	31	.	.	PUNCT
ejpam-804	224	1	definition	definition	NOUN
ejpam-804	224	2	7	7	NUM
ejpam-804	224	3	(	(	PUNCT
ejpam-804	224	4	harmonizable	harmonizable	NOUN
ejpam-804	224	5	-	-	PUNCT
ejpam-804	224	6	integration	integration	NOUN
ejpam-804	224	7	)	)	PUNCT
ejpam-804	224	8	.	.	PUNCT
ejpam-804	225	1	an	an	DET
ejpam-804	225	2	n	n	CCONJ
ejpam-804	225	3	-	-	PUNCT
ejpam-804	225	4	vector	vector	NOUN
ejpam-804	225	5	process	process	NOUN
ejpam-804	225	6	x	x	PROPN
ejpam-804	225	7	t	t	PROPN
ejpam-804	225	8	is	be	AUX
ejpam-804	225	9	harmonizable	harmonizable	ADJ
ejpam-804	225	10	-	-	PUNCT
ejpam-804	225	11	integrated	integrate	VERB
ejpam-804	225	12	of	of	ADP
ejpam-804	225	13	order	order	NOUN
ejpam-804	225	14	d	d	NOUN
ejpam-804	225	15	,	,	PUNCT
ejpam-804	225	16	denoted	denote	VERB
ejpam-804	225	17	by	by	ADP
ejpam-804	225	18	hi(d	hi(d	NOUN
ejpam-804	225	19	)	)	PUNCT
ejpam-804	225	20	,	,	PUNCT
ejpam-804	225	21	if	if	SCONJ
ejpam-804	225	22	there	there	PRON
ejpam-804	225	23	exists	exist	VERB
ejpam-804	225	24	an	an	DET
ejpam-804	225	25	n	n	CCONJ
ejpam-804	225	26	-	-	PUNCT
ejpam-804	225	27	vector	vector	NOUN
ejpam-804	225	28	process	process	NOUN
ejpam-804	225	29	wt	wt	INTJ
ejpam-804	225	30	,	,	PUNCT
ejpam-804	225	31	which	which	PRON
ejpam-804	225	32	is	be	AUX
ejpam-804	225	33	strongly	strongly	ADV
ejpam-804	225	34	harmonizable	harmonizable	ADJ
ejpam-804	225	35	,	,	PUNCT
ejpam-804	225	36	such	such	ADJ
ejpam-804	225	37	that	that	SCONJ
ejpam-804	225	38	(	(	PUNCT
ejpam-804	225	39	1−	1−	NUM
ejpam-804	225	40	l)d	l)d	X
ejpam-804	225	41	x	x	X
ejpam-804	225	42	t	t	NOUN
ejpam-804	225	43	=	=	SYM
ejpam-804	225	44	wt	wt	NUM
ejpam-804	225	45	references	reference	NOUN
ejpam-804	225	46	528	528	NUM
ejpam-804	225	47	definition	definition	NOUN
ejpam-804	225	48	8	8	NUM
ejpam-804	225	49	(	(	PUNCT
ejpam-804	225	50	harmonizable	harmonizable	NOUN
ejpam-804	225	51	-	-	PUNCT
ejpam-804	225	52	cointegration	cointegration	NOUN
ejpam-804	225	53	)	)	PUNCT
ejpam-804	225	54	.	.	PUNCT
ejpam-804	226	1	an	an	DET
ejpam-804	226	2	n	n	CCONJ
ejpam-804	226	3	-	-	PUNCT
ejpam-804	226	4	vector	vector	NOUN
ejpam-804	226	5	process	process	NOUN
ejpam-804	226	6	x	x	PROPN
ejpam-804	226	7	t	t	PROPN
ejpam-804	226	8	harmonizable	harmonizable	ADV
ejpam-804	226	9	-	-	PUNCT
ejpam-804	226	10	integrated	integrate	VERB
ejpam-804	226	11	of	of	ADP
ejpam-804	226	12	order	order	NOUN
ejpam-804	226	13	1	1	NUM
ejpam-804	226	14	is	be	AUX
ejpam-804	226	15	said	say	VERB
ejpam-804	226	16	to	to	PART
ejpam-804	226	17	be	be	AUX
ejpam-804	226	18	harmonizable	harmonizable	ADJ
ejpam-804	226	19	-	-	PUNCT
ejpam-804	226	20	cointegrated	cointegrate	VERB
ejpam-804	226	21	if	if	SCONJ
ejpam-804	226	22	there	there	PRON
ejpam-804	226	23	exists	exist	VERB
ejpam-804	226	24	a	a	DET
ejpam-804	226	25	linear	linear	ADJ
ejpam-804	226	26	combination	combination	NOUN
ejpam-804	226	27	of	of	ADP
ejpam-804	226	28	the	the	DET
ejpam-804	226	29	series	series	NOUN
ejpam-804	226	30	which	which	PRON
ejpam-804	226	31	is	be	AUX
ejpam-804	226	32	hi(0	hi(0	PROPN
ejpam-804	226	33	)	)	PUNCT
ejpam-804	226	34	.	.	PUNCT
ejpam-804	227	1	this	this	PRON
ejpam-804	227	2	means	mean	VERB
ejpam-804	227	3	that	that	SCONJ
ejpam-804	227	4	there	there	PRON
ejpam-804	227	5	exists	exist	VERB
ejpam-804	227	6	β	β	NOUN
ejpam-804	227	7	6=	6=	ADP
ejpam-804	227	8	0	0	NUM
ejpam-804	227	9	such	such	ADJ
ejpam-804	227	10	that	that	SCONJ
ejpam-804	227	11	β	β	PROPN
ejpam-804	227	12	′x	′x	PROPN
ejpam-804	227	13	t	t	PROPN
ejpam-804	227	14	=	=	SYM
ejpam-804	227	15	ǫt	ǫt	PROPN
ejpam-804	227	16	where	where	SCONJ
ejpam-804	227	17	εt	εt	PROPN
ejpam-804	227	18	is	be	AUX
ejpam-804	227	19	strongly	strongly	ADV
ejpam-804	227	20	harmonizable	harmonizable	ADJ
ejpam-804	227	21	.	.	PUNCT
ejpam-804	228	1	note	note	VERB
ejpam-804	228	2	that	that	SCONJ
ejpam-804	228	3	if	if	SCONJ
ejpam-804	228	4	(	(	PUNCT
ejpam-804	228	5	1	1	NUM
ejpam-804	228	6	−	−	NOUN
ejpam-804	228	7	l)x	l)x	X
ejpam-804	228	8	t	t	NOUN
ejpam-804	228	9	=	=	PUNCT
ejpam-804	228	10	wt	wt	AUX
ejpam-804	228	11	has	have	VERB
ejpam-804	228	12	an	an	DET
ejpam-804	228	13	absolutely	absolutely	ADV
ejpam-804	228	14	continuous	continuous	ADJ
ejpam-804	228	15	distribution	distribution	NOUN
ejpam-804	228	16	of	of	ADP
ejpam-804	228	17	masses	masse	NOUN
ejpam-804	228	18	with	with	ADP
ejpam-804	228	19	spectral	spectral	ADJ
ejpam-804	228	20	density	density	NOUN
ejpam-804	228	21	matrix	matrix	NOUN
ejpam-804	228	22	fww(u	fww(u	PROPN
ejpam-804	228	23	,	,	PUNCT
ejpam-804	228	24	v	v	NOUN
ejpam-804	228	25	)	)	PUNCT
ejpam-804	228	26	this	this	PRON
ejpam-804	228	27	implies	imply	VERB
ejpam-804	228	28	that	that	SCONJ
ejpam-804	229	1	β	β	X
ejpam-804	229	2	′	′	NUM
ejpam-804	229	3	fww(u	fww(u	PROPN
ejpam-804	229	4	,	,	PUNCT
ejpam-804	229	5	v)β	v)β	NOUN
ejpam-804	229	6	=	=	SYM
ejpam-804	229	7	0	0	NUM
ejpam-804	229	8	at	at	ADP
ejpam-804	229	9	all	all	DET
ejpam-804	229	10	frequencies	frequency	NOUN
ejpam-804	229	11	(	(	PUNCT
ejpam-804	229	12	u	u	NOUN
ejpam-804	229	13	,	,	PUNCT
ejpam-804	229	14	v	v	NOUN
ejpam-804	229	15	)	)	PUNCT
ejpam-804	229	16	belonging	belong	VERB
ejpam-804	229	17	to	to	ADP
ejpam-804	229	18	[	[	X
ejpam-804	229	19	−π	−π	ADJ
ejpam-804	229	20	,	,	PUNCT
ejpam-804	229	21	π]×	π]×	NOUN
ejpam-804	229	22	[	[	X
ejpam-804	229	23	−π	−π	PROPN
ejpam-804	229	24	,	,	PUNCT
ejpam-804	229	25	π	π	NOUN
ejpam-804	229	26	]	]	X
ejpam-804	229	27	.	.	PUNCT
ejpam-804	230	1	thus	thus	ADV
ejpam-804	230	2	fww(u	fww(u	PROPN
ejpam-804	230	3	,	,	PUNCT
ejpam-804	230	4	v	v	NOUN
ejpam-804	230	5	)	)	PUNCT
ejpam-804	230	6	is	be	AUX
ejpam-804	230	7	singular	singular	ADJ
ejpam-804	230	8	and	and	CCONJ
ejpam-804	230	9	β	β	X
ejpam-804	230	10	lies	lie	VERB
ejpam-804	230	11	in	in	ADP
ejpam-804	230	12	its	its	PRON
ejpam-804	230	13	null	null	ADJ
ejpam-804	230	14	space	space	NOUN
ejpam-804	230	15	.	.	PUNCT
ejpam-804	231	1	4	4	X
ejpam-804	231	2	.	.	X
ejpam-804	231	3	conclusion	conclusion	NOUN
ejpam-804	231	4	in	in	ADP
ejpam-804	231	5	this	this	DET
ejpam-804	231	6	paper	paper	NOUN
ejpam-804	231	7	we	we	PRON
ejpam-804	231	8	have	have	AUX
ejpam-804	231	9	shown	show	VERB
ejpam-804	231	10	that	that	SCONJ
ejpam-804	231	11	the	the	DET
ejpam-804	231	12	class	class	NOUN
ejpam-804	231	13	(	(	PUNCT
ejpam-804	231	14	kf	kf	NOUN
ejpam-804	231	15	)	)	PUNCT
ejpam-804	231	16	of	of	ADP
ejpam-804	231	17	processes	process	NOUN
ejpam-804	231	18	is	be	AUX
ejpam-804	231	19	possibly	possibly	ADV
ejpam-804	231	20	the	the	DET
ejpam-804	231	21	most	most	ADV
ejpam-804	231	22	general	general	ADJ
ejpam-804	231	23	class	class	NOUN
ejpam-804	231	24	of	of	ADP
ejpam-804	231	25	processes	process	NOUN
ejpam-804	231	26	we	we	PRON
ejpam-804	231	27	might	might	AUX
ejpam-804	231	28	hope	hope	VERB
ejpam-804	231	29	to	to	PART
ejpam-804	231	30	study	study	VERB
ejpam-804	231	31	.	.	PUNCT
ejpam-804	232	1	we	we	PRON
ejpam-804	232	2	have	have	AUX
ejpam-804	232	3	generalized	generalize	VERB
ejpam-804	232	4	the	the	DET
ejpam-804	232	5	concept	concept	NOUN
ejpam-804	232	6	of	of	ADP
ejpam-804	232	7	cointegration	cointegration	NOUN
ejpam-804	232	8	to	to	ADP
ejpam-804	232	9	class	class	NOUN
ejpam-804	232	10	(	(	PUNCT
ejpam-804	232	11	kf	kf	NOUN
ejpam-804	232	12	)	)	PUNCT
ejpam-804	232	13	processes	process	NOUN
ejpam-804	232	14	.	.	PUNCT
ejpam-804	233	1	we	we	PRON
ejpam-804	233	2	have	have	AUX
ejpam-804	233	3	considered	consider	VERB
ejpam-804	233	4	the	the	DET
ejpam-804	233	5	situation	situation	NOUN
ejpam-804	233	6	where	where	SCONJ
ejpam-804	233	7	we	we	PRON
ejpam-804	233	8	have	have	VERB
ejpam-804	233	9	non	non	ADJ
ejpam-804	233	10	-	-	ADJ
ejpam-804	233	11	stationary	stationary	ADJ
ejpam-804	233	12	processes	process	NOUN
ejpam-804	233	13	generated	generate	VERB
ejpam-804	233	14	by	by	ADP
ejpam-804	233	15	nonlinear	nonlinear	ADJ
ejpam-804	233	16	systems	system	NOUN
ejpam-804	233	17	which	which	PRON
ejpam-804	233	18	co	co	VERB
ejpam-804	233	19	-	-	NOUN
ejpam-804	233	20	move	move	NOUN
ejpam-804	233	21	according	accord	VERB
ejpam-804	233	22	to	to	ADP
ejpam-804	233	23	a	a	DET
ejpam-804	233	24	linear	linear	ADJ
ejpam-804	233	25	adjustment	adjustment	NOUN
ejpam-804	233	26	process	process	NOUN
ejpam-804	233	27	.	.	PUNCT
ejpam-804	234	1	we	we	PRON
ejpam-804	234	2	have	have	AUX
ejpam-804	234	3	also	also	ADV
ejpam-804	234	4	considered	consider	VERB
ejpam-804	234	5	the	the	DET
ejpam-804	234	6	case	case	NOUN
ejpam-804	234	7	where	where	SCONJ
ejpam-804	234	8	we	we	PRON
ejpam-804	234	9	might	might	AUX
ejpam-804	234	10	have	have	VERB
ejpam-804	234	11	two	two	NUM
ejpam-804	234	12	i(1	i(1	NOUN
ejpam-804	234	13	)	)	PUNCT
ejpam-804	234	14	processes	process	VERB
ejpam-804	234	15	co	co	ADJ
ejpam-804	234	16	-	-	VERB
ejpam-804	234	17	moving	move	VERB
ejpam-804	234	18	according	accord	VERB
ejpam-804	234	19	to	to	ADP
ejpam-804	234	20	a	a	DET
ejpam-804	234	21	nonlinear	nonlinear	ADJ
ejpam-804	234	22	or	or	CCONJ
ejpam-804	234	23	heteroskedastic	heteroskedastic	ADJ
ejpam-804	234	24	adjustment	adjustment	NOUN
ejpam-804	234	25	process	process	NOUN
ejpam-804	234	26	.	.	PUNCT
ejpam-804	235	1	acknowledgements	acknowledgement	NOUN
ejpam-804	235	2	i	i	PRON
ejpam-804	235	3	wish	wish	VERB
ejpam-804	235	4	to	to	PART
ejpam-804	235	5	thank	thank	VERB
ejpam-804	235	6	victor	victor	PROPN
ejpam-804	235	7	solo	solo	PROPN
ejpam-804	235	8	and	and	CCONJ
ejpam-804	235	9	tony	tony	PROPN
ejpam-804	235	10	bryant	bryant	PROPN
ejpam-804	235	11	for	for	ADP
ejpam-804	235	12	providing	provide	VERB
ejpam-804	235	13	many	many	ADJ
ejpam-804	235	14	useful	useful	ADJ
ejpam-804	235	15	references	reference	NOUN
ejpam-804	235	16	and	and	CCONJ
ejpam-804	235	17	helpful	helpful	ADJ
ejpam-804	235	18	discussions	discussion	NOUN
ejpam-804	235	19	.	.	PUNCT
ejpam-804	236	1	all	all	DET
ejpam-804	236	2	errors	error	NOUN
ejpam-804	236	3	are	be	AUX
ejpam-804	236	4	my	my	PRON
ejpam-804	236	5	own	own	ADJ
ejpam-804	236	6	.	.	PUNCT
ejpam-804	237	1	references	reference	NOUN
ejpam-804	237	2	[	[	X
ejpam-804	237	3	1	1	X
ejpam-804	237	4	]	]	PUNCT
ejpam-804	237	5	a	a	DET
ejpam-804	237	6	blanc	blanc	NOUN
ejpam-804	237	7	-	-	PUNCT
ejpam-804	237	8	lapierre	lapierre	PROPN
ejpam-804	237	9	and	and	CCONJ
ejpam-804	237	10	r	r	NOUN
ejpam-804	237	11	fortet	fortet	NOUN
ejpam-804	237	12	.	.	PUNCT
ejpam-804	238	1	theory	theory	NOUN
ejpam-804	238	2	of	of	ADP
ejpam-804	238	3	random	random	ADJ
ejpam-804	238	4	functions	function	NOUN
ejpam-804	238	5	,	,	PUNCT
ejpam-804	238	6	new	new	PROPN
ejpam-804	238	7	york	york	PROPN
ejpam-804	238	8	:	:	PUNCT
ejpam-804	238	9	gordon	gordon	PROPN
ejpam-804	238	10	and	and	CCONJ
ejpam-804	238	11	breach	breach	PROPN
ejpam-804	238	12	,	,	PUNCT
ejpam-804	238	13	1965	1965	NUM
ejpam-804	238	14	.	.	PUNCT
ejpam-804	239	1	[	[	X
ejpam-804	239	2	2	2	NUM
ejpam-804	239	3	]	]	PUNCT
ejpam-804	239	4	s	s	PART
ejpam-804	239	5	cambanis	cambanis	NOUN
ejpam-804	239	6	.	.	PUNCT
ejpam-804	240	1	wavelet	wavelet	NOUN
ejpam-804	240	2	approximation	approximation	NOUN
ejpam-804	240	3	of	of	ADP
ejpam-804	240	4	deterministic	deterministic	ADJ
ejpam-804	240	5	and	and	CCONJ
ejpam-804	240	6	random	random	ADJ
ejpam-804	240	7	signals	signal	NOUN
ejpam-804	240	8	:	:	PUNCT
ejpam-804	240	9	convergence	convergence	NOUN
ejpam-804	240	10	properties	property	NOUN
ejpam-804	240	11	and	and	CCONJ
ejpam-804	240	12	rates	rate	NOUN
ejpam-804	240	13	,	,	PUNCT
ejpam-804	240	14	ieee	ieee	NOUN
ejpam-804	240	15	transactions	transaction	NOUN
ejpam-804	240	16	on	on	ADP
ejpam-804	240	17	information	information	NOUN
ejpam-804	240	18	theory	theory	NOUN
ejpam-804	240	19	,	,	PUNCT
ejpam-804	240	20	40	40	NUM
ejpam-804	240	21	,	,	PUNCT
ejpam-804	240	22	4	4	NUM
ejpam-804	240	23	,	,	PUNCT
ejpam-804	240	24	1013	1013	NUM
ejpam-804	240	25	-	-	SYM
ejpam-804	240	26	29	29	NUM
ejpam-804	240	27	,	,	PUNCT
ejpam-804	240	28	1994	1994	NUM
ejpam-804	240	29	.	.	PUNCT
ejpam-804	241	1	[	[	X
ejpam-804	241	2	3	3	NUM
ejpam-804	241	3	]	]	PUNCT
ejpam-804	241	4	d	d	NOUN
ejpam-804	241	5	corbae	corbae	NOUN
ejpam-804	241	6	,	,	PUNCT
ejpam-804	241	7	s	s	NOUN
ejpam-804	241	8	ouliaris	ouliaris	NOUN
ejpam-804	241	9	,	,	PUNCT
ejpam-804	241	10	and	and	CCONJ
ejpam-804	241	11	p.c.b	p.c.b	NOUN
ejpam-804	241	12	.	.	PUNCT
ejpam-804	242	1	phillips	phillips	PROPN
ejpam-804	242	2	.	.	PUNCT
ejpam-804	243	1	band	band	PROPN
ejpam-804	243	2	spectral	spectral	ADJ
ejpam-804	243	3	regression	regression	NOUN
ejpam-804	243	4	with	with	ADP
ejpam-804	243	5	trending	trend	VERB
ejpam-804	243	6	data	datum	NOUN
ejpam-804	243	7	,	,	PUNCT
ejpam-804	243	8	econometrica	econometrica	PROPN
ejpam-804	243	9	,	,	PUNCT
ejpam-804	243	10	70	70	NUM
ejpam-804	243	11	,	,	PUNCT
ejpam-804	243	12	3	3	NUM
ejpam-804	243	13	,	,	PUNCT
ejpam-804	243	14	1067	1067	NUM
ejpam-804	243	15	-	-	SYM
ejpam-804	243	16	1109	1109	NUM
ejpam-804	243	17	,	,	PUNCT
ejpam-804	243	18	2002	2002	NUM
ejpam-804	243	19	.	.	PUNCT
ejpam-804	244	1	[	[	X
ejpam-804	244	2	4	4	NUM
ejpam-804	244	3	]	]	X
ejpam-804	244	4	r	r	NOUN
ejpam-804	244	5	dalhaus	dalhaus	NOUN
ejpam-804	244	6	.	.	PUNCT
ejpam-804	245	1	fitting	fitting	ADJ
ejpam-804	245	2	time	time	NOUN
ejpam-804	245	3	series	series	NOUN
ejpam-804	245	4	models	model	NOUN
ejpam-804	245	5	to	to	ADP
ejpam-804	245	6	nonstationary	nonstationary	ADJ
ejpam-804	245	7	processes	process	NOUN
ejpam-804	245	8	,	,	PUNCT
ejpam-804	245	9	the	the	DET
ejpam-804	245	10	annals	annal	NOUN
ejpam-804	245	11	of	of	ADP
ejpam-804	245	12	statistics	statistic	NOUN
ejpam-804	245	13	,	,	PUNCT
ejpam-804	245	14	25	25	NUM
ejpam-804	245	15	,	,	PUNCT
ejpam-804	245	16	1	1	NUM
ejpam-804	245	17	,	,	PUNCT
ejpam-804	245	18	1	1	NUM
ejpam-804	245	19	-	-	SYM
ejpam-804	245	20	37	37	NUM
ejpam-804	245	21	,	,	PUNCT
ejpam-804	245	22	1997	1997	NUM
ejpam-804	245	23	.	.	PUNCT
ejpam-804	246	1	[	[	X
ejpam-804	246	2	5	5	NUM
ejpam-804	246	3	]	]	X
ejpam-804	246	4	d	d	X
ejpam-804	246	5	dickey	dickey	PROPN
ejpam-804	246	6	and	and	CCONJ
ejpam-804	246	7	w	w	NOUN
ejpam-804	246	8	fuller	full	ADJ
ejpam-804	246	9	.	.	PUNCT
ejpam-804	247	1	distribution	distribution	NOUN
ejpam-804	247	2	of	of	ADP
ejpam-804	247	3	the	the	DET
ejpam-804	247	4	estimates	estimate	NOUN
ejpam-804	247	5	for	for	ADP
ejpam-804	247	6	autoregressive	autoregressive	ADJ
ejpam-804	247	7	time	time	NOUN
ejpam-804	247	8	series	series	NOUN
ejpam-804	247	9	with	with	ADP
ejpam-804	247	10	a	a	DET
ejpam-804	247	11	unit	unit	NOUN
ejpam-804	247	12	root	root	NOUN
ejpam-804	247	13	,	,	PUNCT
ejpam-804	247	14	journal	journal	NOUN
ejpam-804	247	15	of	of	ADP
ejpam-804	247	16	the	the	DET
ejpam-804	247	17	american	american	PROPN
ejpam-804	247	18	statistical	statistical	PROPN
ejpam-804	247	19	association	association	NOUN
ejpam-804	247	20	,	,	PUNCT
ejpam-804	247	21	74	74	NUM
ejpam-804	247	22	,	,	PUNCT
ejpam-804	247	23	427	427	NUM
ejpam-804	247	24	-	-	SYM
ejpam-804	247	25	31	31	NUM
ejpam-804	247	26	,	,	PUNCT
ejpam-804	247	27	1979	1979	NUM
ejpam-804	247	28	.	.	PUNCT
ejpam-804	248	1	[	[	X
ejpam-804	248	2	6	6	NUM
ejpam-804	248	3	]	]	SYM
ejpam-804	248	4	w	w	NOUN
ejpam-804	248	5	enders	ender	NOUN
ejpam-804	248	6	and	and	CCONJ
ejpam-804	248	7	j	j	PROPN
ejpam-804	248	8	ludlow	ludlow	PROPN
ejpam-804	248	9	.	.	PUNCT
ejpam-804	249	1	tests	test	NOUN
ejpam-804	249	2	for	for	ADP
ejpam-804	249	3	nonlinear	nonlinear	ADJ
ejpam-804	249	4	decay	decay	NOUN
ejpam-804	249	5	using	use	VERB
ejpam-804	249	6	a	a	DET
ejpam-804	249	7	fourier	fourier	NOUN
ejpam-804	249	8	approximation	approximation	NOUN
ejpam-804	249	9	,	,	PUNCT
ejpam-804	249	10	working	working	NOUN
ejpam-804	249	11	paper	paper	NOUN
ejpam-804	249	12	,	,	PUNCT
ejpam-804	249	13	department	department	NOUN
ejpam-804	249	14	of	of	ADP
ejpam-804	249	15	economics	economic	NOUN
ejpam-804	249	16	,	,	PUNCT
ejpam-804	249	17	finance	finance	NOUN
ejpam-804	249	18	and	and	CCONJ
ejpam-804	249	19	legal	legal	ADJ
ejpam-804	249	20	studies	study	NOUN
ejpam-804	249	21	,	,	PUNCT
ejpam-804	249	22	the	the	DET
ejpam-804	249	23	university	university	NOUN
ejpam-804	249	24	of	of	ADP
ejpam-804	249	25	alabama	alabama	PROPN
ejpam-804	249	26	,	,	PUNCT
ejpam-804	249	27	2002	2002	NUM
ejpam-804	249	28	.	.	PUNCT
ejpam-804	250	1	[	[	X
ejpam-804	250	2	7	7	NUM
ejpam-804	250	3	]	]	X
ejpam-804	250	4	r	r	NOUN
ejpam-804	250	5	engle	engle	NOUN
ejpam-804	250	6	and	and	CCONJ
ejpam-804	250	7	c	c	PROPN
ejpam-804	250	8	granger	granger	PROPN
ejpam-804	250	9	.	.	PUNCT
ejpam-804	250	10	cointegration	cointegration	NOUN
ejpam-804	250	11	and	and	CCONJ
ejpam-804	250	12	error	error	NOUN
ejpam-804	250	13	correction	correction	NOUN
ejpam-804	250	14	:	:	PUNCT
ejpam-804	250	15	representation	representation	NOUN
ejpam-804	250	16	,	,	PUNCT
ejpam-804	250	17	estimation	estimation	NOUN
ejpam-804	250	18	and	and	CCONJ
ejpam-804	250	19	testing	testing	NOUN
ejpam-804	250	20	,	,	PUNCT
ejpam-804	250	21	econometrica	econometrica	PROPN
ejpam-804	250	22	,	,	PUNCT
ejpam-804	250	23	55	55	NUM
ejpam-804	250	24	,	,	PUNCT
ejpam-804	250	25	251	251	NUM
ejpam-804	250	26	-	-	SYM
ejpam-804	250	27	76	76	NUM
ejpam-804	250	28	,	,	PUNCT
ejpam-804	250	29	1987	1987	NUM
ejpam-804	250	30	.	.	PUNCT
ejpam-804	251	1	references	reference	NOUN
ejpam-804	251	2	529	529	NUM
ejpam-804	251	3	[	[	X
ejpam-804	251	4	8	8	NUM
ejpam-804	251	5	]	]	X
ejpam-804	251	6	e	e	X
ejpam-804	251	7	gladyshev	gladyshev	PROPN
ejpam-804	251	8	.	.	PUNCT
ejpam-804	252	1	periodically	periodically	ADV
ejpam-804	252	2	correlated	correlate	VERB
ejpam-804	252	3	random	random	ADJ
ejpam-804	252	4	sequences	sequence	NOUN
ejpam-804	252	5	,	,	PUNCT
ejpam-804	252	6	soviet	soviet	ADJ
ejpam-804	252	7	mathematics	mathematic	NOUN
ejpam-804	252	8	,	,	PUNCT
ejpam-804	252	9	2	2	NUM
ejpam-804	252	10	,	,	PUNCT
ejpam-804	252	11	385	385	NUM
ejpam-804	252	12	-	-	SYM
ejpam-804	252	13	88	88	NUM
ejpam-804	252	14	,	,	PUNCT
ejpam-804	252	15	1961	1961	NUM
ejpam-804	252	16	.	.	PUNCT
ejpam-804	253	1	[	[	X
ejpam-804	253	2	9	9	NUM
ejpam-804	253	3	]	]	X
ejpam-804	253	4	s	s	PART
ejpam-804	253	5	gregoir	gregoir	PROPN
ejpam-804	253	6	.	.	PUNCT
ejpam-804	253	7	multivariate	multivariate	PROPN
ejpam-804	253	8	time	time	PROPN
ejpam-804	253	9	series	series	PROPN
ejpam-804	253	10	with	with	ADP
ejpam-804	253	11	various	various	ADJ
ejpam-804	253	12	hidden	hide	VERB
ejpam-804	253	13	unit	unit	NOUN
ejpam-804	253	14	roots	root	NOUN
ejpam-804	253	15	,	,	PUNCT
ejpam-804	253	16	part	part	NOUN
ejpam-804	253	17	i	i	PRON
ejpam-804	253	18	:	:	PUNCT
ejpam-804	253	19	integral	integral	ADJ
ejpam-804	253	20	operator	operator	NOUN
ejpam-804	253	21	algebra	algebra	NOUN
ejpam-804	253	22	and	and	CCONJ
ejpam-804	253	23	representation	representation	NOUN
ejpam-804	253	24	theorem	theorem	VERB
ejpam-804	253	25	.	.	PROPN
ejpam-804	253	26	econometric	econometric	PROPN
ejpam-804	253	27	theory	theory	NOUN
ejpam-804	253	28	,	,	PUNCT
ejpam-804	253	29	15	15	NUM
ejpam-804	253	30	,	,	PUNCT
ejpam-804	253	31	435	435	NUM
ejpam-804	253	32	-	-	SYM
ejpam-804	253	33	468	468	NUM
ejpam-804	253	34	,	,	PUNCT
ejpam-804	253	35	1999a	1999a	NUM
ejpam-804	253	36	.	.	PUNCT
ejpam-804	254	1	[	[	X
ejpam-804	254	2	10	10	NUM
ejpam-804	254	3	]	]	X
ejpam-804	254	4	s	s	PART
ejpam-804	254	5	gregoir	gregoir	PROPN
ejpam-804	254	6	.	.	PUNCT
ejpam-804	254	7	multivariate	multivariate	PROPN
ejpam-804	254	8	time	time	PROPN
ejpam-804	254	9	series	series	PROPN
ejpam-804	254	10	with	with	ADP
ejpam-804	254	11	various	various	ADJ
ejpam-804	254	12	hidden	hide	VERB
ejpam-804	254	13	unit	unit	NOUN
ejpam-804	254	14	roots	root	NOUN
ejpam-804	254	15	,	,	PUNCT
ejpam-804	254	16	part	part	PROPN
ejpam-804	254	17	ii	ii	PROPN
ejpam-804	254	18	:	:	PUNCT
ejpam-804	254	19	estimation	estimation	NOUN
ejpam-804	254	20	and	and	CCONJ
ejpam-804	254	21	testing	testing	NOUN
ejpam-804	254	22	.	.	PUNCT
ejpam-804	255	1	econometric	econometric	PROPN
ejpam-804	255	2	theory	theory	NOUN
ejpam-804	255	3	,	,	PUNCT
ejpam-804	255	4	15	15	NUM
ejpam-804	255	5	,	,	PUNCT
ejpam-804	255	6	469	469	NUM
ejpam-804	255	7	-	-	NUM
ejpam-804	255	8	518	518	NUM
ejpam-804	255	9	,	,	PUNCT
ejpam-804	255	10	1999b	1999b	NUM
ejpam-804	255	11	.	.	PUNCT
ejpam-804	256	1	[	[	X
ejpam-804	256	2	11	11	NUM
ejpam-804	256	3	]	]	X
ejpam-804	256	4	s	s	X
ejpam-804	256	5	gregoir	gregoir	NOUN
ejpam-804	256	6	and	and	CCONJ
ejpam-804	256	7	g	g	NOUN
ejpam-804	256	8	laroque	laroque	NOUN
ejpam-804	256	9	.	.	PUNCT
ejpam-804	257	1	multivariate	multivariate	NOUN
ejpam-804	257	2	time	time	NOUN
ejpam-804	257	3	series	series	PROPN
ejpam-804	257	4	:	:	PUNCT
ejpam-804	257	5	a	a	DET
ejpam-804	257	6	polynomial	polynomial	ADJ
ejpam-804	257	7	error	error	NOUN
ejpam-804	257	8	correction	correction	NOUN
ejpam-804	257	9	representation	representation	NOUN
ejpam-804	257	10	theorem	theorem	VERB
ejpam-804	257	11	.	.	PROPN
ejpam-804	257	12	econometric	econometric	PROPN
ejpam-804	257	13	theory	theory	NOUN
ejpam-804	257	14	,	,	PUNCT
ejpam-804	257	15	9	9	NUM
ejpam-804	257	16	,	,	PUNCT
ejpam-804	257	17	329	329	NUM
ejpam-804	257	18	-	-	SYM
ejpam-804	257	19	342	342	NUM
ejpam-804	257	20	,	,	PUNCT
ejpam-804	257	21	1993	1993	NUM
ejpam-804	257	22	.	.	PUNCT
ejpam-804	258	1	[	[	X
ejpam-804	258	2	12	12	NUM
ejpam-804	258	3	]	]	X
ejpam-804	258	4	d.	d.	PROPN
ejpam-804	258	5	harris	harris	PROPN
ejpam-804	258	6	,	,	PUNCT
ejpam-804	258	7	b	b	PROPN
ejpam-804	258	8	mccabe	mccabe	PROPN
ejpam-804	258	9	and	and	CCONJ
ejpam-804	258	10	s	s	VERB
ejpam-804	258	11	leybourne	leybourne	ADJ
ejpam-804	258	12	.	.	PUNCT
ejpam-804	259	1	stochastic	stochastic	ADJ
ejpam-804	259	2	cointegration	cointegration	NOUN
ejpam-804	259	3	:	:	PUNCT
ejpam-804	259	4	estimation	estimation	NOUN
ejpam-804	259	5	and	and	CCONJ
ejpam-804	259	6	inference	inference	NOUN
ejpam-804	259	7	,	,	PUNCT
ejpam-804	259	8	journal	journal	NOUN
ejpam-804	259	9	of	of	ADP
ejpam-804	259	10	econometrics	econometric	NOUN
ejpam-804	259	11	,	,	PUNCT
ejpam-804	259	12	111	111	NUM
ejpam-804	259	13	,	,	PUNCT
ejpam-804	259	14	2	2	NUM
ejpam-804	259	15	,	,	PUNCT
ejpam-804	259	16	363	363	NUM
ejpam-804	259	17	-	-	SYM
ejpam-804	259	18	384	384	NUM
ejpam-804	259	19	,	,	PUNCT
ejpam-804	259	20	2002	2002	NUM
ejpam-804	259	21	.	.	PUNCT
ejpam-804	260	1	[	[	X
ejpam-804	260	2	13	13	NUM
ejpam-804	260	3	]	]	SYM
ejpam-804	260	4	s	s	X
ejpam-804	261	1	johansen	johansen	PROPN
ejpam-804	261	2	.	.	PUNCT
ejpam-804	261	3	likelihood	likelihood	NOUN
ejpam-804	261	4	-	-	PUNCT
ejpam-804	261	5	based	base	VERB
ejpam-804	261	6	inference	inference	NOUN
ejpam-804	261	7	in	in	ADP
ejpam-804	261	8	cointegrated	cointegrate	VERB
ejpam-804	261	9	autoregressive	autoregressive	ADJ
ejpam-804	261	10	models	model	NOUN
ejpam-804	261	11	,	,	PUNCT
ejpam-804	261	12	oxford	oxford	PROPN
ejpam-804	261	13	:	:	PUNCT
ejpam-804	261	14	oxford	oxford	PROPN
ejpam-804	261	15	university	university	PROPN
ejpam-804	261	16	press	press	NOUN
ejpam-804	261	17	,	,	PUNCT
ejpam-804	261	18	1996	1996	NUM
ejpam-804	261	19	.	.	PUNCT
ejpam-804	262	1	[	[	X
ejpam-804	262	2	14	14	NUM
ejpam-804	262	3	]	]	X
ejpam-804	262	4	c	c	PROPN
ejpam-804	262	5	jordan	jordan	PROPN
ejpam-804	262	6	.	.	PUNCT
ejpam-804	263	1	calculus	calculus	PROPN
ejpam-804	263	2	of	of	ADP
ejpam-804	263	3	finite	finite	PROPN
ejpam-804	263	4	differences	difference	NOUN
ejpam-804	263	5	,	,	PUNCT
ejpam-804	263	6	2nd	2nd	ADJ
ejpam-804	263	7	ed	ed	NOUN
ejpam-804	263	8	.	.	PROPN
ejpam-804	263	9	,	,	PUNCT
ejpam-804	263	10	chelsea	chelsea	PROPN
ejpam-804	263	11	,	,	PUNCT
ejpam-804	263	12	1950	1950	NUM
ejpam-804	263	13	.	.	PUNCT
ejpam-804	264	1	[	[	X
ejpam-804	264	2	15	15	NUM
ejpam-804	264	3	]	]	X
ejpam-804	264	4	r	r	NOUN
ejpam-804	264	5	joyeux	joyeux	NOUN
ejpam-804	264	6	.	.	PUNCT
ejpam-804	265	1	slowly	slowly	ADV
ejpam-804	265	2	changing	change	VERB
ejpam-804	265	3	processes	process	NOUN
ejpam-804	265	4	and	and	CCONJ
ejpam-804	265	5	harmonizability	harmonizability	NOUN
ejpam-804	265	6	,	,	PUNCT
ejpam-804	265	7	journal	journal	NOUN
ejpam-804	265	8	of	of	ADP
ejpam-804	265	9	time	time	NOUN
ejpam-804	265	10	series	series	PROPN
ejpam-804	265	11	analysis	analysis	NOUN
ejpam-804	265	12	,	,	PUNCT
ejpam-804	265	13	8	8	NUM
ejpam-804	265	14	,	,	PUNCT
ejpam-804	265	15	4	4	NUM
ejpam-804	265	16	,	,	PUNCT
ejpam-804	265	17	425	425	NUM
ejpam-804	265	18	-	-	SYM
ejpam-804	265	19	431	431	NUM
ejpam-804	265	20	,	,	PUNCT
ejpam-804	265	21	1987	1987	NUM
ejpam-804	265	22	.	.	PUNCT
ejpam-804	266	1	[	[	X
ejpam-804	266	2	16	16	NUM
ejpam-804	266	3	]	]	X
ejpam-804	266	4	r	r	NOUN
ejpam-804	266	5	joyeux	joyeux	NOUN
ejpam-804	266	6	.	.	PUNCT
ejpam-804	267	1	tests	test	NOUN
ejpam-804	267	2	for	for	ADP
ejpam-804	267	3	seasonal	seasonal	ADJ
ejpam-804	267	4	cointegration	cointegration	NOUN
ejpam-804	267	5	using	use	VERB
ejpam-804	267	6	principal	principal	ADJ
ejpam-804	267	7	components	component	NOUN
ejpam-804	267	8	,	,	PUNCT
ejpam-804	267	9	journal	journal	NOUN
ejpam-804	267	10	of	of	ADP
ejpam-804	267	11	time	time	NOUN
ejpam-804	267	12	series	series	PROPN
ejpam-804	267	13	analysis	analysis	NOUN
ejpam-804	267	14	,	,	PUNCT
ejpam-804	267	15	13	13	NUM
ejpam-804	267	16	,	,	PUNCT
ejpam-804	267	17	2	2	NUM
ejpam-804	267	18	,	,	PUNCT
ejpam-804	267	19	109	109	NUM
ejpam-804	267	20	-	-	SYM
ejpam-804	267	21	118	118	NUM
ejpam-804	267	22	,	,	PUNCT
ejpam-804	267	23	1992	1992	NUM
ejpam-804	267	24	.	.	PUNCT
ejpam-804	268	1	[	[	X
ejpam-804	268	2	17	17	NUM
ejpam-804	268	3	]	]	X
ejpam-804	268	4	j	j	PROPN
ejpam-804	268	5	kampé	kampé	PROPN
ejpam-804	268	6	de	de	PROPN
ejpam-804	268	7	fériet	fériet	PROPN
ejpam-804	268	8	and	and	CCONJ
ejpam-804	268	9	f.n	f.n	PROPN
ejpam-804	268	10	.	.	PROPN
ejpam-804	268	11	frenkiel	frenkiel	PROPN
ejpam-804	268	12	.	.	PUNCT
ejpam-804	268	13	correlation	correlation	NOUN
ejpam-804	268	14	and	and	CCONJ
ejpam-804	268	15	spectra	spectra	NOUN
ejpam-804	268	16	of	of	ADP
ejpam-804	268	17	nonstationary	nonstationary	ADJ
ejpam-804	268	18	random	random	ADJ
ejpam-804	268	19	functions	function	NOUN
ejpam-804	268	20	,	,	PUNCT
ejpam-804	268	21	math	math	NOUN
ejpam-804	268	22	.	.	PUNCT
ejpam-804	269	1	comp	comp	PROPN
ejpam-804	269	2	.	.	PUNCT
ejpam-804	270	1	10	10	NUM
ejpam-804	270	2	,	,	PUNCT
ejpam-804	270	3	1	1	NUM
ejpam-804	270	4	-	-	SYM
ejpam-804	270	5	21	21	NUM
ejpam-804	270	6	,	,	PUNCT
ejpam-804	270	7	1962	1962	NUM
ejpam-804	270	8	.	.	PUNCT
ejpam-804	271	1	[	[	X
ejpam-804	271	2	18	18	NUM
ejpam-804	271	3	]	]	X
ejpam-804	271	4	k	k	PROPN
ejpam-804	271	5	lii	lii	PROPN
ejpam-804	271	6	and	and	CCONJ
ejpam-804	271	7	m	m	PROPN
ejpam-804	271	8	rosenblatt	rosenblatt	NOUN
ejpam-804	271	9	.	.	PUNCT
ejpam-804	272	1	linear	linear	PROPN
ejpam-804	272	2	spectral	spectral	ADJ
ejpam-804	272	3	analysis	analysis	NOUN
ejpam-804	272	4	for	for	ADP
ejpam-804	272	5	harmonizable	harmonizable	ADJ
ejpam-804	272	6	processes	process	NOUN
ejpam-804	272	7	,	,	PUNCT
ejpam-804	272	8	proceedings	proceeding	NOUN
ejpam-804	272	9	of	of	ADP
ejpam-804	272	10	the	the	DET
ejpam-804	272	11	national	national	PROPN
ejpam-804	272	12	academy	academy	PROPN
ejpam-804	272	13	of	of	ADP
ejpam-804	272	14	sciences	sciences	PROPN
ejpam-804	272	15	,	,	PUNCT
ejpam-804	272	16	usa	usa	PROPN
ejpam-804	272	17	,	,	PUNCT
ejpam-804	272	18	95	95	NUM
ejpam-804	272	19	,	,	PUNCT
ejpam-804	272	20	1	1	NUM
ejpam-804	272	21	-	-	SYM
ejpam-804	272	22	9	9	NUM
ejpam-804	272	23	,	,	PUNCT
ejpam-804	272	24	1998	1998	NUM
ejpam-804	272	25	.	.	PUNCT
ejpam-804	273	1	[	[	X
ejpam-804	273	2	19	19	NUM
ejpam-804	273	3	]	]	PUNCT
ejpam-804	273	4	m	m	VERB
ejpam-804	273	5	loéve	loéve	NOUN
ejpam-804	273	6	.	.	PUNCT
ejpam-804	274	1	probability	probability	NOUN
ejpam-804	274	2	theory	theory	NOUN
ejpam-804	274	3	,	,	PUNCT
ejpam-804	274	4	3rd	3rd	ADJ
ejpam-804	274	5	edition	edition	NOUN
ejpam-804	274	6	,	,	PUNCT
ejpam-804	274	7	princeton	princeton	PROPN
ejpam-804	274	8	:	:	PUNCT
ejpam-804	274	9	van	van	PROPN
ejpam-804	274	10	nostrand	nostrand	PROPN
ejpam-804	274	11	,	,	PUNCT
ejpam-804	274	12	1963	1963	NUM
ejpam-804	274	13	.	.	PUNCT
ejpam-804	275	1	[	[	X
ejpam-804	275	2	20	20	NUM
ejpam-804	275	3	]	]	PUNCT
ejpam-804	275	4	a	a	DET
ejpam-804	275	5	miamee	miamee	NOUN
ejpam-804	275	6	and	and	CCONJ
ejpam-804	275	7	h	h	NOUN
ejpam-804	275	8	salehi	salehi	NOUN
ejpam-804	275	9	.	.	PUNCT
ejpam-804	276	1	harmonizability	harmonizability	NOUN
ejpam-804	276	2	,	,	PUNCT
ejpam-804	276	3	v	v	NOUN
ejpam-804	276	4	-	-	PUNCT
ejpam-804	276	5	boundedness	boundedness	NOUN
ejpam-804	276	6	and	and	CCONJ
ejpam-804	276	7	stationary	stationary	ADJ
ejpam-804	276	8	dilation	dilation	NOUN
ejpam-804	276	9	of	of	ADP
ejpam-804	276	10	stochastic	stochastic	ADJ
ejpam-804	276	11	processes	process	NOUN
ejpam-804	276	12	,	,	PUNCT
ejpam-804	276	13	indiana	indiana	PROPN
ejpam-804	276	14	university	university	PROPN
ejpam-804	276	15	mathematical	mathematical	ADJ
ejpam-804	276	16	journal	journal	NOUN
ejpam-804	276	17	,	,	PUNCT
ejpam-804	276	18	27	27	NUM
ejpam-804	276	19	,	,	PUNCT
ejpam-804	276	20	37	37	NUM
ejpam-804	276	21	-	-	SYM
ejpam-804	276	22	50	50	NUM
ejpam-804	276	23	,	,	PUNCT
ejpam-804	276	24	1978	1978	NUM
ejpam-804	276	25	.	.	PUNCT
ejpam-804	277	1	[	[	X
ejpam-804	277	2	21	21	NUM
ejpam-804	277	3	]	]	X
ejpam-804	277	4	h	h	PROPN
ejpam-804	277	5	niemi	niemi	PROPN
ejpam-804	277	6	.	.	PUNCT
ejpam-804	278	1	stochastic	stochastic	ADJ
ejpam-804	278	2	processes	process	NOUN
ejpam-804	278	3	as	as	SCONJ
ejpam-804	278	4	fourier	fourier	NOUN
ejpam-804	278	5	transforms	transform	NOUN
ejpam-804	278	6	of	of	ADP
ejpam-804	278	7	stochastic	stochastic	ADJ
ejpam-804	278	8	measures	measure	NOUN
ejpam-804	278	9	,	,	PUNCT
ejpam-804	278	10	ann	ann	PROPN
ejpam-804	278	11	.	.	PUNCT
ejpam-804	278	12	acad	acad	PROPN
ejpam-804	278	13	.	.	PUNCT
ejpam-804	279	1	sci	sci	PROPN
ejpam-804	279	2	.	.	PUNCT
ejpam-804	279	3	fenn	fenn	PROPN
ejpam-804	279	4	.	.	PUNCT
ejpam-804	280	1	ai	ai	PROPN
ejpam-804	280	2	math	math	PROPN
ejpam-804	280	3	.	.	PUNCT
ejpam-804	281	1	,	,	PUNCT
ejpam-804	281	2	591	591	NUM
ejpam-804	281	3	,	,	PUNCT
ejpam-804	281	4	1	1	NUM
ejpam-804	281	5	-	-	SYM
ejpam-804	281	6	47	47	NUM
ejpam-804	281	7	,	,	PUNCT
ejpam-804	281	8	1975	1975	NUM
ejpam-804	281	9	.	.	PUNCT
ejpam-804	282	1	[	[	X
ejpam-804	282	2	22	22	NUM
ejpam-804	282	3	]	]	X
ejpam-804	282	4	e	e	X
ejpam-804	282	5	parzen	parzen	PROPN
ejpam-804	282	6	.	.	PUNCT
ejpam-804	283	1	spectral	spectral	ADJ
ejpam-804	283	2	analysis	analysis	NOUN
ejpam-804	283	3	of	of	ADP
ejpam-804	283	4	asymptotically	asymptotically	ADV
ejpam-804	283	5	stationary	stationary	ADJ
ejpam-804	283	6	time	time	NOUN
ejpam-804	283	7	series	series	PROPN
ejpam-804	283	8	,	,	PUNCT
ejpam-804	283	9	bulletin	bulletin	NOUN
ejpam-804	283	10	international	international	NOUN
ejpam-804	283	11	of	of	ADP
ejpam-804	283	12	the	the	DET
ejpam-804	283	13	statistical	statistical	ADJ
ejpam-804	283	14	institute	institute	NOUN
ejpam-804	283	15	,	,	PUNCT
ejpam-804	283	16	39	39	NUM
ejpam-804	283	17	,	,	PUNCT
ejpam-804	283	18	87	87	NUM
ejpam-804	283	19	-	-	SYM
ejpam-804	283	20	103	103	NUM
ejpam-804	283	21	,	,	PUNCT
ejpam-804	283	22	1962	1962	NUM
ejpam-804	283	23	.	.	PUNCT
ejpam-804	284	1	[	[	X
ejpam-804	284	2	23	23	NUM
ejpam-804	284	3	]	]	X
ejpam-804	284	4	m	m	VERB
ejpam-804	284	5	priestley	priestley	NOUN
ejpam-804	284	6	.	.	PUNCT
ejpam-804	285	1	evolutionary	evolutionary	ADJ
ejpam-804	285	2	spectra	spectra	PROPN
ejpam-804	285	3	and	and	CCONJ
ejpam-804	285	4	non	non	ADJ
ejpam-804	285	5	-	-	ADJ
ejpam-804	285	6	stationary	stationary	ADJ
ejpam-804	285	7	processes	process	NOUN
ejpam-804	285	8	,	,	PUNCT
ejpam-804	285	9	journal	journal	NOUN
ejpam-804	285	10	of	of	ADP
ejpam-804	285	11	the	the	DET
ejpam-804	285	12	royal	royal	ADJ
ejpam-804	285	13	statistical	statistical	ADJ
ejpam-804	285	14	society	society	NOUN
ejpam-804	285	15	,	,	PUNCT
ejpam-804	285	16	b	b	NOUN
ejpam-804	285	17	,	,	PUNCT
ejpam-804	285	18	27	27	NUM
ejpam-804	285	19	,	,	PUNCT
ejpam-804	285	20	204	204	NUM
ejpam-804	285	21	-	-	SYM
ejpam-804	285	22	237	237	NUM
ejpam-804	285	23	,	,	PUNCT
ejpam-804	285	24	1965	1965	NUM
ejpam-804	285	25	.	.	PUNCT
ejpam-804	286	1	[	[	X
ejpam-804	286	2	24	24	NUM
ejpam-804	286	3	]	]	SYM
ejpam-804	286	4	m	m	VERB
ejpam-804	286	5	priestley	priestley	NOUN
ejpam-804	286	6	and	and	CCONJ
ejpam-804	286	7	h	h	NOUN
ejpam-804	286	8	tong	tong	PROPN
ejpam-804	286	9	.	.	PUNCT
ejpam-804	287	1	on	on	ADP
ejpam-804	287	2	the	the	DET
ejpam-804	287	3	analysis	analysis	NOUN
ejpam-804	287	4	of	of	ADP
ejpam-804	287	5	bivariate	bivariate	ADJ
ejpam-804	287	6	non	non	ADJ
ejpam-804	287	7	-	-	ADJ
ejpam-804	287	8	stationary	stationary	ADJ
ejpam-804	287	9	processes	process	NOUN
ejpam-804	287	10	,	,	PUNCT
ejpam-804	287	11	journal	journal	NOUN
ejpam-804	287	12	of	of	ADP
ejpam-804	287	13	the	the	DET
ejpam-804	287	14	royal	royal	ADJ
ejpam-804	287	15	statistical	statistical	ADJ
ejpam-804	287	16	society	society	NOUN
ejpam-804	287	17	,	,	PUNCT
ejpam-804	287	18	b	b	NOUN
ejpam-804	287	19	,	,	PUNCT
ejpam-804	287	20	35	35	NUM
ejpam-804	287	21	,	,	PUNCT
ejpam-804	287	22	153	153	NUM
ejpam-804	287	23	-	-	SYM
ejpam-804	287	24	166	166	NUM
ejpam-804	287	25	and	and	CCONJ
ejpam-804	287	26	179	179	NUM
ejpam-804	287	27	-	-	SYM
ejpam-804	287	28	188	188	NUM
ejpam-804	287	29	,	,	PUNCT
ejpam-804	287	30	1973	1973	NUM
ejpam-804	287	31	.	.	PUNCT
ejpam-804	288	1	references	reference	NOUN
ejpam-804	288	2	530	530	NUM
ejpam-804	289	1	[	[	X
ejpam-804	289	2	25	25	NUM
ejpam-804	289	3	]	]	X
ejpam-804	289	4	m	m	VERB
ejpam-804	289	5	rao	rao	PROPN
ejpam-804	289	6	.	.	PUNCT
ejpam-804	290	1	covariance	covariance	VERB
ejpam-804	290	2	analysis	analysis	NOUN
ejpam-804	290	3	of	of	ADP
ejpam-804	290	4	some	some	DET
ejpam-804	290	5	nonstationary	nonstationary	ADJ
ejpam-804	290	6	time	time	NOUN
ejpam-804	290	7	series	series	PROPN
ejpam-804	290	8	,	,	PUNCT
ejpam-804	290	9	development	development	NOUN
ejpam-804	290	10	in	in	ADP
ejpam-804	290	11	statistics	statistic	NOUN
ejpam-804	290	12	,	,	PUNCT
ejpam-804	290	13	vol	vol	NOUN
ejpam-804	290	14	.	.	PROPN
ejpam-804	290	15	1	1	NUM
ejpam-804	290	16	,	,	PUNCT
ejpam-804	290	17	171	171	NUM
ejpam-804	290	18	-	-	SYM
ejpam-804	290	19	225	225	NUM
ejpam-804	290	20	,	,	PUNCT
ejpam-804	290	21	academic	academic	ADJ
ejpam-804	290	22	press	press	NOUN
ejpam-804	290	23	,	,	PUNCT
ejpam-804	290	24	new	new	PROPN
ejpam-804	290	25	york	york	PROPN
ejpam-804	290	26	,	,	PUNCT
ejpam-804	290	27	1978	1978	NUM
ejpam-804	290	28	.	.	PUNCT
ejpam-804	291	1	[	[	X
ejpam-804	291	2	26	26	NUM
ejpam-804	291	3	]	]	X
ejpam-804	291	4	m	m	VERB
ejpam-804	291	5	rao	rao	NOUN
ejpam-804	291	6	.	.	PUNCT
ejpam-804	292	1	harmonizable	harmonizable	ADJ
ejpam-804	292	2	processes	process	NOUN
ejpam-804	292	3	:	:	PUNCT
ejpam-804	292	4	structure	structure	NOUN
ejpam-804	292	5	theory	theory	NOUN
ejpam-804	292	6	,	,	PUNCT
ejpam-804	292	7	enseign	enseign	PROPN
ejpam-804	292	8	.	.	PUNCT
ejpam-804	293	1	math	math	NOUN
ejpam-804	293	2	.	.	PUNCT
ejpam-804	294	1	,	,	PUNCT
ejpam-804	294	2	28	28	NUM
ejpam-804	294	3	,	,	PUNCT
ejpam-804	294	4	295	295	NUM
ejpam-804	294	5	-	-	SYM
ejpam-804	294	6	351	351	NUM
ejpam-804	294	7	,	,	PUNCT
ejpam-804	294	8	1982	1982	NUM
ejpam-804	294	9	.	.	PUNCT
ejpam-804	295	1	[	[	X
ejpam-804	295	2	27	27	NUM
ejpam-804	295	3	]	]	X
ejpam-804	295	4	y	y	PROPN
ejpam-804	295	5	rozanov	rozanov	PROPN
ejpam-804	295	6	.	.	PUNCT
ejpam-804	296	1	spectral	spectral	ADJ
ejpam-804	296	2	analysis	analysis	NOUN
ejpam-804	296	3	of	of	ADP
ejpam-804	296	4	abstract	abstract	ADJ
ejpam-804	296	5	functions	function	NOUN
ejpam-804	296	6	,	,	PUNCT
ejpam-804	296	7	theory	theory	NOUN
ejpam-804	296	8	of	of	ADP
ejpam-804	296	9	probability	probability	NOUN
ejpam-804	296	10	and	and	CCONJ
ejpam-804	296	11	its	its	PRON
ejpam-804	296	12	applications	application	NOUN
ejpam-804	296	13	,	,	PUNCT
ejpam-804	296	14	4	4	NUM
ejpam-804	296	15	,	,	PUNCT
ejpam-804	296	16	271	271	NUM
ejpam-804	296	17	-	-	SYM
ejpam-804	296	18	287	287	NUM
ejpam-804	296	19	,	,	PUNCT
ejpam-804	296	20	1959	1959	NUM
ejpam-804	296	21	.	.	PUNCT
ejpam-804	297	1	[	[	X
ejpam-804	297	2	28	28	NUM
ejpam-804	297	3	]	]	X
ejpam-804	297	4	p	p	PROPN
ejpam-804	297	5	wong	wong	PROPN
ejpam-804	297	6	.	.	PUNCT
ejpam-804	297	7	wavelet	wavelet	NOUN
ejpam-804	297	8	decomposition	decomposition	NOUN
ejpam-804	297	9	of	of	ADP
ejpam-804	297	10	harmonizable	harmonizable	ADJ
ejpam-804	297	11	random	random	ADJ
ejpam-804	297	12	processes	process	NOUN
ejpam-804	297	13	,	,	PUNCT
ejpam-804	297	14	ieee	ieee	NOUN
ejpam-804	297	15	transactions	transaction	NOUN
ejpam-804	297	16	on	on	ADP
ejpam-804	297	17	information	information	NOUN
ejpam-804	297	18	theory	theory	NOUN
ejpam-804	297	19	,	,	PUNCT
ejpam-804	297	20	39	39	NUM
ejpam-804	297	21	,	,	PUNCT
ejpam-804	297	22	1	1	NUM
ejpam-804	297	23	,	,	PUNCT
ejpam-804	297	24	7	7	NUM
ejpam-804	297	25	-	-	SYM
ejpam-804	297	26	18	18	NUM
ejpam-804	297	27	,	,	PUNCT
ejpam-804	297	28	1993	1993	NUM
ejpam-804	297	29	.	.	PUNCT
ejpam-804	298	1	[	[	X
ejpam-804	298	2	29	29	NUM
ejpam-804	298	3	]	]	X
ejpam-804	298	4	a	a	DET
ejpam-804	298	5	yaglom	yaglom	NOUN
ejpam-804	298	6	.	.	PUNCT
ejpam-804	299	1	correlation	correlation	NOUN
ejpam-804	299	2	theory	theory	NOUN
ejpam-804	299	3	of	of	ADP
ejpam-804	299	4	stationary	stationary	ADJ
ejpam-804	299	5	and	and	CCONJ
ejpam-804	299	6	related	related	ADJ
ejpam-804	299	7	random	random	ADJ
ejpam-804	299	8	functions	function	NOUN
ejpam-804	299	9	:	:	PUNCT
ejpam-804	299	10	basic	basic	ADJ
ejpam-804	299	11	results	result	NOUN
ejpam-804	299	12	,	,	PUNCT
ejpam-804	299	13	i	i	PRON
ejpam-804	299	14	and	and	CCONJ
ejpam-804	299	15	ii	ii	PROPN
ejpam-804	299	16	,	,	PUNCT
ejpam-804	299	17	new	new	PROPN
ejpam-804	299	18	york	york	PROPN
ejpam-804	299	19	:	:	PUNCT
ejpam-804	299	20	springer	springer	NOUN
ejpam-804	299	21	verlag	verlag	PROPN
ejpam-804	299	22	,	,	PUNCT
ejpam-804	299	23	1986	1986	NUM
ejpam-804	299	24	.	.	PUNCT