id	sid	tid	token	lemma	pos
cusj-6360	1	1	buy	buy	VERB
cusj-6360	1	2	signal	signal	NOUN
cusj-6360	1	3	from	from	ADP
cusj-6360	1	4	limit	limit	NOUN
cusj-6360	1	5	theorem	theorem	VERB
cusj-6360	1	6	yiqiao	yiqiao	PROPN
cusj-6360	1	7	yin	yin	PROPN
cusj-6360	1	8	statistics	statistics	PROPN
cusj-6360	1	9	department	department	PROPN
cusj-6360	1	10	columbia	columbia	PROPN
cusj-6360	1	11	university	university	PROPN
cusj-6360	1	12	november	november	PROPN
cusj-6360	1	13	2	2	NUM
cusj-6360	1	14	,	,	PUNCT
cusj-6360	1	15	2017	2017	NUM
cusj-6360	1	16	abstract	abstract	ADJ
cusj-6360	1	17	this	this	DET
cusj-6360	1	18	paper	paper	NOUN
cusj-6360	1	19	studies	study	NOUN
cusj-6360	1	20	price	price	NOUN
cusj-6360	1	21	actions	action	NOUN
cusj-6360	1	22	in	in	ADP
cusj-6360	1	23	capital	capital	NOUN
cusj-6360	1	24	market	market	NOUN
cusj-6360	1	25	as	as	ADP
cusj-6360	1	26	a	a	DET
cusj-6360	1	27	random	random	ADJ
cusj-6360	1	28	walk	walk	NOUN
cusj-6360	1	29	from	from	ADP
cusj-6360	1	30	limit	limit	NOUN
cusj-6360	1	31	theorems	theorem	NOUN
cusj-6360	1	32	.	.	PUNCT
cusj-6360	2	1	through	through	ADP
cusj-6360	2	2	clear	clear	ADJ
cusj-6360	2	3	construction	construction	NOUN
cusj-6360	2	4	,	,	PUNCT
cusj-6360	2	5	we	we	PRON
cusj-6360	2	6	derive	derive	VERB
cusj-6360	2	7	algorithms	algorithm	NOUN
cusj-6360	2	8	from	from	ADP
cusj-6360	2	9	a	a	DET
cusj-6360	2	10	series	series	NOUN
cusj-6360	2	11	of	of	ADP
cusj-6360	2	12	theorems	theorem	NOUN
cusj-6360	2	13	to	to	PART
cusj-6360	2	14	create	create	VERB
cusj-6360	2	15	standardized	standardized	ADJ
cusj-6360	2	16	buy	buy	NOUN
cusj-6360	2	17	signals	signal	NOUN
cusj-6360	2	18	given	give	VERB
cusj-6360	2	19	a	a	DET
cusj-6360	2	20	trader	trader	NOUN
cusj-6360	2	21	’s	’s	PART
cusj-6360	2	22	committed	commit	VERB
cusj-6360	2	23	frequency	frequency	NOUN
cusj-6360	2	24	to	to	PART
cusj-6360	2	25	participate	participate	VERB
cusj-6360	2	26	in	in	ADP
cusj-6360	2	27	the	the	DET
cusj-6360	2	28	market	market	NOUN
cusj-6360	2	29	.	.	PUNCT
cusj-6360	3	1	1	1	NUM
cusj-6360	3	2	introduction	introduction	NOUN
cusj-6360	3	3	security	security	NOUN
cusj-6360	3	4	prices	price	NOUN
cusj-6360	3	5	follow	follow	VERB
cusj-6360	3	6	random	random	ADJ
cusj-6360	3	7	walk	walk	NOUN
cusj-6360	3	8	.	.	PUNCT
cusj-6360	4	1	although	although	SCONJ
cusj-6360	4	2	some	some	DET
cusj-6360	4	3	scholars	scholar	NOUN
cusj-6360	4	4	doubt	doubt	VERB
cusj-6360	4	5	the	the	DET
cusj-6360	4	6	concept	concept	NOUN
cusj-6360	4	7	of	of	ADP
cusj-6360	4	8	efficient	efficient	ADJ
cusj-6360	4	9	market	market	NOUN
cusj-6360	4	10	hypothesis	hypothesis	NOUN
cusj-6360	4	11	,	,	PUNCT
cusj-6360	4	12	there	there	PRON
cusj-6360	4	13	are	be	VERB
cusj-6360	4	14	fruitful	fruitful	ADJ
cusj-6360	4	15	amount	amount	NOUN
cusj-6360	4	16	of	of	ADP
cusj-6360	4	17	previous	previous	ADJ
cusj-6360	4	18	research	research	NOUN
cusj-6360	4	19	exploring	explore	VERB
cusj-6360	4	20	and	and	CCONJ
cusj-6360	4	21	studying	study	VERB
cusj-6360	4	22	this	this	DET
cusj-6360	4	23	topic	topic	NOUN
cusj-6360	4	24	.	.	PUNCT
cusj-6360	5	1	some	some	DET
cusj-6360	5	2	notable	notable	ADJ
cusj-6360	5	3	papers	paper	NOUN
cusj-6360	5	4	are	be	AUX
cusj-6360	5	5	by	by	ADP
cusj-6360	5	6	fama	fama	NOUN
cusj-6360	5	7	and	and	CCONJ
cusj-6360	5	8	french	french	ADJ
cusj-6360	5	9	[	[	X
cusj-6360	5	10	2	2	NUM
cusj-6360	5	11	]	]	PUNCT
cusj-6360	5	12	,	,	PUNCT
cusj-6360	5	13	[	[	X
cusj-6360	5	14	3	3	NUM
cusj-6360	5	15	]	]	PUNCT
cusj-6360	5	16	,	,	PUNCT
cusj-6360	5	17	[	[	X
cusj-6360	5	18	4	4	NUM
cusj-6360	5	19	]	]	PUNCT
cusj-6360	5	20	,	,	PUNCT
cusj-6360	5	21	and	and	CCONJ
cusj-6360	5	22	[	[	X
cusj-6360	5	23	5	5	NUM
cusj-6360	5	24	]	]	PUNCT
cusj-6360	5	25	.	.	PUNCT
cusj-6360	6	1	other	other	ADJ
cusj-6360	6	2	scholars	scholar	NOUN
cusj-6360	6	3	such	such	ADJ
cusj-6360	6	4	as	as	ADP
cusj-6360	6	5	malkiel	malkiel	PROPN
cusj-6360	6	6	have	have	AUX
cusj-6360	6	7	also	also	ADV
cusj-6360	6	8	provided	provide	VERB
cusj-6360	6	9	persuasive	persuasive	ADJ
cusj-6360	6	10	empirical	empirical	ADJ
cusj-6360	6	11	evidence	evidence	NOUN
cusj-6360	6	12	that	that	SCONJ
cusj-6360	6	13	we	we	PRON
cusj-6360	6	14	do	do	AUX
cusj-6360	6	15	observe	observe	VERB
cusj-6360	6	16	data	datum	NOUN
cusj-6360	6	17	in	in	ADP
cusj-6360	6	18	favor	favor	NOUN
cusj-6360	6	19	of	of	ADP
cusj-6360	6	20	efficient	efficient	ADJ
cusj-6360	6	21	market	market	NOUN
cusj-6360	6	22	hypothesis	hypothesis	NOUN
cusj-6360	6	23	[	[	X
cusj-6360	6	24	6	6	NUM
cusj-6360	6	25	]	]	PUNCT
cusj-6360	6	26	.	.	PUNCT
cusj-6360	7	1	an	an	DET
cusj-6360	7	2	important	important	ADJ
cusj-6360	7	3	contribution	contribution	NOUN
cusj-6360	7	4	from	from	ADP
cusj-6360	7	5	yin	yin	PROPN
cusj-6360	7	6	(	(	PUNCT
cusj-6360	7	7	2017	2017	NUM
cusj-6360	7	8	)	)	PUNCT
cusj-6360	8	1	[	[	X
cusj-6360	8	2	7	7	X
cusj-6360	8	3	]	]	PUNCT
cusj-6360	8	4	was	be	AUX
cusj-6360	8	5	the	the	DET
cusj-6360	8	6	idea	idea	NOUN
cusj-6360	8	7	and	and	CCONJ
cusj-6360	8	8	theoretical	theoretical	ADJ
cusj-6360	8	9	notion	notion	NOUN
cusj-6360	8	10	of	of	ADP
cusj-6360	8	11	optimal	optimal	ADJ
cusj-6360	8	12	level	level	NOUN
cusj-6360	8	13	in	in	ADP
cusj-6360	8	14	security	security	NOUN
cusj-6360	8	15	prices	price	NOUN
cusj-6360	8	16	.	.	PUNCT
cusj-6360	9	1	their	their	PRON
cusj-6360	9	2	work	work	NOUN
cusj-6360	9	3	raised	raise	VERB
cusj-6360	9	4	a	a	DET
cusj-6360	9	5	concept	concept	NOUN
cusj-6360	9	6	that	that	SCONJ
cusj-6360	9	7	the	the	DET
cusj-6360	9	8	anomaly	anomaly	NOUN
cusj-6360	9	9	prices	price	NOUN
cusj-6360	9	10	can	can	AUX
cusj-6360	9	11	be	be	AUX
cusj-6360	9	12	corrected	correct	VERB
cusj-6360	9	13	which	which	PRON
cusj-6360	9	14	was	be	AUX
cusj-6360	9	15	a	a	DET
cusj-6360	9	16	notion	notion	NOUN
cusj-6360	9	17	not	not	PART
cusj-6360	9	18	yet	yet	ADV
cusj-6360	9	19	discovered	discover	VERB
cusj-6360	9	20	in	in	ADP
cusj-6360	9	21	the	the	DET
cusj-6360	9	22	field	field	NOUN
cusj-6360	9	23	of	of	ADP
cusj-6360	9	24	probabilistic	probabilistic	ADJ
cusj-6360	9	25	price	price	NOUN
cusj-6360	9	26	analysis	analysis	NOUN
cusj-6360	9	27	.	.	PUNCT
cusj-6360	10	1	we	we	PRON
cusj-6360	10	2	took	take	VERB
cusj-6360	10	3	this	this	DET
cusj-6360	10	4	notion	notion	NOUN
cusj-6360	10	5	as	as	ADP
cusj-6360	10	6	a	a	DET
cusj-6360	10	7	foundation	foundation	NOUN
cusj-6360	10	8	and	and	CCONJ
cusj-6360	10	9	further	far	ADV
cusj-6360	10	10	explore	explore	VERB
cusj-6360	10	11	this	this	DET
cusj-6360	10	12	field	field	NOUN
cusj-6360	10	13	of	of	ADP
cusj-6360	10	14	security	security	NOUN
cusj-6360	10	15	price	price	NOUN
cusj-6360	10	16	random	random	ADJ
cusj-6360	10	17	walk	walk	NOUN
cusj-6360	10	18	.	.	PUNCT
cusj-6360	11	1	we	we	PRON
cusj-6360	11	2	discovered	discover	VERB
cusj-6360	11	3	that	that	SCONJ
cusj-6360	11	4	a	a	DET
cusj-6360	11	5	series	series	NOUN
cusj-6360	11	6	of	of	ADP
cusj-6360	11	7	constructions	construction	NOUN
cusj-6360	11	8	can	can	AUX
cusj-6360	11	9	be	be	AUX
cusj-6360	11	10	built	build	VERB
cusj-6360	11	11	to	to	PART
cusj-6360	11	12	form	form	VERB
cusj-6360	11	13	standard	standard	ADJ
cusj-6360	11	14	normal	normal	ADJ
cusj-6360	11	15	distributions	distribution	NOUN
cusj-6360	11	16	.	.	PUNCT
cusj-6360	12	1	we	we	PRON
cusj-6360	12	2	will	will	AUX
cusj-6360	12	3	further	far	ADV
cusj-6360	12	4	prove	prove	VERB
cusj-6360	12	5	these	these	DET
cusj-6360	12	6	results	result	NOUN
cusj-6360	12	7	(	(	PUNCT
cusj-6360	12	8	see	see	VERB
cusj-6360	12	9	appendix	appendix	NOUN
cusj-6360	12	10	)	)	PUNCT
cusj-6360	12	11	and	and	CCONJ
cusj-6360	12	12	develop	develop	VERB
cusj-6360	12	13	a	a	DET
cusj-6360	12	14	series	series	NOUN
cusj-6360	12	15	of	of	ADP
cusj-6360	12	16	trade	trade	NOUN
cusj-6360	12	17	-	-	PUNCT
cusj-6360	12	18	able	able	ADJ
cusj-6360	12	19	signals	signal	NOUN
cusj-6360	12	20	from	from	ADP
cusj-6360	12	21	these	these	DET
cusj-6360	12	22	theories	theory	NOUN
cusj-6360	12	23	.	.	PUNCT
cusj-6360	13	1	the	the	DET
cusj-6360	13	2	hunger	hunger	NOUN
cusj-6360	13	3	for	for	ADP
cusj-6360	13	4	this	this	DET
cusj-6360	13	5	type	type	NOUN
cusj-6360	13	6	of	of	ADP
cusj-6360	13	7	work	work	NOUN
cusj-6360	13	8	is	be	AUX
cusj-6360	13	9	necessary	necessary	ADJ
cusj-6360	13	10	for	for	ADP
cusj-6360	13	11	the	the	DET
cusj-6360	13	12	industry	industry	NOUN
cusj-6360	13	13	because	because	SCONJ
cusj-6360	13	14	conventional	conventional	ADJ
cusj-6360	13	15	asset	asset	NOUN
cusj-6360	13	16	pricing	pricing	NOUN
cusj-6360	13	17	models	model	NOUN
cusj-6360	13	18	do	do	AUX
cusj-6360	13	19	not	not	PART
cusj-6360	13	20	signal	signal	VERB
cusj-6360	13	21	buyers	buyer	NOUN
cusj-6360	13	22	when	when	SCONJ
cusj-6360	13	23	to	to	PART
cusj-6360	13	24	involve	involve	VERB
cusj-6360	13	25	in	in	ADP
cusj-6360	13	26	the	the	DET
cusj-6360	13	27	market	market	NOUN
cusj-6360	13	28	.	.	PUNCT
cusj-6360	14	1	moreover	moreover	ADV
cusj-6360	14	2	,	,	PUNCT
cusj-6360	14	3	for	for	ADP
cusj-6360	14	4	retail	retail	ADJ
cusj-6360	14	5	traders	trader	NOUN
cusj-6360	14	6	with	with	ADP
cusj-6360	14	7	a	a	DET
cusj-6360	14	8	fixed	fix	VERB
cusj-6360	14	9	trading	trading	NOUN
cusj-6360	14	10	frequency	frequency	NOUN
cusj-6360	14	11	(	(	PUNCT
cusj-6360	14	12	assuming	assume	VERB
cusj-6360	14	13	rational	rational	ADJ
cusj-6360	14	14	retail	retail	ADJ
cusj-6360	14	15	traders	trader	NOUN
cusj-6360	14	16	)	)	PUNCT
cusj-6360	14	17	,	,	PUNCT
cusj-6360	14	18	it	it	PRON
cusj-6360	14	19	only	only	ADV
cusj-6360	14	20	makes	make	VERB
cusj-6360	14	21	sense	sense	NOUN
cusj-6360	14	22	for	for	SCONJ
cusj-6360	14	23	them	they	PRON
cusj-6360	14	24	to	to	PART
cusj-6360	14	25	participate	participate	VERB
cusj-6360	14	26	in	in	ADP
cusj-6360	14	27	the	the	DET
cusj-6360	14	28	“	"	PUNCT
cusj-6360	14	29	low	low	ADJ
cusj-6360	14	30	”	"	PUNCT
cusj-6360	14	31	prices	price	NOUN
cusj-6360	14	32	consistent	consistent	ADJ
cusj-6360	14	33	with	with	ADP
cusj-6360	14	34	their	their	PRON
cusj-6360	14	35	frequency	frequency	NOUN
cusj-6360	14	36	.	.	PUNCT
cusj-6360	15	1	there	there	PRON
cusj-6360	15	2	is	be	VERB
cusj-6360	15	3	currently	currently	ADV
cusj-6360	15	4	no	no	DET
cusj-6360	15	5	models	model	NOUN
cusj-6360	15	6	presenting	present	VERB
cusj-6360	15	7	us	we	PRON
cusj-6360	15	8	any	any	DET
cusj-6360	15	9	algorithms	algorithm	NOUN
cusj-6360	15	10	in	in	ADP
cusj-6360	15	11	that	that	DET
cusj-6360	15	12	sort	sort	NOUN
cusj-6360	15	13	.	.	PUNCT
cusj-6360	16	1	this	this	PRON
cusj-6360	16	2	motivates	motivate	VERB
cusj-6360	16	3	us	we	PRON
cusj-6360	16	4	to	to	PART
cusj-6360	16	5	formalize	formalize	VERB
cusj-6360	16	6	these	these	DET
cusj-6360	16	7	algorithms	algorithm	NOUN
cusj-6360	16	8	from	from	ADP
cusj-6360	16	9	theorems	theorem	NOUN
cusj-6360	16	10	we	we	PRON
cusj-6360	16	11	developed	develop	VERB
cusj-6360	16	12	and	and	CCONJ
cusj-6360	16	13	we	we	PRON
cusj-6360	16	14	aim	aim	VERB
cusj-6360	16	15	to	to	PART
cusj-6360	16	16	provide	provide	VERB
cusj-6360	16	17	traders	trader	NOUN
cusj-6360	16	18	a	a	DET
cusj-6360	16	19	consistent	consistent	ADJ
cusj-6360	16	20	buy	buy	VERB
cusj-6360	16	21	strategy	strategy	NOUN
cusj-6360	16	22	so	so	SCONJ
cusj-6360	16	23	that	that	SCONJ
cusj-6360	16	24	one	one	PRON
cusj-6360	16	25	can	can	AUX
cusj-6360	16	26	trade	trade	VERB
cusj-6360	16	27	,	,	PUNCT
cusj-6360	16	28	whatever	whatever	DET
cusj-6360	16	29	strategy	strategy	NOUN
cusj-6360	16	30	one	one	NUM
cusj-6360	16	31	trades	trade	NOUN
cusj-6360	16	32	,	,	PUNCT
cusj-6360	16	33	at	at	ADP
cusj-6360	16	34	a	a	DET
cusj-6360	16	35	systematically	systematically	ADV
cusj-6360	16	36	low	low	ADJ
cusj-6360	16	37	price	price	NOUN
cusj-6360	16	38	.	.	PUNCT
cusj-6360	17	1	2	2	NUM
cusj-6360	17	2	theoretical	theoretical	ADJ
cusj-6360	17	3	framework	framework	NOUN
cusj-6360	17	4	in	in	ADP
cusj-6360	17	5	this	this	DET
cusj-6360	17	6	section	section	NOUN
cusj-6360	17	7	,	,	PUNCT
cusj-6360	17	8	we	we	PRON
cusj-6360	17	9	first	first	ADV
cusj-6360	17	10	present	present	ADJ
cusj-6360	17	11	,	,	PUNCT
cusj-6360	17	12	in	in	ADP
cusj-6360	17	13	§	§	NOUN
cusj-6360	17	14	2.1	2.1	NUM
cusj-6360	17	15	,	,	PUNCT
cusj-6360	17	16	the	the	DET
cusj-6360	17	17	architecture	architecture	NOUN
cusj-6360	17	18	of	of	ADP
cusj-6360	17	19	the	the	DET
cusj-6360	17	20	theorems	theorem	NOUN
cusj-6360	17	21	,	,	PUNCT
cusj-6360	17	22	which	which	PRON
cusj-6360	17	23	are	be	AUX
cusj-6360	17	24	discussed	discuss	VERB
cusj-6360	17	25	in	in	ADP
cusj-6360	17	26	§	§	PROPN
cusj-6360	17	27	2.2	2.2	NUM
cusj-6360	17	28	.	.	PUNCT
cusj-6360	18	1	we	we	PRON
cusj-6360	18	2	formalize	formalize	VERB
cusj-6360	18	3	the	the	DET
cusj-6360	18	4	theorems	theorem	NOUN
cusj-6360	18	5	based	base	VERB
cusj-6360	18	6	on	on	ADP
cusj-6360	18	7	the	the	DET
cusj-6360	18	8	notion	notion	NOUN
cusj-6360	18	9	of	of	ADP
cusj-6360	18	10	central	central	ADJ
cusj-6360	18	11	limit	limit	NOUN
cusj-6360	18	12	theorems	theorem	NOUN
cusj-6360	18	13	,	,	PUNCT
cusj-6360	18	14	which	which	PRON
cusj-6360	18	15	are	be	AUX
cusj-6360	18	16	proved	prove	VERB
cusj-6360	18	17	in	in	ADP
cusj-6360	18	18	respect	respect	NOUN
cusj-6360	18	19	to	to	ADP
cusj-6360	18	20	the	the	DET
cusj-6360	18	21	order	order	NOUN
cusj-6360	18	22	of	of	ADP
cusj-6360	18	23	theorems	theorem	NOUN
cusj-6360	18	24	in	in	ADP
cusj-6360	18	25	§	§	NOUN
cusj-6360	18	26	5	5	NUM
cusj-6360	18	27	appendix	appendix	NOUN
cusj-6360	18	28	.	.	PUNCT
cusj-6360	19	1	continuing	continue	VERB
cusj-6360	19	2	from	from	ADP
cusj-6360	19	3	the	the	DET
cusj-6360	19	4	proved	proved	ADJ
cusj-6360	19	5	theorems	theorem	NOUN
cusj-6360	19	6	,	,	PUNCT
cusj-6360	19	7	we	we	PRON
cusj-6360	19	8	provide	provide	VERB
cusj-6360	19	9	the	the	DET
cusj-6360	19	10	construction	construction	NOUN
cusj-6360	19	11	of	of	ADP
cusj-6360	19	12	a	a	DET
cusj-6360	19	13	series	series	NOUN
cusj-6360	19	14	of	of	ADP
cusj-6360	19	15	algorithms	algorithm	NOUN
cusj-6360	19	16	in	in	ADP
cusj-6360	19	17	§	§	PROPN
cusj-6360	19	18	3	3	NUM
cusj-6360	19	19	.	.	NOUN
cusj-6360	19	20	2.1	2.1	NUM
cusj-6360	19	21	architecture	architecture	NOUN
cusj-6360	19	22	definition	definition	NOUN
cusj-6360	19	23	2.1.1	2.1.1	NUM
cusj-6360	19	24	.	.	PUNCT
cusj-6360	20	1	for	for	ADP
cusj-6360	20	2	each	each	DET
cusj-6360	20	3	company	company	NOUN
cusj-6360	20	4	i	i	PRON
cusj-6360	20	5	at	at	ADP
cusj-6360	20	6	a	a	DET
cusj-6360	20	7	time	time	NOUN
cusj-6360	20	8	t	t	NOUN
cusj-6360	20	9	,	,	PUNCT
cusj-6360	20	10	we	we	PRON
cusj-6360	20	11	observe	observe	VERB
cusj-6360	20	12	a	a	DET
cusj-6360	20	13	price	price	NOUN
cusj-6360	20	14	,	,	PUNCT
cusj-6360	20	15	that	that	ADV
cusj-6360	20	16	is	is	ADV
cusj-6360	20	17	,	,	PUNCT
cusj-6360	20	18	pi	pi	PROPN
cusj-6360	20	19	,	,	PUNCT
cusj-6360	20	20	t	t	PROPN
cusj-6360	20	21	(	(	PUNCT
cusj-6360	20	22	2.1.1	2.1.1	NUM
cusj-6360	20	23	)	)	PUNCT
cusj-6360	20	24	definition	definition	NOUN
cusj-6360	20	25	2.1.2	2.1.2	NUM
cusj-6360	20	26	.	.	PUNCT
cusj-6360	20	27	sman	sman	NOUN
cusj-6360	20	28	=	=	SYM
cusj-6360	20	29	1	1	NUM
cusj-6360	20	30	n	n	NUM
cusj-6360	20	31	t−n∑	t−n∑	NOUN
cusj-6360	21	1	i	i	NOUN
cusj-6360	21	2	=	=	NOUN
cusj-6360	21	3	n	n	NUM
cusj-6360	21	4	pi	pi	NOUN
cusj-6360	21	5	,	,	PUNCT
cusj-6360	21	6	t−n	t−n	NOUN
cusj-6360	21	7	(	(	PUNCT
cusj-6360	21	8	2.1.2	2.1.2	NUM
cusj-6360	21	9	)	)	PUNCT
cusj-6360	21	10	definition	definition	NOUN
cusj-6360	21	11	2.1.3	2.1.3	NUM
cusj-6360	21	12	.	.	PUNCT
cusj-6360	22	1	let	let	VERB
cusj-6360	22	2	n	n	PRON
cusj-6360	22	3	be	be	AUX
cusj-6360	22	4	the	the	DET
cusj-6360	22	5	same	same	ADJ
cusj-6360	22	6	value	value	NOUN
cusj-6360	22	7	from	from	ADP
cusj-6360	22	8	definition	definition	NOUN
cusj-6360	22	9	2.1.2	2.1.2	NUM
cusj-6360	22	10	,	,	PUNCT
cusj-6360	22	11	denote	denote	VERB
cusj-6360	22	12	eman	eman	NOUN
cusj-6360	22	13	=	=	SYM
cusj-6360	22	14	(	(	PUNCT
cusj-6360	22	15	pi	pi	NOUN
cusj-6360	22	16	,	,	PUNCT
cusj-6360	22	17	t	t	NOUN
cusj-6360	22	18	−	−	PROPN
cusj-6360	22	19	eman−1)×m+	eman−1)×m+	NOUN
cusj-6360	22	20	eman−1	eman−1	PROPN
cusj-6360	22	21	(	(	PUNCT
cusj-6360	22	22	2.1.3	2.1.3	NUM
cusj-6360	22	23	)	)	PUNCT
cusj-6360	22	24	while	while	SCONJ
cusj-6360	22	25	m	m	VERB
cusj-6360	22	26	=	=	SYM
cusj-6360	22	27	2	2	NUM
cusj-6360	22	28	n+1	n+1	NUM
cusj-6360	22	29	.	.	PUNCT
cusj-6360	23	1	2.2	2.2	NUM
cusj-6360	23	2	theories	theory	NOUN
cusj-6360	23	3	theorem	theorem	VERB
cusj-6360	23	4	2.2.1	2.2.1	NUM
cusj-6360	23	5	.	.	PUNCT
cusj-6360	24	1	for	for	ADP
cusj-6360	24	2	some	some	DET
cusj-6360	24	3	n	n	NOUN
cusj-6360	24	4	,	,	PUNCT
cusj-6360	24	5	suppose	suppose	VERB
cusj-6360	24	6	we	we	PRON
cusj-6360	24	7	have	have	VERB
cusj-6360	24	8	price	price	NOUN
cusj-6360	24	9	by	by	ADP
cusj-6360	24	10	definition	definition	NOUN
cusj-6360	24	11	2.1.1	2.1.1	NUM
cusj-6360	24	12	and	and	CCONJ
cusj-6360	24	13	sma	sma	VERB
cusj-6360	24	14	by	by	ADP
cusj-6360	24	15	definition	definition	NOUN
cusj-6360	24	16	2.1.2	2.1.2	NUM
cusj-6360	24	17	,	,	PUNCT
cusj-6360	24	18	then	then	ADV
cusj-6360	24	19	we	we	PRON
cusj-6360	24	20	have	have	VERB
cusj-6360	24	21	pi	pi	NOUN
cusj-6360	24	22	,	,	PUNCT
cusj-6360	24	23	n	n	CCONJ
cusj-6360	24	24	−	−	PROPN
cusj-6360	24	25	sman	sman	ADJ
cusj-6360	24	26	⇒	⇒	VERB
cusj-6360	24	27	χ	χ	X
cusj-6360	24	28	(	(	PUNCT
cusj-6360	24	29	2.2.1	2.2.1	NUM
cusj-6360	24	30	)	)	PUNCT
cusj-6360	24	31	while	while	SCONJ
cusj-6360	24	32	χ	χ	NOUN
cusj-6360	24	33	is	be	AUX
cusj-6360	24	34	the	the	DET
cusj-6360	24	35	stand	stand	VERB
cusj-6360	24	36	normal	normal	ADJ
cusj-6360	24	37	distribution	distribution	NOUN
cusj-6360	24	38	.	.	PUNCT
cusj-6360	25	1	theorem	theorem	NOUN
cusj-6360	25	2	2.2.2	2.2.2	NUM
cusj-6360	25	3	.	.	PUNCT
cusj-6360	26	1	let	let	VERB
cusj-6360	26	2	the	the	DET
cusj-6360	26	3	distance	distance	NOUN
cusj-6360	26	4	between	between	ADP
cusj-6360	26	5	price	price	NOUN
cusj-6360	26	6	and	and	CCONJ
cusj-6360	26	7	moving	move	VERB
cusj-6360	26	8	average	average	ADJ
cusj-6360	26	9	to	to	PART
cusj-6360	26	10	be	be	AUX
cusj-6360	26	11	d	d	ADP
cusj-6360	26	12	which	which	PRON
cusj-6360	26	13	is	be	AUX
cusj-6360	26	14	defined	define	VERB
cusj-6360	26	15	as	as	ADP
cusj-6360	26	16	di	di	NOUN
cusj-6360	26	17	:	:	PUNCT
cusj-6360	26	18	=	=	SYM
cusj-6360	26	19	pn	pn	PROPN
cusj-6360	26	20	−	−	PROPN
cusj-6360	26	21	sman	sman	NOUN
cusj-6360	26	22	while	while	SCONJ
cusj-6360	26	23	i	i	PRON
cusj-6360	26	24	=	=	SYM
cusj-6360	26	25	n	n	CCONJ
cusj-6360	26	26	,	,	PUNCT
cusj-6360	26	27	and	and	CCONJ
cusj-6360	26	28	then	then	ADV
cusj-6360	26	29	we	we	PRON
cusj-6360	26	30	can	can	AUX
cusj-6360	26	31	consider	consider	VERB
cusj-6360	26	32	di	di	NOUN
cusj-6360	26	33	to	to	PART
cusj-6360	26	34	be	be	AUX
cusj-6360	26	35	i.i.d	i.i.d	ADJ
cusj-6360	26	36	.	.	PUNCT
cusj-6360	27	1	with	with	ADP
cusj-6360	27	2	edi	edi	PROPN
cusj-6360	27	3	=	=	SYM
cusj-6360	27	4	0	0	PROPN
cusj-6360	27	5	and	and	CCONJ
cusj-6360	27	6	edi	edi	PROPN
cusj-6360	27	7	=	=	PROPN
cusj-6360	27	8	σ2	σ2	PROPN
cusj-6360	27	9	∈	∈	PROPN
cusj-6360	27	10	(	(	PUNCT
cusj-6360	27	11	0,∞	0,∞	NUM
cusj-6360	27	12	)	)	PUNCT
cusj-6360	27	13	.	.	PUNCT
cusj-6360	28	1	then	then	ADV
cusj-6360	28	2	n∑	n∑	INTJ
cusj-6360	28	3	m=1	m=1	X
cusj-6360	29	1	dm	dm	INTJ
cusj-6360	29	2	/	/	SYM
cusj-6360	29	3	(	(	PUNCT
cusj-6360	29	4	n∑	n∑	PROPN
cusj-6360	29	5	m=1	m=1	PROPN
cusj-6360	29	6	d2	d2	PROPN
cusj-6360	29	7	m	m	PROPN
cusj-6360	29	8	)	)	PUNCT
cusj-6360	29	9	1/2	1/2	NUM
cusj-6360	29	10	⇒	⇒	NOUN
cusj-6360	29	11	χ	χ	X
cusj-6360	29	12	(	(	PUNCT
cusj-6360	29	13	2.2.2	2.2.2	NUM
cusj-6360	29	14	)	)	PUNCT
cusj-6360	29	15	while	while	SCONJ
cusj-6360	29	16	χ	χ	NOUN
cusj-6360	29	17	is	be	AUX
cusj-6360	29	18	the	the	DET
cusj-6360	29	19	stand	stand	VERB
cusj-6360	29	20	normal	normal	ADJ
cusj-6360	29	21	distribution	distribution	NOUN
cusj-6360	29	22	.	.	PUNCT
cusj-6360	30	1	theorem	theorem	ADJ
cusj-6360	30	2	2.2.3	2.2.3	NUM
cusj-6360	30	3	.	.	PUNCT
cusj-6360	31	1	let	let	VERB
cusj-6360	31	2	the	the	DET
cusj-6360	31	3	distance	distance	NOUN
cusj-6360	31	4	between	between	ADP
cusj-6360	31	5	price	price	NOUN
cusj-6360	31	6	and	and	CCONJ
cusj-6360	31	7	moving	move	VERB
cusj-6360	31	8	average	average	ADJ
cusj-6360	31	9	to	to	PART
cusj-6360	31	10	be	be	AUX
cusj-6360	31	11	d	d	ADP
cusj-6360	31	12	which	which	PRON
cusj-6360	31	13	is	be	AUX
cusj-6360	31	14	defined	define	VERB
cusj-6360	31	15	as	as	ADP
cusj-6360	31	16	di	di	NOUN
cusj-6360	31	17	:	:	PUNCT
cusj-6360	31	18	=	=	SYM
cusj-6360	31	19	pn	pn	PROPN
cusj-6360	31	20	−	−	PROPN
cusj-6360	31	21	sman	sman	NOUN
cusj-6360	31	22	while	while	SCONJ
cusj-6360	31	23	i	i	PRON
cusj-6360	31	24	=	=	SYM
cusj-6360	31	25	n	n	CCONJ
cusj-6360	31	26	,	,	PUNCT
cusj-6360	31	27	and	and	CCONJ
cusj-6360	31	28	then	then	ADV
cusj-6360	31	29	we	we	PRON
cusj-6360	31	30	can	can	AUX
cusj-6360	31	31	consider	consider	VERB
cusj-6360	31	32	di	di	NOUN
cusj-6360	31	33	to	to	PART
cusj-6360	31	34	be	be	AUX
cusj-6360	31	35	i.i.d	i.i.d	ADJ
cusj-6360	31	36	.	.	PUNCT
cusj-6360	32	1	with	with	ADP
cusj-6360	32	2	edi	edi	PROPN
cusj-6360	32	3	=	=	SYM
cusj-6360	32	4	0	0	PROPN
cusj-6360	32	5	and	and	CCONJ
cusj-6360	32	6	edi	edi	PROPN
cusj-6360	32	7	=	=	PROPN
cusj-6360	32	8	σ2	σ2	PROPN
cusj-6360	32	9	∈	∈	PROPN
cusj-6360	32	10	(	(	PUNCT
cusj-6360	32	11	0,∞	0,∞	NOUN
cusj-6360	32	12	)	)	PUNCT
cusj-6360	32	13	.	.	PUNCT
cusj-6360	33	1	let	let	VERB
cusj-6360	33	2	sn	sn	NOUN
cusj-6360	33	3	=	=	PUNCT
cusj-6360	33	4	d1	d1	PROPN
cusj-6360	33	5	+	+	CCONJ
cusj-6360	33	6	·	·	PUNCT
cusj-6360	33	7	·	·	PUNCT
cusj-6360	33	8	·	·	PUNCT
cusj-6360	34	1	+	+	CCONJ
cusj-6360	34	2	dn	dn	AUX
cusj-6360	34	3	.	.	PROPN
cusj-6360	34	4	let	let	VERB
cusj-6360	34	5	nn	nn	X
cusj-6360	34	6	be	be	AUX
cusj-6360	34	7	a	a	DET
cusj-6360	34	8	sequence	sequence	NOUN
cusj-6360	34	9	of	of	ADP
cusj-6360	34	10	nonnegative	nonnegative	ADJ
cusj-6360	34	11	integer	integer	NOUN
cusj-6360	34	12	-	-	PUNCT
cusj-6360	34	13	valued	value	VERB
cusj-6360	34	14	random	random	ADJ
cusj-6360	34	15	variables	variable	NOUN
cusj-6360	34	16	and	and	CCONJ
cusj-6360	34	17	cn	cn	VERB
cusj-6360	34	18	a	a	DET
cusj-6360	34	19	sequence	sequence	NOUN
cusj-6360	34	20	of	of	ADP
cusj-6360	34	21	integers	integer	NOUN
cusj-6360	34	22	with	with	ADP
cusj-6360	34	23	cn	cn	PROPN
cusj-6360	34	24	→	→	SYM
cusj-6360	34	25	∞	∞	PROPN
cusj-6360	34	26	and	and	CCONJ
cusj-6360	34	27	nn	nn	PROPN
cusj-6360	34	28	/	/	SYM
cusj-6360	34	29	cn	cn	PROPN
cusj-6360	34	30	→	→	SYM
cusj-6360	34	31	1	1	NUM
cusj-6360	34	32	in	in	ADP
cusj-6360	34	33	probability	probability	NOUN
cusj-6360	34	34	.	.	PUNCT
cusj-6360	35	1	then	then	ADV
cusj-6360	35	2	snn	snn	PROPN
cusj-6360	35	3	/σ	/σ	PUNCT
cusj-6360	35	4	√	√	VERB
cusj-6360	35	5	an	an	DET
cusj-6360	35	6	(	(	PUNCT
cusj-6360	35	7	2.2.3	2.2.3	NUM
cusj-6360	35	8	)	)	PUNCT
cusj-6360	35	9	where	where	SCONJ
cusj-6360	35	10	χ	χ	NOUN
cusj-6360	35	11	is	be	AUX
cusj-6360	35	12	a	a	DET
cusj-6360	35	13	standard	standard	ADJ
cusj-6360	35	14	normal	normal	ADJ
cusj-6360	35	15	distribution	distribution	NOUN
cusj-6360	35	16	.	.	PUNCT
cusj-6360	36	1	1	1	NUM
cusj-6360	36	2	buy	buy	VERB
cusj-6360	36	3	signal	signal	NOUN
cusj-6360	36	4	from	from	ADP
cusj-6360	36	5	limit	limit	NOUN
cusj-6360	36	6	theorem	theorem	ADJ
cusj-6360	36	7	[	[	PUNCT
cusj-6360	36	8	by	by	ADP
cusj-6360	36	9	yiqiao	yiqiao	PROPN
cusj-6360	36	10	yin	yin	PROPN
cusj-6360	36	11	]	]	PUNCT
cusj-6360	36	12	§	§	PROPN
cusj-6360	36	13	4	4	NUM
cusj-6360	36	14	theorem	theorem	ADJ
cusj-6360	36	15	2.2.4	2.2.4	NUM
cusj-6360	36	16	.	.	PUNCT
cusj-6360	37	1	let	let	VERB
cusj-6360	37	2	the	the	DET
cusj-6360	37	3	distance	distance	NOUN
cusj-6360	37	4	between	between	ADP
cusj-6360	37	5	price	price	NOUN
cusj-6360	37	6	and	and	CCONJ
cusj-6360	37	7	moving	move	VERB
cusj-6360	37	8	average	average	ADJ
cusj-6360	37	9	to	to	PART
cusj-6360	37	10	be	be	AUX
cusj-6360	37	11	d	d	ADP
cusj-6360	37	12	which	which	PRON
cusj-6360	37	13	is	be	AUX
cusj-6360	37	14	defined	define	VERB
cusj-6360	37	15	as	as	ADP
cusj-6360	37	16	di	di	NOUN
cusj-6360	37	17	:	:	PUNCT
cusj-6360	37	18	=	=	SYM
cusj-6360	37	19	pn	pn	PROPN
cusj-6360	37	20	−	−	PROPN
cusj-6360	37	21	sman	sman	NOUN
cusj-6360	37	22	while	while	SCONJ
cusj-6360	37	23	i	i	PRON
cusj-6360	37	24	=	=	SYM
cusj-6360	37	25	n	n	CCONJ
cusj-6360	37	26	,	,	PUNCT
cusj-6360	37	27	and	and	CCONJ
cusj-6360	37	28	then	then	ADV
cusj-6360	37	29	we	we	PRON
cusj-6360	37	30	can	can	AUX
cusj-6360	37	31	consider	consider	VERB
cusj-6360	37	32	di	di	NOUN
cusj-6360	37	33	to	to	PART
cusj-6360	37	34	be	be	AUX
cusj-6360	37	35	i.i.d	i.i.d	ADJ
cusj-6360	37	36	.	.	PUNCT
cusj-6360	38	1	with	with	ADP
cusj-6360	38	2	edi	edi	PROPN
cusj-6360	38	3	=	=	SYM
cusj-6360	38	4	0	0	PROPN
cusj-6360	38	5	and	and	CCONJ
cusj-6360	38	6	edi	edi	PROPN
cusj-6360	38	7	=	=	PROPN
cusj-6360	38	8	σ2	σ2	PROPN
cusj-6360	38	9	∈	∈	PROPN
cusj-6360	38	10	(	(	PUNCT
cusj-6360	38	11	0,∞	0,∞	NOUN
cusj-6360	38	12	)	)	PUNCT
cusj-6360	38	13	.	.	PUNCT
cusj-6360	39	1	let	let	VERB
cusj-6360	39	2	sn	sn	NOUN
cusj-6360	39	3	=	=	PUNCT
cusj-6360	39	4	d1	d1	PROPN
cusj-6360	39	5	+	+	CCONJ
cusj-6360	39	6	·	·	PUNCT
cusj-6360	39	7	·	·	PUNCT
cusj-6360	39	8	·	·	PUNCT
cusj-6360	40	1	+	+	CCONJ
cusj-6360	40	2	dn	dn	X
cusj-6360	40	3	.	.	NOUN
cusj-6360	40	4	let	let	AUX
cusj-6360	40	5	nt	not	PART
cusj-6360	40	6	=	=	PUNCT
cusj-6360	40	7	sup{m	sup{m	NOUN
cusj-6360	40	8	:	:	PUNCT
cusj-6360	40	9	sm	sm	PROPN
cusj-6360	40	10	≤	≤	PROPN
cusj-6360	40	11	t	t	PROPN
cusj-6360	40	12	}	}	PUNCT
cusj-6360	40	13	.	.	PUNCT
cusj-6360	41	1	then	then	ADV
cusj-6360	41	2	as	as	ADP
cusj-6360	41	3	t→∞	t→∞	NUM
cusj-6360	41	4	,	,	PUNCT
cusj-6360	41	5	(	(	PUNCT
cusj-6360	41	6	µnt	µnt	NOUN
cusj-6360	41	7	−	−	PROPN
cusj-6360	41	8	t)/(σ2t/µ)1/2	t)/(σ2t/µ)1/2	NOUN
cusj-6360	41	9	⇒	⇒	NOUN
cusj-6360	41	10	χ	χ	X
cusj-6360	41	11	(	(	PUNCT
cusj-6360	41	12	2.2.4	2.2.4	NUM
cusj-6360	41	13	)	)	PUNCT
cusj-6360	41	14	while	while	SCONJ
cusj-6360	41	15	χ	χ	NOUN
cusj-6360	41	16	is	be	AUX
cusj-6360	41	17	the	the	DET
cusj-6360	41	18	stand	stand	NOUN
cusj-6360	41	19	normal	normal	ADJ
cusj-6360	41	20	distribution	distribution	NOUN
cusj-6360	41	21	.	.	PUNCT
cusj-6360	41	22	3	3	NUM
cusj-6360	41	23	algorithms	algorithm	NOUN
cusj-6360	41	24	this	this	DET
cusj-6360	41	25	section	section	NOUN
cusj-6360	41	26	we	we	PRON
cusj-6360	41	27	take	take	VERB
cusj-6360	41	28	the	the	DET
cusj-6360	41	29	theorems	theorem	NOUN
cusj-6360	41	30	above	above	ADV
cusj-6360	41	31	,	,	PUNCT
cusj-6360	41	32	from	from	ADP
cusj-6360	41	33	§	§	NOUN
cusj-6360	41	34	2	2	NUM
cusj-6360	41	35	theoretical	theoretical	ADJ
cusj-6360	41	36	framework	framework	NOUN
cusj-6360	41	37	,	,	PUNCT
cusj-6360	41	38	as	as	SCONJ
cusj-6360	41	39	given	give	VERB
cusj-6360	41	40	and	and	CCONJ
cusj-6360	41	41	we	we	PRON
cusj-6360	41	42	introduce	introduce	VERB
cusj-6360	41	43	a	a	DET
cusj-6360	41	44	series	series	NOUN
cusj-6360	41	45	of	of	ADP
cusj-6360	41	46	algorithms	algorithm	NOUN
cusj-6360	41	47	targeting	target	VERB
cusj-6360	41	48	buy	buy	NOUN
cusj-6360	41	49	signals	signal	NOUN
cusj-6360	41	50	.	.	PUNCT
cusj-6360	42	1	algorithm	algorithm	PROPN
cusj-6360	42	2	3.0.1	3.0.1	NUM
cusj-6360	42	3	.	.	PUNCT
cusj-6360	43	1	given	give	VERB
cusj-6360	43	2	a	a	DET
cusj-6360	43	3	buy	buy	NOUN
cusj-6360	43	4	frequency	frequency	NOUN
cusj-6360	43	5	by	by	ADP
cusj-6360	43	6	an	an	DET
cusj-6360	43	7	investor	investor	NOUN
cusj-6360	43	8	c	c	NOUN
cusj-6360	43	9	,	,	PUNCT
cusj-6360	43	10	for	for	ADP
cusj-6360	43	11	all	all	DET
cusj-6360	43	12	i	i	PRON
cusj-6360	43	13	in	in	ADP
cusj-6360	43	14	a	a	DET
cusj-6360	43	15	stock	stock	NOUN
cusj-6360	43	16	pool	pool	NOUN
cusj-6360	43	17	of	of	ADP
cusj-6360	43	18	companies	company	NOUN
cusj-6360	43	19	:	:	PUNCT
cusj-6360	43	20	step	step	NOUN
cusj-6360	43	21	1	1	NUM
cusj-6360	43	22	.	.	PUNCT
cusj-6360	43	23	observe	observe	VERB
cusj-6360	43	24	price	price	NOUN
cusj-6360	43	25	pt	pt	NOUN
cusj-6360	43	26	for	for	ADP
cusj-6360	43	27	each	each	DET
cusj-6360	43	28	company	company	NOUN
cusj-6360	43	29	step	step	VERB
cusj-6360	43	30	2	2	NUM
cusj-6360	43	31	.	.	PUNCT
cusj-6360	43	32	store	store	NOUN
cusj-6360	43	33	pi	pi	PROPN
cusj-6360	43	34	,	,	PUNCT
cusj-6360	43	35	t	t	PROPN
cusj-6360	43	36	step	step	NOUN
cusj-6360	43	37	3	3	NUM
cusj-6360	43	38	.	.	PUNCT
cusj-6360	43	39	compute	compute	PROPN
cusj-6360	43	40	sman	sman	NOUN
cusj-6360	43	41	dn	dn	INTJ
cusj-6360	43	42	:	:	PUNCT
cusj-6360	43	43	=	=	SYM
cusj-6360	44	1	pi	pi	NOUN
cusj-6360	44	2	,	,	PUNCT
cusj-6360	44	3	n	n	CCONJ
cusj-6360	44	4	−	−	PROPN
cusj-6360	44	5	sman	sman	ADJ
cusj-6360	44	6	step	step	NOUN
cusj-6360	44	7	4	4	NUM
cusj-6360	44	8	.	.	PUNCT
cusj-6360	45	1	if	if	SCONJ
cusj-6360	45	2	dn	dn	ADP
cusj-6360	45	3	≤	≤	NUM
cusj-6360	45	4	c	c	X
cusj-6360	45	5	,	,	PUNCT
cusj-6360	45	6	print	print	NOUN
cusj-6360	45	7	”	"	PUNCT
cusj-6360	45	8	+1	+1	PROPN
cusj-6360	45	9	”	"	PUNCT
cusj-6360	45	10	;	;	PUNCT
cusj-6360	45	11	else	else	ADV
cusj-6360	45	12	,	,	PUNCT
cusj-6360	45	13	print	print	NOUN
cusj-6360	45	14	”	"	PUNCT
cusj-6360	45	15	0	0	NUM
cusj-6360	45	16	”	"	PUNCT
cusj-6360	45	17	.	.	PUNCT
cusj-6360	46	1	print	print	VERB
cusj-6360	46	2	a	a	DET
cusj-6360	46	3	collection	collection	NOUN
cusj-6360	46	4	of	of	ADP
cusj-6360	46	5	”	"	PUNCT
cusj-6360	46	6	+1	+1	PROPN
cusj-6360	46	7	”	"	PUNCT
cusj-6360	46	8	per	per	ADP
cusj-6360	46	9	company	company	NOUN
cusj-6360	46	10	i	i	PRON
cusj-6360	46	11	per	per	ADP
cusj-6360	46	12	n.	n.	NOUN
cusj-6360	46	13	as	as	ADP
cusj-6360	46	14	the	the	DET
cusj-6360	46	15	first	first	ADJ
cusj-6360	46	16	algorithm	algorithm	NOUN
cusj-6360	46	17	in	in	ADP
cusj-6360	46	18	the	the	DET
cusj-6360	46	19	section	section	NOUN
cusj-6360	46	20	,	,	PUNCT
cusj-6360	46	21	it	it	PRON
cusj-6360	46	22	has	have	VERB
cusj-6360	46	23	a	a	DET
cusj-6360	46	24	very	very	ADV
cusj-6360	46	25	intuitive	intuitive	ADJ
cusj-6360	46	26	understanding	understanding	NOUN
cusj-6360	46	27	.	.	PUNCT
cusj-6360	47	1	one	one	PRON
cusj-6360	47	2	can	can	AUX
cusj-6360	47	3	simply	simply	ADV
cusj-6360	47	4	observe	observe	VERB
cusj-6360	47	5	price	price	NOUN
cusj-6360	47	6	and	and	CCONJ
cusj-6360	47	7	computes	compute	VERB
cusj-6360	47	8	its	its	PRON
cusj-6360	47	9	sma	sma	NOUN
cusj-6360	47	10	.	.	PUNCT
cusj-6360	48	1	then	then	ADV
cusj-6360	48	2	one	one	NUM
cusj-6360	48	3	needs	need	VERB
cusj-6360	48	4	to	to	PART
cusj-6360	48	5	look	look	VERB
cusj-6360	48	6	at	at	ADP
cusj-6360	48	7	the	the	DET
cusj-6360	48	8	difference	difference	NOUN
cusj-6360	48	9	between	between	ADP
cusj-6360	48	10	price	price	NOUN
cusj-6360	48	11	and	and	CCONJ
cusj-6360	48	12	sma	sma	VERB
cusj-6360	48	13	to	to	PART
cusj-6360	48	14	know	know	VERB
cusj-6360	48	15	how	how	SCONJ
cusj-6360	48	16	often	often	ADV
cusj-6360	48	17	should	should	AUX
cusj-6360	48	18	he	he	PRON
cusj-6360	48	19	buy	buy	AUX
cusj-6360	48	20	given	give	VERB
cusj-6360	48	21	that	that	SCONJ
cusj-6360	48	22	he	he	PRON
cusj-6360	48	23	has	have	VERB
cusj-6360	48	24	a	a	DET
cusj-6360	48	25	fixed	fix	VERB
cusj-6360	48	26	frequency	frequency	NOUN
cusj-6360	48	27	.	.	PUNCT
cusj-6360	49	1	this	this	PRON
cusj-6360	49	2	is	be	AUX
cusj-6360	49	3	and	and	CCONJ
cusj-6360	49	4	will	will	AUX
cusj-6360	49	5	always	always	ADV
cusj-6360	49	6	be	be	AUX
cusj-6360	49	7	true	true	ADJ
cusj-6360	49	8	because	because	SCONJ
cusj-6360	49	9	the	the	DET
cusj-6360	49	10	difference	difference	NOUN
cusj-6360	49	11	of	of	ADP
cusj-6360	49	12	price	price	NOUN
cusj-6360	49	13	and	and	CCONJ
cusj-6360	49	14	sma	sma	NOUN
cusj-6360	49	15	follows	follow	VERB
cusj-6360	49	16	random	random	ADJ
cusj-6360	49	17	walk	walk	NOUN
cusj-6360	49	18	,	,	PUNCT
cusj-6360	49	19	as	as	SCONJ
cusj-6360	49	20	stated	state	VERB
cusj-6360	49	21	in	in	ADP
cusj-6360	49	22	theorem	theorem	ADJ
cusj-6360	49	23	2.2.2	2.2.2	NUM
cusj-6360	49	24	and	and	CCONJ
cusj-6360	49	25	proved	prove	VERB
cusj-6360	49	26	in	in	ADP
cusj-6360	49	27	appendix	appendix	NOUN
cusj-6360	49	28	.	.	PUNCT
cusj-6360	50	1	this	this	PRON
cusj-6360	50	2	means	mean	VERB
cusj-6360	50	3	that	that	SCONJ
cusj-6360	50	4	this	this	DET
cusj-6360	50	5	time	time	NOUN
cusj-6360	50	6	-	-	PUNCT
cusj-6360	50	7	series	series	NOUN
cusj-6360	50	8	difference	difference	NOUN
cusj-6360	50	9	we	we	PRON
cusj-6360	50	10	are	be	AUX
cusj-6360	50	11	looking	look	VERB
cusj-6360	50	12	at	at	ADP
cusj-6360	50	13	goes	go	VERB
cusj-6360	50	14	up	up	ADV
cusj-6360	50	15	or	or	CCONJ
cusj-6360	50	16	down	down	ADV
cusj-6360	50	17	but	but	CCONJ
cusj-6360	50	18	stay	stay	VERB
cusj-6360	50	19	in	in	ADP
cusj-6360	50	20	the	the	DET
cusj-6360	50	21	middle	middle	NOUN
cusj-6360	50	22	most	most	ADV
cusj-6360	50	23	often	often	ADV
cusj-6360	50	24	.	.	PUNCT
cusj-6360	51	1	such	such	ADJ
cusj-6360	51	2	bell	bell	NOUN
cusj-6360	51	3	-	-	PUNCT
cusj-6360	51	4	shape	shape	NOUN
cusj-6360	51	5	curve	curve	NOUN
cusj-6360	51	6	can	can	AUX
cusj-6360	51	7	give	give	VERB
cusj-6360	51	8	as	as	ADP
cusj-6360	51	9	a	a	DET
cusj-6360	51	10	precise	precise	ADJ
cusj-6360	51	11	probability	probability	NOUN
cusj-6360	51	12	distribution	distribution	NOUN
cusj-6360	51	13	and	and	CCONJ
cusj-6360	51	14	we	we	PRON
cusj-6360	51	15	can	can	AUX
cusj-6360	51	16	mark	mark	VERB
cusj-6360	51	17	down	down	ADP
cusj-6360	51	18	an	an	DET
cusj-6360	51	19	exact	exact	ADJ
cusj-6360	51	20	price	price	NOUN
cusj-6360	51	21	level	level	NOUN
cusj-6360	51	22	given	give	VERB
cusj-6360	51	23	a	a	DET
cusj-6360	51	24	frequency	frequency	NOUN
cusj-6360	51	25	we	we	PRON
cusj-6360	51	26	want	want	VERB
cusj-6360	51	27	to	to	PART
cusj-6360	51	28	participate	participate	VERB
cusj-6360	51	29	in	in	ADP
cusj-6360	51	30	the	the	DET
cusj-6360	51	31	market	market	NOUN
cusj-6360	51	32	.	.	PUNCT
cusj-6360	52	1	algorithm	algorithm	PROPN
cusj-6360	52	2	3.0.2	3.0.2	NUM
cusj-6360	52	3	.	.	PUNCT
cusj-6360	53	1	given	give	VERB
cusj-6360	53	2	a	a	DET
cusj-6360	53	3	buy	buy	NOUN
cusj-6360	53	4	frequency	frequency	NOUN
cusj-6360	53	5	buy	buy	VERB
cusj-6360	53	6	an	an	DET
cusj-6360	53	7	investor	investor	NOUN
cusj-6360	53	8	c	c	NOUN
cusj-6360	53	9	,	,	PUNCT
cusj-6360	53	10	for	for	ADP
cusj-6360	53	11	all	all	DET
cusj-6360	53	12	i	i	PRON
cusj-6360	53	13	in	in	ADP
cusj-6360	53	14	a	a	DET
cusj-6360	53	15	stock	stock	NOUN
cusj-6360	53	16	pool	pool	NOUN
cusj-6360	53	17	of	of	ADP
cusj-6360	53	18	companies	company	NOUN
cusj-6360	53	19	:	:	PUNCT
cusj-6360	53	20	step	step	NOUN
cusj-6360	53	21	1	1	NUM
cusj-6360	53	22	.	.	PUNCT
cusj-6360	54	1	observe	observe	VERB
cusj-6360	54	2	price	price	NOUN
cusj-6360	54	3	pt	pt	NOUN
cusj-6360	54	4	for	for	ADP
cusj-6360	54	5	each	each	DET
cusj-6360	54	6	company	company	NOUN
cusj-6360	54	7	step	step	VERB
cusj-6360	54	8	2	2	NUM
cusj-6360	54	9	.	.	PUNCT
cusj-6360	54	10	store	store	NOUN
cusj-6360	54	11	pi	pi	PROPN
cusj-6360	54	12	,	,	PUNCT
cusj-6360	54	13	t	t	PROPN
cusj-6360	54	14	step	step	NOUN
cusj-6360	54	15	3	3	NUM
cusj-6360	54	16	.	.	PUNCT
cusj-6360	55	1	compute	compute	NOUN
cusj-6360	56	1	dn	dn	NOUN
cusj-6360	56	2	:	:	PUNCT
cusj-6360	56	3	=	=	SYM
cusj-6360	57	1	pi	pi	NOUN
cusj-6360	57	2	,	,	PUNCT
cusj-6360	57	3	n	n	CCONJ
cusj-6360	57	4	−	−	PROPN
cusj-6360	57	5	sman	sman	ADJ
cusj-6360	57	6	signaln	signaln	NOUN
cusj-6360	57	7	:	:	PUNCT
cusj-6360	58	1	=	=	SYM
cusj-6360	58	2	n∑	n∑	PROPN
cusj-6360	58	3	m=1	m=1	X
cusj-6360	58	4	dm	dm	INTJ
cusj-6360	58	5	/	/	SYM
cusj-6360	58	6	(	(	PUNCT
cusj-6360	58	7	n∑	n∑	PROPN
cusj-6360	58	8	m=1	m=1	PROPN
cusj-6360	58	9	d2	d2	PROPN
cusj-6360	58	10	m	m	PROPN
cusj-6360	58	11	)	)	PUNCT
cusj-6360	58	12	1/2	1/2	NUM
cusj-6360	58	13	step	step	NOUN
cusj-6360	58	14	4	4	NUM
cusj-6360	58	15	.	.	PUNCT
cusj-6360	59	1	if	if	SCONJ
cusj-6360	59	2	signaln	signaln	ADJ
cusj-6360	59	3	≤	≤	NOUN
cusj-6360	59	4	c	c	NOUN
cusj-6360	59	5	,	,	PUNCT
cusj-6360	59	6	print	print	NOUN
cusj-6360	59	7	”	"	PUNCT
cusj-6360	59	8	+1	+1	PROPN
cusj-6360	59	9	”	"	PUNCT
cusj-6360	59	10	;	;	PUNCT
cusj-6360	59	11	else	else	ADV
cusj-6360	59	12	,	,	PUNCT
cusj-6360	59	13	print	print	NOUN
cusj-6360	59	14	”	"	PUNCT
cusj-6360	59	15	0	0	NUM
cusj-6360	59	16	”	"	PUNCT
cusj-6360	59	17	.	.	PUNCT
cusj-6360	60	1	print	print	VERB
cusj-6360	60	2	a	a	DET
cusj-6360	60	3	collection	collection	NOUN
cusj-6360	60	4	of	of	ADP
cusj-6360	60	5	”	"	PUNCT
cusj-6360	60	6	+1	+1	PROPN
cusj-6360	60	7	”	"	PUNCT
cusj-6360	60	8	per	per	ADP
cusj-6360	60	9	company	company	NOUN
cusj-6360	60	10	i	i	PRON
cusj-6360	60	11	per	per	ADP
cusj-6360	60	12	n.	n.	PROPN
cusj-6360	60	13	algorithm	algorithm	PROPN
cusj-6360	60	14	3.0.2	3.0.2	NUM
cusj-6360	60	15	takes	take	VERB
cusj-6360	60	16	algorithm	algorithm	NOUN
cusj-6360	60	17	3.0.1	3.0.1	NUM
cusj-6360	60	18	as	as	ADP
cusj-6360	60	19	a	a	DET
cusj-6360	60	20	building	building	NOUN
cusj-6360	60	21	block	block	NOUN
cusj-6360	60	22	and	and	CCONJ
cusj-6360	60	23	expand	expand	VERB
cusj-6360	60	24	the	the	DET
cusj-6360	60	25	idea	idea	NOUN
cusj-6360	60	26	and	and	CCONJ
cusj-6360	60	27	we	we	PRON
cusj-6360	60	28	can	can	AUX
cusj-6360	60	29	normalized	normalize	VERB
cusj-6360	60	30	the	the	DET
cusj-6360	60	31	distance	distance	NOUN
cusj-6360	60	32	(	(	PUNCT
cusj-6360	60	33	or	or	CCONJ
cusj-6360	60	34	difference	difference	NOUN
cusj-6360	60	35	)	)	PUNCT
cusj-6360	60	36	of	of	ADP
cusj-6360	60	37	summation	summation	NOUN
cusj-6360	60	38	of	of	ADP
cusj-6360	60	39	a	a	DET
cusj-6360	60	40	series	series	NOUN
cusj-6360	60	41	of	of	ADP
cusj-6360	60	42	distances	distance	NOUN
cusj-6360	60	43	by	by	ADP
cusj-6360	60	44	square	square	ADJ
cusj-6360	60	45	root	root	NOUN
cusj-6360	60	46	of	of	ADP
cusj-6360	60	47	its	its	PRON
cusj-6360	60	48	own	own	ADJ
cusj-6360	60	49	value	value	NOUN
cusj-6360	60	50	to	to	PART
cusj-6360	60	51	construct	construct	VERB
cusj-6360	60	52	buy	buy	NOUN
cusj-6360	60	53	signals	signal	NOUN
cusj-6360	60	54	.	.	PUNCT
cusj-6360	61	1	algorithm	algorithm	PROPN
cusj-6360	61	2	3.0.3	3.0.3	NUM
cusj-6360	61	3	.	.	PUNCT
cusj-6360	62	1	given	give	VERB
cusj-6360	62	2	a	a	DET
cusj-6360	62	3	buy	buy	NOUN
cusj-6360	62	4	frequency	frequency	NOUN
cusj-6360	62	5	by	by	ADP
cusj-6360	62	6	an	an	DET
cusj-6360	62	7	investor	investor	NOUN
cusj-6360	62	8	c	c	NOUN
cusj-6360	62	9	,	,	PUNCT
cusj-6360	62	10	for	for	ADP
cusj-6360	62	11	all	all	DET
cusj-6360	62	12	i	i	PRON
cusj-6360	62	13	in	in	ADP
cusj-6360	62	14	a	a	DET
cusj-6360	62	15	stock	stock	NOUN
cusj-6360	62	16	pool	pool	NOUN
cusj-6360	62	17	of	of	ADP
cusj-6360	62	18	companies	company	NOUN
cusj-6360	62	19	:	:	PUNCT
cusj-6360	62	20	step	step	NOUN
cusj-6360	62	21	1	1	NUM
cusj-6360	62	22	.	.	PUNCT
cusj-6360	62	23	observe	observe	VERB
cusj-6360	62	24	price	price	NOUN
cusj-6360	62	25	pt	pt	NOUN
cusj-6360	62	26	for	for	ADP
cusj-6360	62	27	each	each	DET
cusj-6360	62	28	company	company	NOUN
cusj-6360	62	29	step	step	VERB
cusj-6360	62	30	2	2	NUM
cusj-6360	62	31	.	.	PUNCT
cusj-6360	62	32	store	store	NOUN
cusj-6360	62	33	pi	pi	PROPN
cusj-6360	62	34	,	,	PUNCT
cusj-6360	62	35	t	t	PROPN
cusj-6360	62	36	step	step	NOUN
cusj-6360	62	37	3	3	NUM
cusj-6360	62	38	.	.	PUNCT
cusj-6360	62	39	compute	compute	PROPN
cusj-6360	62	40	snn	snn	PROPN
cusj-6360	62	41	=	=	SYM
cusj-6360	62	42	d1	d1	PROPN
cusj-6360	62	43	+	+	CCONJ
cusj-6360	62	44	·	·	PUNCT
cusj-6360	62	45	·	·	PUNCT
cusj-6360	62	46	·	·	PUNCT
cusj-6360	63	1	+	+	CCONJ
cusj-6360	63	2	dn	dn	X
cusj-6360	63	3	,	,	PUNCT
cusj-6360	63	4	σ	σ	PROPN
cusj-6360	63	5	is	be	AUX
cusj-6360	63	6	the	the	DET
cusj-6360	63	7	variance	variance	NOUN
cusj-6360	63	8	of	of	ADP
cusj-6360	63	9	di	di	NOUN
cusj-6360	63	10	,	,	PUNCT
cusj-6360	63	11	self	self	NOUN
cusj-6360	63	12	-	-	PUNCT
cusj-6360	63	13	normn	normn	NOUN
cusj-6360	63	14	:	:	PUNCT
cusj-6360	63	15	=	=	SYM
cusj-6360	63	16	snn	snn	PROPN
cusj-6360	63	17	/	/	SYM
cusj-6360	63	18	σ	σ	PROPN
cusj-6360	63	19	√	√	PROPN
cusj-6360	63	20	an	an	DET
cusj-6360	63	21	step	step	NOUN
cusj-6360	63	22	4	4	NUM
cusj-6360	63	23	.	.	PUNCT
cusj-6360	64	1	if	if	SCONJ
cusj-6360	64	2	self	self	NOUN
cusj-6360	64	3	−normn	−normn	VERB
cusj-6360	64	4	≤	≤	NUM
cusj-6360	64	5	c	c	NOUN
cusj-6360	64	6	,	,	PUNCT
cusj-6360	64	7	print	print	NOUN
cusj-6360	64	8	”	"	PUNCT
cusj-6360	64	9	+1	+1	PROPN
cusj-6360	64	10	”	"	PUNCT
cusj-6360	64	11	;	;	PUNCT
cusj-6360	64	12	else	else	ADV
cusj-6360	64	13	,	,	PUNCT
cusj-6360	64	14	print	print	NOUN
cusj-6360	64	15	”	"	PUNCT
cusj-6360	64	16	0	0	NUM
cusj-6360	64	17	”	"	PUNCT
cusj-6360	64	18	.	.	PUNCT
cusj-6360	65	1	print	print	VERB
cusj-6360	65	2	a	a	DET
cusj-6360	65	3	collection	collection	NOUN
cusj-6360	65	4	of	of	ADP
cusj-6360	65	5	”	"	PUNCT
cusj-6360	65	6	+1	+1	PROPN
cusj-6360	65	7	”	"	PUNCT
cusj-6360	65	8	per	per	ADP
cusj-6360	65	9	company	company	NOUN
cusj-6360	65	10	i	i	PRON
cusj-6360	65	11	per	per	ADP
cusj-6360	65	12	n.	n.	PROPN
cusj-6360	65	13	algorithm	algorithm	PROPN
cusj-6360	65	14	3.0.2	3.0.2	NUM
cusj-6360	65	15	brought	bring	VERB
cusj-6360	65	16	up	up	ADP
cusj-6360	65	17	the	the	DET
cusj-6360	65	18	notion	notion	NOUN
cusj-6360	65	19	of	of	ADP
cusj-6360	65	20	normalizing	normalize	VERB
cusj-6360	65	21	by	by	ADP
cusj-6360	65	22	square	square	NOUN
cusj-6360	65	23	of	of	ADP
cusj-6360	65	24	its	its	PRON
cusj-6360	65	25	own	own	ADJ
cusj-6360	65	26	value	value	NOUN
cusj-6360	65	27	.	.	PUNCT
cusj-6360	66	1	it	it	PRON
cusj-6360	66	2	is	be	AUX
cusj-6360	66	3	also	also	ADV
cusj-6360	66	4	practical	practical	ADJ
cusj-6360	66	5	to	to	PART
cusj-6360	66	6	normalize	normalize	VERB
cusj-6360	66	7	by	by	ADP
cusj-6360	66	8	itself	itself	PRON
cusj-6360	66	9	,	,	PUNCT
cusj-6360	66	10	which	which	PRON
cusj-6360	66	11	is	be	AUX
cusj-6360	66	12	what	what	PRON
cusj-6360	66	13	algorithm	algorithm	NOUN
cusj-6360	66	14	3.0.3	3.0.3	NUM
cusj-6360	66	15	was	be	AUX
cusj-6360	66	16	attempting	attempt	VERB
cusj-6360	66	17	to	to	PART
cusj-6360	66	18	do	do	VERB
cusj-6360	66	19	.	.	PUNCT
cusj-6360	67	1	algorithm	algorithm	PROPN
cusj-6360	67	2	3.0.4	3.0.4	NUM
cusj-6360	67	3	.	.	PUNCT
cusj-6360	68	1	given	give	VERB
cusj-6360	68	2	a	a	DET
cusj-6360	68	3	buy	buy	NOUN
cusj-6360	68	4	frequency	frequency	NOUN
cusj-6360	68	5	buy	buy	VERB
cusj-6360	68	6	an	an	DET
cusj-6360	68	7	investor	investor	NOUN
cusj-6360	68	8	c	c	NOUN
cusj-6360	68	9	,	,	PUNCT
cusj-6360	68	10	for	for	ADP
cusj-6360	68	11	all	all	DET
cusj-6360	68	12	i	i	PRON
cusj-6360	68	13	in	in	ADP
cusj-6360	68	14	a	a	DET
cusj-6360	68	15	stock	stock	NOUN
cusj-6360	68	16	pool	pool	NOUN
cusj-6360	68	17	of	of	ADP
cusj-6360	68	18	companies	company	NOUN
cusj-6360	68	19	:	:	PUNCT
cusj-6360	68	20	step	step	NOUN
cusj-6360	68	21	1	1	NUM
cusj-6360	68	22	.	.	PUNCT
cusj-6360	69	1	observe	observe	VERB
cusj-6360	69	2	price	price	NOUN
cusj-6360	69	3	pt	pt	NOUN
cusj-6360	69	4	for	for	ADP
cusj-6360	69	5	each	each	DET
cusj-6360	69	6	company	company	NOUN
cusj-6360	69	7	step	step	VERB
cusj-6360	69	8	2	2	NUM
cusj-6360	69	9	.	.	PUNCT
cusj-6360	69	10	store	store	NOUN
cusj-6360	69	11	pi	pi	PROPN
cusj-6360	69	12	,	,	PUNCT
cusj-6360	69	13	t	t	PROPN
cusj-6360	69	14	step	step	NOUN
cusj-6360	69	15	3	3	NUM
cusj-6360	69	16	.	.	PUNCT
cusj-6360	69	17	compute	compute	VERB
cusj-6360	69	18	the	the	DET
cusj-6360	69	19	mean	mean	ADJ
cusj-6360	69	20	µ	µ	NOUN
cusj-6360	69	21	and	and	CCONJ
cusj-6360	69	22	the	the	DET
cusj-6360	69	23	variance	variance	NOUN
cusj-6360	69	24	σ	σ	PROPN
cusj-6360	69	25	,	,	PUNCT
cusj-6360	69	26	renewaln	renewaln	ADJ
cusj-6360	69	27	:	:	PUNCT
cusj-6360	70	1	=	=	SYM
cusj-6360	70	2	(	(	PUNCT
cusj-6360	70	3	µnt	µnt	NOUN
cusj-6360	70	4	−	−	PROPN
cusj-6360	70	5	t)/(σ2t/µ)1/2	t)/(σ2t/µ)1/2	NOUN
cusj-6360	70	6	⇒	⇒	NOUN
cusj-6360	70	7	χ	χ	DET
cusj-6360	70	8	step	step	NOUN
cusj-6360	70	9	4	4	NUM
cusj-6360	70	10	.	.	PUNCT
cusj-6360	71	1	if	if	SCONJ
cusj-6360	71	2	renewaln	renewaln	PRON
cusj-6360	71	3	≤	≤	NUM
cusj-6360	71	4	c	c	NOUN
cusj-6360	71	5	,	,	PUNCT
cusj-6360	71	6	print	print	NOUN
cusj-6360	71	7	”	"	PUNCT
cusj-6360	71	8	+1	+1	PROPN
cusj-6360	71	9	”	"	PUNCT
cusj-6360	71	10	;	;	PUNCT
cusj-6360	71	11	else	else	ADV
cusj-6360	71	12	,	,	PUNCT
cusj-6360	71	13	print	print	NOUN
cusj-6360	71	14	”	"	PUNCT
cusj-6360	71	15	0	0	NUM
cusj-6360	71	16	”	"	PUNCT
cusj-6360	71	17	.	.	PUNCT
cusj-6360	72	1	print	print	VERB
cusj-6360	72	2	a	a	DET
cusj-6360	72	3	collection	collection	NOUN
cusj-6360	72	4	of	of	ADP
cusj-6360	72	5	”	"	PUNCT
cusj-6360	72	6	+1	+1	PROPN
cusj-6360	72	7	”	"	PUNCT
cusj-6360	72	8	per	per	ADP
cusj-6360	72	9	company	company	NOUN
cusj-6360	72	10	i	i	PRON
cusj-6360	72	11	per	per	ADP
cusj-6360	72	12	n.	n.	NOUN
cusj-6360	72	13	besides	besides	SCONJ
cusj-6360	72	14	notions	notion	NOUN
cusj-6360	72	15	of	of	ADP
cusj-6360	72	16	self	self	NOUN
cusj-6360	72	17	-	-	PUNCT
cusj-6360	72	18	normalizing	normalizing	ADJ
cusj-6360	72	19	,	,	PUNCT
cusj-6360	72	20	we	we	PRON
cusj-6360	72	21	can	can	AUX
cusj-6360	72	22	also	also	ADV
cusj-6360	72	23	construct	construct	VERB
cusj-6360	72	24	standard	standard	ADJ
cusj-6360	72	25	normal	normal	ADJ
cusj-6360	72	26	distribution	distribution	NOUN
cusj-6360	72	27	by	by	ADP
cusj-6360	72	28	taking	take	VERB
cusj-6360	72	29	time	time	NOUN
cusj-6360	72	30	,	,	PUNCT
cusj-6360	72	31	risk	risk	NOUN
cusj-6360	72	32	,	,	PUNCT
cusj-6360	72	33	and	and	CCONJ
cusj-6360	72	34	mean	mean	VERB
cusj-6360	72	35	into	into	ADP
cusj-6360	72	36	consideration	consideration	NOUN
cusj-6360	72	37	.	.	PUNCT
cusj-6360	73	1	such	such	ADJ
cusj-6360	73	2	“	"	PUNCT
cusj-6360	73	3	renewal	renewal	NOUN
cusj-6360	73	4	”	"	PUNCT
cusj-6360	73	5	process	process	NOUN
cusj-6360	73	6	can	can	AUX
cusj-6360	73	7	be	be	AUX
cusj-6360	73	8	done	do	VERB
cusj-6360	73	9	without	without	ADP
cusj-6360	73	10	breaking	break	VERB
cusj-6360	73	11	the	the	DET
cusj-6360	73	12	form	form	NOUN
cusj-6360	73	13	of	of	ADP
cusj-6360	73	14	standard	standard	ADJ
cusj-6360	73	15	normal	normal	ADJ
cusj-6360	73	16	distribution	distribution	NOUN
cusj-6360	73	17	.	.	PUNCT
cusj-6360	74	1	for	for	ADP
cusj-6360	74	2	traders	trader	NOUN
cusj-6360	74	3	who	who	PRON
cusj-6360	74	4	are	be	AUX
cusj-6360	74	5	interested	interested	ADJ
cusj-6360	74	6	in	in	ADP
cusj-6360	74	7	looking	look	VERB
cusj-6360	74	8	at	at	ADP
cusj-6360	74	9	more	more	ADJ
cusj-6360	74	10	parameters	parameter	NOUN
cusj-6360	74	11	,	,	PUNCT
cusj-6360	74	12	there	there	PRON
cusj-6360	74	13	is	be	VERB
cusj-6360	74	14	such	such	ADJ
cusj-6360	74	15	freedom	freedom	NOUN
cusj-6360	74	16	to	to	PART
cusj-6360	74	17	do	do	AUX
cusj-6360	74	18	so	so	ADV
cusj-6360	74	19	.	.	PUNCT
cusj-6360	75	1	algorithm	algorithm	PROPN
cusj-6360	75	2	3.0.5	3.0.5	NUM
cusj-6360	75	3	.	.	PUNCT
cusj-6360	75	4	given	give	VERB
cusj-6360	75	5	results	result	NOUN
cusj-6360	75	6	from	from	ADP
cusj-6360	75	7	the	the	DET
cusj-6360	75	8	above	above	ADJ
cusj-6360	75	9	algorithms	algorithm	NOUN
cusj-6360	75	10	,	,	PUNCT
cusj-6360	75	11	that	that	ADV
cusj-6360	75	12	is	is	ADV
cusj-6360	75	13	,	,	PUNCT
cusj-6360	75	14	algorithms	algorithms	PROPN
cusj-6360	75	15	3.0.1	3.0.1	NUM
cusj-6360	75	16	,	,	PUNCT
cusj-6360	75	17	3.0.2	3.0.2	NUM
cusj-6360	75	18	,	,	PUNCT
cusj-6360	75	19	3.0.3	3.0.3	NUM
cusj-6360	75	20	,	,	PUNCT
cusj-6360	75	21	and	and	CCONJ
cusj-6360	75	22	3.0.4	3.0.4	NUM
cusj-6360	75	23	,	,	PUNCT
cusj-6360	75	24	run	run	VERB
cusj-6360	75	25	step	step	NOUN
cusj-6360	75	26	1	1	NUM
cusj-6360	75	27	.	.	PUNCT
cusj-6360	76	1	retreat	retreat	NOUN
cusj-6360	76	2	(	(	PUNCT
cusj-6360	76	3	dn	dn	PROPN
cusj-6360	76	4	)	)	PUNCT
cusj-6360	76	5	,	,	PUNCT
cusj-6360	76	6	(	(	PUNCT
cusj-6360	76	7	signaln	signaln	NOUN
cusj-6360	76	8	)	)	PUNCT
cusj-6360	76	9	,	,	PUNCT
cusj-6360	76	10	(	(	PUNCT
cusj-6360	76	11	self	self	NOUN
cusj-6360	76	12	-	-	PUNCT
cusj-6360	76	13	normn	normn	NOUN
cusj-6360	76	14	)	)	PUNCT
cusj-6360	76	15	,	,	PUNCT
cusj-6360	76	16	and	and	CCONJ
cusj-6360	76	17	(	(	PUNCT
cusj-6360	76	18	renewaln	renewaln	NOUN
cusj-6360	76	19	)	)	PUNCT
cusj-6360	76	20	.	.	PUNCT
cusj-6360	77	1	step	step	NOUN
cusj-6360	77	2	2	2	NUM
cusj-6360	77	3	.	.	PUNCT
cusj-6360	78	1	each	each	DET
cusj-6360	78	2	i	i	PRON
cusj-6360	78	3	,	,	PUNCT
cusj-6360	78	4	at	at	ADP
cusj-6360	78	5	any	any	DET
cusj-6360	78	6	time	time	NOUN
cusj-6360	78	7	t	t	PROPN
cusj-6360	78	8	,	,	PUNCT
cusj-6360	78	9	compute	compute	NOUN
cusj-6360	78	10	buy	buy	VERB
cusj-6360	78	11	:	:	PUNCT
cusj-6360	78	12	∑	∑	ADP
cusj-6360	78	13	all	all	DET
cusj-6360	78	14	signals	signal	NOUN
cusj-6360	78	15	:	:	PUNCT
cusj-6360	78	16	=	=	SYM
cusj-6360	78	17	val(dn)+val(signaln	val(dn)+val(signaln	X
cusj-6360	78	18	)	)	PUNCT
cusj-6360	78	19	+	+	NOUN
cusj-6360	78	20	val(self	val(self	PRON
cusj-6360	78	21	−normn	−normn	ADJ
cusj-6360	78	22	)	)	PUNCT
cusj-6360	78	23	+	+	ADJ
cusj-6360	78	24	val(renewaln	val(renewaln	NOUN
cusj-6360	78	25	)	)	PUNCT
cusj-6360	78	26	step	step	NOUN
cusj-6360	78	27	3	3	NUM
cusj-6360	78	28	.	.	PUNCT
cusj-6360	78	29	print(t	print(t	PROPN
cusj-6360	78	30	)	)	PUNCT
cusj-6360	78	31	;	;	PUNCT
cusj-6360	78	32	print(buy	print(buy	NOUN
cusj-6360	78	33	)	)	PUNCT
cusj-6360	78	34	.	.	PUNCT
cusj-6360	79	1	that	that	PRON
cusj-6360	79	2	is	be	AUX
cusj-6360	79	3	,	,	PUNCT
cusj-6360	79	4	buy	buy	VERB
cusj-6360	79	5	=	=	PUNCT
cusj-6360	79	6			PRON
cusj-6360	79	7	very	very	ADV
cusj-6360	79	8	heavy	heavy	ADJ
cusj-6360	79	9	,	,	PUNCT
cusj-6360	79	10	b	b	NOUN
cusj-6360	79	11	=	=	SYM
cusj-6360	79	12	4	4	NUM
cusj-6360	79	13	heavy	heavy	ADJ
cusj-6360	79	14	,	,	PUNCT
cusj-6360	79	15	b	b	X
cusj-6360	79	16	=	=	SYM
cusj-6360	79	17	3	3	NUM
cusj-6360	79	18	not	not	PART
cusj-6360	79	19	that	that	ADV
cusj-6360	79	20	heavy	heavy	ADJ
cusj-6360	79	21	,	,	PUNCT
cusj-6360	79	22	b	b	NOUN
cusj-6360	79	23	=	=	SYM
cusj-6360	79	24	2	2	NUM
cusj-6360	79	25	tiny	tiny	ADJ
cusj-6360	79	26	,	,	PUNCT
cusj-6360	79	27	b	b	NOUN
cusj-6360	79	28	=	=	SYM
cusj-6360	79	29	1	1	NUM
cusj-6360	79	30	do	do	VERB
cusj-6360	79	31	nothing	nothing	PRON
cusj-6360	79	32	,	,	PUNCT
cusj-6360	79	33	b	b	X
cusj-6360	79	34	=	=	SYM
cusj-6360	79	35	0	0	NUM
cusj-6360	79	36	page	page	NOUN
cusj-6360	79	37	2	2	NUM
cusj-6360	79	38	buy	buy	NOUN
cusj-6360	79	39	signal	signal	NOUN
cusj-6360	79	40	from	from	ADP
cusj-6360	79	41	limit	limit	NOUN
cusj-6360	79	42	theorem	theorem	ADJ
cusj-6360	79	43	[	[	PUNCT
cusj-6360	79	44	by	by	ADP
cusj-6360	79	45	yiqiao	yiqiao	PROPN
cusj-6360	79	46	yin	yin	PROPN
cusj-6360	79	47	]	]	PUNCT
cusj-6360	79	48	§	§	PROPN
cusj-6360	79	49	5	5	NUM
cusj-6360	79	50	while	while	SCONJ
cusj-6360	79	51	b	b	NOUN
cusj-6360	79	52	is	be	AUX
cusj-6360	79	53	a	a	DET
cusj-6360	79	54	discrete	discrete	ADJ
cusj-6360	79	55	time	time	NOUN
cusj-6360	79	56	-	-	PUNCT
cusj-6360	79	57	series	series	NOUN
cusj-6360	79	58	function	function	NOUN
cusj-6360	79	59	of	of	ADP
cusj-6360	79	60	time	time	NOUN
cusj-6360	79	61	t	t	PROPN
cusj-6360	79	62	,	,	PUNCT
cusj-6360	79	63	i.e.	i.e.	X
cusj-6360	79	64	b(t	b(t	NOUN
cusj-6360	79	65	)	)	PUNCT
cusj-6360	79	66	:	:	PUNCT
cusj-6360	79	67	z→	z→	NUM
cusj-6360	79	68	{	{	PUNCT
cusj-6360	79	69	0	0	NUM
cusj-6360	79	70	,	,	PUNCT
cusj-6360	79	71	1	1	NUM
cusj-6360	79	72	,	,	PUNCT
cusj-6360	79	73	2	2	NUM
cusj-6360	79	74	,	,	PUNCT
cusj-6360	79	75	3	3	NUM
cusj-6360	79	76	,	,	PUNCT
cusj-6360	79	77	4	4	NUM
cusj-6360	79	78	}	}	PUNCT
cusj-6360	79	79	.	.	PUNCT
cusj-6360	80	1	4	4	NUM
cusj-6360	80	2	conclusion	conclusion	NOUN
cusj-6360	80	3	this	this	DET
cusj-6360	80	4	paper	paper	NOUN
cusj-6360	80	5	starts	start	VERB
cusj-6360	80	6	with	with	ADP
cusj-6360	80	7	a	a	DET
cusj-6360	80	8	strong	strong	ADJ
cusj-6360	80	9	motivation	motivation	NOUN
cusj-6360	80	10	§	§	NOUN
cusj-6360	80	11	1	1	NUM
cusj-6360	80	12	and	and	CCONJ
cusj-6360	80	13	introduced	introduce	VERB
cusj-6360	80	14	the	the	DET
cusj-6360	80	15	background	background	NOUN
cusj-6360	80	16	of	of	ADP
cusj-6360	80	17	why	why	SCONJ
cusj-6360	80	18	we	we	PRON
cusj-6360	80	19	study	study	VERB
cusj-6360	80	20	security	security	NOUN
cusj-6360	80	21	prices	price	NOUN
cusj-6360	80	22	in	in	ADP
cusj-6360	80	23	such	such	ADJ
cusj-6360	80	24	construction	construction	NOUN
cusj-6360	80	25	.	.	PUNCT
cusj-6360	81	1	next	next	ADV
cusj-6360	81	2	,	,	PUNCT
cusj-6360	81	3	we	we	PRON
cusj-6360	81	4	present	present	VERB
cusj-6360	81	5	a	a	DET
cusj-6360	81	6	clear	clear	ADJ
cusj-6360	81	7	architecture	architecture	NOUN
cusj-6360	81	8	,	,	PUNCT
cusj-6360	81	9	in	in	ADP
cusj-6360	81	10	§	§	NOUN
cusj-6360	81	11	2	2	NUM
cusj-6360	81	12	,	,	PUNCT
cusj-6360	81	13	and	and	CCONJ
cusj-6360	81	14	a	a	DET
cusj-6360	81	15	series	series	NOUN
cusj-6360	81	16	of	of	ADP
cusj-6360	81	17	theorems	theorem	NOUN
cusj-6360	81	18	under	under	ADP
cusj-6360	81	19	such	such	ADJ
cusj-6360	81	20	building	building	NOUN
cusj-6360	81	21	blocks	block	NOUN
cusj-6360	81	22	.	.	PUNCT
cusj-6360	82	1	continuing	continue	VERB
cusj-6360	82	2	with	with	ADP
cusj-6360	82	3	the	the	DET
cusj-6360	82	4	results	result	NOUN
cusj-6360	82	5	from	from	ADP
cusj-6360	82	6	theorems	theorem	NOUN
cusj-6360	82	7	which	which	PRON
cusj-6360	82	8	we	we	PRON
cusj-6360	82	9	can	can	AUX
cusj-6360	82	10	collect	collect	VERB
cusj-6360	82	11	empirically	empirically	ADV
cusj-6360	82	12	,	,	PUNCT
cusj-6360	82	13	we	we	PRON
cusj-6360	82	14	develop	develop	VERB
cusj-6360	82	15	trade	trade	NOUN
cusj-6360	82	16	-	-	PUNCT
cusj-6360	82	17	able	able	ADJ
cusj-6360	82	18	algorithms	algorithm	NOUN
cusj-6360	82	19	§	§	NOUN
cusj-6360	82	20	3	3	NUM
cusj-6360	82	21	.	.	PUNCT
cusj-6360	83	1	in	in	ADP
cusj-6360	83	2	summary	summary	NOUN
cusj-6360	83	3	,	,	PUNCT
cusj-6360	83	4	we	we	PRON
cusj-6360	83	5	believe	believe	VERB
cusj-6360	83	6	such	such	ADJ
cusj-6360	83	7	algorithms	algorithm	NOUN
cusj-6360	83	8	can	can	AUX
cusj-6360	83	9	build	build	VERB
cusj-6360	83	10	a	a	DET
cusj-6360	83	11	capital	capital	NOUN
cusj-6360	83	12	market	market	NOUN
cusj-6360	83	13	with	with	ADP
cusj-6360	83	14	less	less	ADJ
cusj-6360	83	15	risk	risk	NOUN
cusj-6360	83	16	(	(	PUNCT
cusj-6360	83	17	an	an	DET
cusj-6360	83	18	anomaly	anomaly	NOUN
cusj-6360	83	19	corrector	corrector	NOUN
cusj-6360	83	20	)	)	PUNCT
cusj-6360	83	21	.	.	PUNCT
cusj-6360	84	1	for	for	ADP
cusj-6360	84	2	future	future	ADJ
cusj-6360	84	3	reference	reference	NOUN
cusj-6360	84	4	,	,	PUNCT
cusj-6360	84	5	we	we	PRON
cusj-6360	84	6	believe	believe	VERB
cusj-6360	84	7	our	our	PRON
cusj-6360	84	8	attempts	attempt	NOUN
cusj-6360	84	9	also	also	ADV
cusj-6360	84	10	opened	open	VERB
cusj-6360	84	11	up	up	ADP
cusj-6360	84	12	a	a	DET
cusj-6360	84	13	lot	lot	NOUN
cusj-6360	84	14	more	more	ADJ
cusj-6360	84	15	potential	potential	ADJ
cusj-6360	84	16	research	research	NOUN
cusj-6360	84	17	problems	problem	NOUN
cusj-6360	84	18	.	.	PUNCT
cusj-6360	85	1	for	for	ADP
cusj-6360	85	2	example	example	NOUN
cusj-6360	85	3	,	,	PUNCT
cusj-6360	85	4	what	what	PRON
cusj-6360	85	5	would	would	AUX
cusj-6360	85	6	happen	happen	VERB
cusj-6360	85	7	if	if	SCONJ
cusj-6360	85	8	everyone	everyone	PRON
cusj-6360	85	9	starts	start	VERB
cusj-6360	85	10	to	to	PART
cusj-6360	85	11	use	use	VERB
cusj-6360	85	12	this	this	DET
cusj-6360	85	13	strategy	strategy	NOUN
cusj-6360	85	14	?	?	PUNCT
cusj-6360	86	1	another	another	DET
cusj-6360	86	2	great	great	ADJ
cusj-6360	86	3	question	question	NOUN
cusj-6360	86	4	can	can	AUX
cusj-6360	86	5	be	be	AUX
cusj-6360	86	6	,	,	PUNCT
cusj-6360	86	7	what	what	PRON
cusj-6360	86	8	would	would	AUX
cusj-6360	86	9	be	be	AUX
cusj-6360	86	10	an	an	DET
cusj-6360	86	11	ideal	ideal	NOUN
cusj-6360	86	12	(	(	PUNCT
cusj-6360	86	13	although	although	SCONJ
cusj-6360	86	14	state	state	NOUN
cusj-6360	86	15	-	-	PUNCT
cusj-6360	86	16	of	of	ADP
cusj-6360	86	17	-	-	PUNCT
cusj-6360	86	18	art	art	NOUN
cusj-6360	86	19	)	)	PUNCT
cusj-6360	86	20	game	game	NOUN
cusj-6360	86	21	plan	plan	NOUN
cusj-6360	86	22	after	after	SCONJ
cusj-6360	86	23	the	the	DET
cusj-6360	86	24	algorithm	algorithm	NOUN
cusj-6360	86	25	tells	tell	VERB
cusj-6360	86	26	traders	trader	NOUN
cusj-6360	86	27	to	to	PART
cusj-6360	86	28	buy	buy	VERB
cusj-6360	86	29	?	?	PUNCT
cusj-6360	87	1	in	in	ADP
cusj-6360	87	2	macro	macro	ADJ
cusj-6360	87	3	point	point	NOUN
cusj-6360	87	4	of	of	ADP
cusj-6360	87	5	view	view	NOUN
cusj-6360	87	6	,	,	PUNCT
cusj-6360	87	7	how	how	SCONJ
cusj-6360	87	8	would	would	AUX
cusj-6360	87	9	an	an	DET
cusj-6360	87	10	economy	economy	NOUN
cusj-6360	87	11	perform	perform	VERB
cusj-6360	87	12	in	in	ADP
cusj-6360	87	13	long	long	ADJ
cusj-6360	87	14	run	run	NOUN
cusj-6360	87	15	if	if	SCONJ
cusj-6360	87	16	one	one	NUM
cusj-6360	87	17	implements	implement	VERB
cusj-6360	87	18	this	this	DET
cusj-6360	87	19	strategy	strategy	NOUN
cusj-6360	87	20	in	in	ADP
cusj-6360	87	21	a	a	DET
cusj-6360	87	22	larger	large	ADJ
cusj-6360	87	23	scale	scale	NOUN
cusj-6360	87	24	?	?	PUNCT
cusj-6360	88	1	what	what	PRON
cusj-6360	88	2	if	if	SCONJ
cusj-6360	88	3	an	an	DET
cusj-6360	88	4	unknown	unknown	ADJ
cusj-6360	88	5	outside	outside	ADJ
cusj-6360	88	6	monetary	monetary	ADJ
cusj-6360	88	7	force	force	NOUN
cusj-6360	88	8	enter	enter	VERB
cusj-6360	88	9	the	the	DET
cusj-6360	88	10	market	market	NOUN
cusj-6360	88	11	and	and	CCONJ
cusj-6360	88	12	act	act	VERB
cusj-6360	88	13	as	as	ADP
cusj-6360	88	14	an	an	DET
cusj-6360	88	15	anomaly	anomaly	NOUN
cusj-6360	88	16	,	,	PUNCT
cusj-6360	88	17	how	how	SCONJ
cusj-6360	88	18	would	would	AUX
cusj-6360	88	19	this	this	DET
cusj-6360	88	20	algorithm	algorithm	NOUN
cusj-6360	88	21	deal	deal	VERB
cusj-6360	88	22	with	with	ADP
cusj-6360	88	23	such	such	ADJ
cusj-6360	88	24	situation	situation	NOUN
cusj-6360	88	25	?	?	PUNCT
cusj-6360	89	1	5	5	NUM
cusj-6360	89	2	appendix	appendix	VERB
cusj-6360	89	3	5.1	5.1	NUM
cusj-6360	89	4	proof	proof	NOUN
cusj-6360	89	5	of	of	ADP
cusj-6360	89	6	theorem	theorem	ADJ
cusj-6360	89	7	2.2.1	2.2.1	NUM
cusj-6360	89	8	this	this	PRON
cusj-6360	89	9	is	be	AUX
cusj-6360	89	10	a	a	DET
cusj-6360	89	11	relatively	relatively	ADV
cusj-6360	89	12	easy	easy	ADJ
cusj-6360	89	13	proof	proof	NOUN
cusj-6360	89	14	since	since	SCONJ
cusj-6360	89	15	the	the	DET
cusj-6360	89	16	definition	definition	NOUN
cusj-6360	89	17	follow	follow	VERB
cusj-6360	89	18	the	the	DET
cusj-6360	89	19	premises	premise	NOUN
cusj-6360	89	20	of	of	ADP
cusj-6360	89	21	the	the	DET
cusj-6360	89	22	central	central	ADJ
cusj-6360	89	23	limit	limit	NOUN
cusj-6360	89	24	theorem	theorem	VERB
cusj-6360	89	25	.	.	PUNCT
cusj-6360	90	1	that	that	PRON
cusj-6360	90	2	is	is	ADV
cusj-6360	90	3	,	,	PUNCT
cusj-6360	90	4	we	we	PRON
cusj-6360	90	5	have	have	VERB
cusj-6360	90	6	pi	pi	NOUN
cusj-6360	90	7	,	,	PUNCT
cusj-6360	90	8	n	n	NOUN
cusj-6360	90	9	and	and	CCONJ
cusj-6360	90	10	sman	sman	NOUN
cusj-6360	90	11	that	that	PRON
cusj-6360	90	12	are	be	AUX
cusj-6360	90	13	i.i.d	i.i.d	ADP
cusj-6360	90	14	..	..	PUNCT
cusj-6360	90	15	then	then	ADV
cusj-6360	90	16	by	by	ADP
cusj-6360	90	17	c.l.t	c.l.t	NOUN
cusj-6360	90	18	.	.	PROPN
cusj-6360	90	19	,	,	PUNCT
cusj-6360	90	20	pi	pi	NOUN
cusj-6360	90	21	,	,	PUNCT
cusj-6360	90	22	n−sman	n−sman	ADJ
cusj-6360	90	23	⇒	⇒	NOUN
cusj-6360	90	24	χ	χ	X
cusj-6360	90	25	while	while	SCONJ
cusj-6360	90	26	χ	χ	PROPN
cusj-6360	90	27	stands	stand	VERB
cusj-6360	90	28	for	for	ADP
cusj-6360	90	29	standard	standard	ADJ
cusj-6360	90	30	normal	normal	ADJ
cusj-6360	90	31	distribution	distribution	NOUN
cusj-6360	90	32	.	.	PUNCT
cusj-6360	91	1	q.e.d	q.e.d	PROPN
cusj-6360	91	2	.	.	PUNCT
cusj-6360	92	1	5.2	5.2	NUM
cusj-6360	92	2	proof	proof	NOUN
cusj-6360	92	3	of	of	ADP
cusj-6360	92	4	theorem	theorem	NOUN
cusj-6360	92	5	2.2.2	2.2.2	NUM
cusj-6360	92	6	from	from	ADP
cusj-6360	92	7	weak	weak	ADJ
cusj-6360	92	8	law	law	NOUN
cusj-6360	92	9	we	we	PRON
cusj-6360	92	10	know	know	VERB
cusj-6360	92	11	that	that	SCONJ
cusj-6360	92	12	n∑	n∑	PROPN
cusj-6360	92	13	m=1	m=1	AUX
cusj-6360	92	14	d2	d2	PROPN
cusj-6360	92	15	m	m	PROPN
cusj-6360	92	16	/	/	SYM
cusj-6360	92	17	nσ	nσ	PROPN
cusj-6360	92	18	2	2	NUM
cusj-6360	92	19	→	→	SYM
cusj-6360	92	20	1	1	NUM
cusj-6360	92	21	.	.	PUNCT
cusj-6360	92	22	also	also	ADV
cusj-6360	92	23	note	note	VERB
cusj-6360	92	24	y−1/2	y−1/2	PROPN
cusj-6360	92	25	s	s	PROPN
cusj-6360	92	26	continuous	continuous	ADJ
cusj-6360	92	27	at	at	ADP
cusj-6360	92	28	1	1	NUM
cusj-6360	92	29	,	,	PUNCT
cusj-6360	92	30	then	then	ADV
cusj-6360	92	31	we	we	PRON
cusj-6360	92	32	have	have	AUX
cusj-6360	92	33	(	(	PUNCT
cusj-6360	92	34	σ2n	σ2n	X
cusj-6360	92	35	/	/	SYM
cusj-6360	92	36	n∑	n∑	PROPN
cusj-6360	92	37	m=1	m=1	PROPN
cusj-6360	92	38	d2	d2	PROPN
cusj-6360	92	39	m	m	PROPN
cusj-6360	92	40	)	)	PUNCT
cusj-6360	92	41	1/2	1/2	NUM
cusj-6360	92	42	→	→	SYM
cusj-6360	92	43	1	1	NUM
cusj-6360	92	44	,	,	PUNCT
cusj-6360	92	45	in	in	ADP
cusj-6360	92	46	prob	prob	NOUN
cusj-6360	92	47	.	.	PROPN
cusj-6360	92	48	,	,	PUNCT
cusj-6360	92	49	see	see	VERB
cusj-6360	92	50	?	?	PUNCT
cusj-6360	93	1	∑n	∑n	PROPN
cusj-6360	94	1	m=1	m=1	AUX
cusj-6360	94	2	dm	dm	PROPN
cusj-6360	94	3	σ	σ	NOUN
cusj-6360	94	4	√	√	PROPN
cusj-6360	94	5	n	n	CCONJ
cusj-6360	94	6	(	(	PUNCT
cusj-6360	94	7	σ2n∑n	σ2n∑n	VERB
cusj-6360	94	8	m=1	m=1	PROPN
cusj-6360	94	9	d2	d2	PROPN
cusj-6360	94	10	m	m	PROPN
cusj-6360	94	11	)	)	PUNCT
cusj-6360	94	12	1/2	1/2	NUM
cusj-6360	94	13	⇒	⇒	NOUN
cusj-6360	94	14	χ	χ	X
cusj-6360	94	15	·	·	PUNCT
cusj-6360	94	16	1	1	NUM
cusj-6360	94	17	,	,	PUNCT
cusj-6360	94	18	from	from	ADP
cusj-6360	94	19	?	?	PUNCT
cusj-6360	95	1	=	=	NOUN
cusj-6360	96	1	χ	χ	NOUN
cusj-6360	96	2	notice	notice	VERB
cusj-6360	96	3	that	that	SCONJ
cusj-6360	96	4	the	the	PRON
cusj-6360	96	5	?	?	PUNCT
cusj-6360	96	6	is	be	AUX
cusj-6360	96	7	because	because	SCONJ
cusj-6360	96	8	in	in	ADP
cusj-6360	96	9	weak	weak	ADJ
cusj-6360	96	10	convergence	convergence	NOUN
cusj-6360	96	11	,	,	PUNCT
cusj-6360	96	12	there	there	PRON
cusj-6360	96	13	is	be	VERB
cusj-6360	96	14	a	a	DET
cusj-6360	96	15	theorem	theorem	NOUN
cusj-6360	96	16	stated	state	VERB
cusj-6360	96	17	that	that	SCONJ
cusj-6360	96	18	xn	xn	PROPN
cusj-6360	96	19	⇒	⇒	PROPN
cusj-6360	96	20	x∞	x∞	PROPN
cusj-6360	97	1	if	if	SCONJ
cusj-6360	97	2	and	and	CCONJ
cusj-6360	97	3	only	only	ADV
cusj-6360	97	4	if	if	SCONJ
cusj-6360	97	5	for	for	ADP
cusj-6360	97	6	every	every	DET
cusj-6360	97	7	bounded	bound	VERB
cusj-6360	97	8	continuous	continuous	ADJ
cusj-6360	97	9	function	function	NOUN
cusj-6360	97	10	g	g	NOUN
cusj-6360	97	11	we	we	PRON
cusj-6360	97	12	have	have	VERB
cusj-6360	97	13	eg(xn)→	eg(xn)→	PROPN
cusj-6360	97	14	eg(x∞	eg(x∞	NOUN
cusj-6360	97	15	)	)	PUNCT
cusj-6360	97	16	.	.	PUNCT
cusj-6360	98	1	since	since	SCONJ
cusj-6360	98	2	we	we	PRON
cusj-6360	98	3	discussed	discuss	VERB
cusj-6360	98	4	the	the	DET
cusj-6360	98	5	continuity	continuity	NOUN
cusj-6360	98	6	of	of	ADP
cusj-6360	98	7	function	function	NOUN
cusj-6360	98	8	y−1/2	y−1/2	ADJ
cusj-6360	98	9	at	at	ADP
cusj-6360	98	10	1	1	NUM
cusj-6360	98	11	,	,	PUNCT
cusj-6360	98	12	this	this	DET
cusj-6360	98	13	line	line	NOUN
cusj-6360	98	14	is	be	AUX
cusj-6360	98	15	valid	valid	ADJ
cusj-6360	98	16	.	.	PUNCT
cusj-6360	99	1	q.e.d	q.e.d	PROPN
cusj-6360	99	2	.	.	PUNCT
cusj-6360	99	3	remark	remark	PROPN
cusj-6360	99	4	5.2.1	5.2.1	NUM
cusj-6360	99	5	.	.	PUNCT
cusj-6360	100	1	from	from	ADP
cusj-6360	100	2	[	[	X
cusj-6360	100	3	1	1	NUM
cusj-6360	100	4	]	]	PUNCT
cusj-6360	100	5	,	,	PUNCT
cusj-6360	100	6	section	section	NOUN
cusj-6360	100	7	2	2	NUM
cusj-6360	100	8	,	,	PUNCT
cusj-6360	100	9	the	the	DET
cusj-6360	100	10	theorem	theorem	NOUN
cusj-6360	100	11	stated	state	VERB
cusj-6360	100	12	the	the	DET
cusj-6360	100	13	following	following	NOUN
cusj-6360	100	14	.	.	PUNCT
cusj-6360	101	1	suppose	suppose	VERB
cusj-6360	101	2	xn	xn	PROPN
cusj-6360	101	3	⇒	⇒	PROPN
cusj-6360	101	4	x	x	PROPN
cusj-6360	101	5	,	,	PUNCT
cusj-6360	101	6	yn	yn	PRON
cusj-6360	101	7	≥	≥	NOUN
cusj-6360	101	8	0	0	NUM
cusj-6360	101	9	,	,	PUNCT
cusj-6360	101	10	and	and	CCONJ
cusj-6360	101	11	yn	yn	PRON
cusj-6360	101	12	⇒	⇒	VERB
cusj-6360	101	13	c	c	PROPN
cusj-6360	101	14	,	,	PUNCT
cusj-6360	101	15	where	where	SCONJ
cusj-6360	101	16	c	c	AUX
cusj-6360	101	17	>	>	X
cusj-6360	101	18	0	0	NUM
cusj-6360	101	19	is	be	AUX
cusj-6360	101	20	a	a	DET
cusj-6360	101	21	constant	constant	ADJ
cusj-6360	101	22	,	,	PUNCT
cusj-6360	101	23	then	then	ADV
cusj-6360	101	24	xnyn	xnyn	PROPN
cusj-6360	101	25	⇒	⇒	PROPN
cusj-6360	101	26	cx	cx	PROPN
cusj-6360	101	27	.	.	PUNCT
cusj-6360	102	1	5.3	5.3	NUM
cusj-6360	102	2	proof	proof	NOUN
cusj-6360	102	3	of	of	ADP
cusj-6360	102	4	theorem	theorem	ADJ
cusj-6360	102	5	2.2.3	2.2.3	NUM
cusj-6360	102	6	from	from	ADP
cusj-6360	102	7	kolmogorov	kolmogorov	PROPN
cusj-6360	102	8	’s	’s	PART
cusj-6360	102	9	inequality	inequality	NOUN
cusj-6360	102	10	we	we	PRON
cusj-6360	102	11	know	know	VERB
cusj-6360	102	12	p	p	X
cusj-6360	102	13	(	(	PUNCT
cusj-6360	102	14	max	max	PROPN
cusj-6360	102	15	(	(	PUNCT
cusj-6360	102	16	1−ε)cn≤m≤(1+ε)cn	1−ε)cn≤m≤(1+ε)cn	NOUN
cusj-6360	102	17	|sm	|sm	X
cusj-6360	102	18	−	−	PROPN
cusj-6360	102	19	s[(1−ε)cn]|	s[(1−ε)cn]|	X
cusj-6360	102	20	)	)	PUNCT
cusj-6360	102	21	≤	≤	NUM
cusj-6360	102	22	2ε	2ε	NUM
cusj-6360	102	23	/	/	SYM
cusj-6360	102	24	δ2	δ2	VERB
cusj-6360	102	25	if	if	SCONJ
cusj-6360	102	26	dn	dn	PROPN
cusj-6360	102	27	=	=	SYM
cusj-6360	102	28	snn	snn	X
cusj-6360	102	29	/σ	/σ	PUNCT
cusj-6360	102	30	√	√	INTJ
cusj-6360	103	1	cn	cn	INTJ
cusj-6360	103	2	and	and	CCONJ
cusj-6360	103	3	yn	yn	NOUN
cusj-6360	103	4	=	=	PUNCT
cusj-6360	103	5	scn	scn	PROPN
cusj-6360	103	6	/	/	SYM
cusj-6360	103	7	σ	σ	PROPN
cusj-6360	103	8	√	√	PROPN
cusj-6360	104	1	cn	cn	INTJ
cusj-6360	104	2	,	,	PUNCT
cusj-6360	104	3	then	then	ADV
cusj-6360	104	4	it	it	PRON
cusj-6360	104	5	follows	follow	VERB
cusj-6360	104	6	that	that	SCONJ
cusj-6360	104	7	lim	lim	PROPN
cusj-6360	104	8	sup	sup	VERB
cusj-6360	104	9	n→∞	n→∞	PRON
cusj-6360	104	10	p	p	NOUN
cusj-6360	104	11	(	(	PUNCT
cusj-6360	104	12	|dn	|dn	NUM
cusj-6360	104	13	−	−	PROPN
cusj-6360	104	14	yn|	yn|	PROPN
cusj-6360	104	15	>	>	X
cusj-6360	104	16	δ	δ	PROPN
cusj-6360	104	17	)	)	PUNCT
cusj-6360	104	18	≤	≤	PUNCT
cusj-6360	104	19	2ε	2ε	NUM
cusj-6360	104	20	/	/	SYM
cusj-6360	104	21	δ2,∀ε	δ2,∀ε	PROPN
cusj-6360	104	22	then	then	ADV
cusj-6360	104	23	we	we	PRON
cusj-6360	104	24	have	have	VERB
cusj-6360	104	25	p	p	NOUN
cusj-6360	104	26	(	(	PUNCT
cusj-6360	104	27	|dn	|dn	NUM
cusj-6360	104	28	−	−	PROPN
cusj-6360	104	29	yn|	yn|	PROPN
cusj-6360	104	30	>	>	X
cusj-6360	104	31	δ	δ	PROPN
cusj-6360	104	32	)	)	PUNCT
cusj-6360	104	33	→	→	SYM
cusj-6360	104	34	0	0	NUM
cusj-6360	104	35	for	for	ADP
cusj-6360	104	36	each	each	DET
cusj-6360	104	37	δ	δ	PROPN
cusj-6360	104	38	>	>	X
cusj-6360	104	39	0	0	NUM
cusj-6360	104	40	,	,	PUNCT
cusj-6360	104	41	i.e.	i.e.	X
cusj-6360	104	42	,	,	PUNCT
cusj-6360	104	43	xn	xn	PROPN
cusj-6360	104	44	−	−	PROPN
cusj-6360	104	45	yn	yn	PROPN
cusj-6360	104	46	→	→	SYM
cusj-6360	104	47	0	0	NUM
cusj-6360	104	48	in	in	ADP
cusj-6360	104	49	probability	probability	NOUN
cusj-6360	104	50	.	.	PUNCT
cusj-6360	105	1	this	this	PRON
cusj-6360	105	2	is	be	AUX
cusj-6360	105	3	because	because	SCONJ
cusj-6360	105	4	of	of	ADP
cusj-6360	105	5	the	the	DET
cusj-6360	105	6	cnverging	cnverge	VERB
cusj-6360	105	7	together	together	ADV
cusj-6360	105	8	lemma	lemma	PROPN
cusj-6360	105	9	stated	state	VERB
cusj-6360	105	10	in	in	ADP
cusj-6360	105	11	weak	weak	ADJ
cusj-6360	105	12	convergence	convergence	NOUN
cusj-6360	105	13	part	part	NOUN
cusj-6360	105	14	of	of	ADP
cusj-6360	105	15	[	[	X
cusj-6360	105	16	1	1	NUM
cusj-6360	105	17	]	]	PUNCT
cusj-6360	105	18	.	.	PUNCT
cusj-6360	106	1	we	we	PRON
cusj-6360	106	2	state	state	VERB
cusj-6360	106	3	the	the	DET
cusj-6360	106	4	theorem	theorem	NOUN
cusj-6360	106	5	in	in	ADP
cusj-6360	106	6	remark	remark	NOUN
cusj-6360	106	7	below	below	ADV
cusj-6360	106	8	.	.	PUNCT
cusj-6360	107	1	q.e.d	q.e.d	PROPN
cusj-6360	107	2	.	.	PUNCT
cusj-6360	107	3	remark	remark	PROPN
cusj-6360	107	4	5.3.1	5.3.1	NUM
cusj-6360	107	5	.	.	PUNCT
cusj-6360	108	1	suppose	suppose	VERB
cusj-6360	108	2	xn	xn	PROPN
cusj-6360	108	3	⇒	⇒	PROPN
cusj-6360	108	4	x	x	PUNCT
cusj-6360	108	5	and	and	CCONJ
cusj-6360	108	6	yn	yn	PRON
cusj-6360	108	7	⇒	⇒	VERB
cusj-6360	109	1	c	c	PROPN
cusj-6360	109	2	,	,	PUNCT
cusj-6360	109	3	where	where	SCONJ
cusj-6360	109	4	c	c	PROPN
cusj-6360	109	5	is	be	AUX
cusj-6360	109	6	a	a	DET
cusj-6360	109	7	constant	constant	ADJ
cusj-6360	109	8	then	then	ADV
cusj-6360	109	9	xn	xn	PROPN
cusj-6360	110	1	+	+	NUM
cusj-6360	110	2	yn	yn	PROPN
cusj-6360	110	3	⇒	⇒	NOUN
cusj-6360	110	4	x	x	PUNCT
cusj-6360	111	1	+	+	CCONJ
cusj-6360	111	2	c.	c.	NOUN
cusj-6360	111	3	a	a	DET
cusj-6360	111	4	useful	useful	ADJ
cusj-6360	111	5	consequence	consequence	NOUN
cusj-6360	111	6	is	be	AUX
cusj-6360	111	7	that	that	SCONJ
cusj-6360	111	8	if	if	SCONJ
cusj-6360	111	9	xn	xn	PROPN
cusj-6360	111	10	⇒	⇒	VERB
cusj-6360	111	11	x	x	PUNCT
cusj-6360	111	12	and	and	CCONJ
cusj-6360	111	13	zn	zn	PROPN
cusj-6360	111	14	−xn	−xn	NUM
cusj-6360	111	15	⇒	⇒	NOUN
cusj-6360	111	16	0	0	PUNCT
cusj-6360	112	1	then	then	ADV
cusj-6360	112	2	xn	xn	PROPN
cusj-6360	112	3	⇒	⇒	PROPN
cusj-6360	112	4	x.	x.	NOUN
cusj-6360	113	1	5.4	5.4	NUM
cusj-6360	113	2	proof	proof	NOUN
cusj-6360	113	3	of	of	ADP
cusj-6360	113	4	theorem	theorem	ADJ
cusj-6360	113	5	2.2.3	2.2.3	NUM
cusj-6360	113	6	from	from	ADP
cusj-6360	113	7	convergence	convergence	NOUN
cusj-6360	113	8	theorem	theorem	NOUN
cusj-6360	113	9	,	,	PUNCT
cusj-6360	113	10	we	we	PRON
cusj-6360	113	11	know	know	VERB
cusj-6360	113	12	that	that	SCONJ
cusj-6360	113	13	nt	not	PART
cusj-6360	113	14	tµ	tµ	PRON
cusj-6360	113	15	→	→	SYM
cusj-6360	113	16	1	1	NUM
cusj-6360	113	17	so	so	ADV
cusj-6360	113	18	from	from	ADP
cusj-6360	113	19	theorem	theorem	ADJ
cusj-6360	113	20	2.2.3	2.2.3	NUM
cusj-6360	113	21	we	we	PRON
cusj-6360	113	22	have	have	VERB
cusj-6360	113	23	sn	sn	NOUN
cusj-6360	113	24	−	−	PROPN
cusj-6360	113	25	µnt	µnt	PROPN
cusj-6360	113	26	σ	σ	PROPN
cusj-6360	113	27	√	√	VERB
cusj-6360	113	28	t/µ	t/µ	PROPN
cusj-6360	113	29	→	→	SYM
cusj-6360	113	30	0	0	NUM
cusj-6360	113	31	then	then	ADV
cusj-6360	113	32	it	it	PRON
cusj-6360	113	33	is	be	AUX
cusj-6360	113	34	sufficient	sufficient	ADJ
cusj-6360	113	35	to	to	PART
cusj-6360	113	36	show	show	VERB
cusj-6360	113	37	(	(	PUNCT
cusj-6360	113	38	sn	sn	ADV
cusj-6360	113	39	−	−	PROPN
cusj-6360	113	40	t)/	t)/	PROPN
cusj-6360	114	1	√	√	ADP
cusj-6360	114	2	t→	t→	NOUN
cusj-6360	114	3	0	0	PUNCT
cusj-6360	114	4	since	since	SCONJ
cusj-6360	114	5	it	it	PRON
cusj-6360	114	6	follows	follow	VERB
cusj-6360	114	7	that	that	SCONJ
cusj-6360	114	8	(	(	PUNCT
cusj-6360	114	9	µnt−t)√	µnt−t)√	NOUN
cusj-6360	114	10	σ2t/µ	σ2t/µ	CCONJ
cusj-6360	114	11	⇒	⇒	PROPN
cusj-6360	114	12	χ	χ	X
cusj-6360	114	13	.	.	PUNCT
cusj-6360	115	1	we	we	PRON
cusj-6360	115	2	have	have	AUX
cusj-6360	115	3	given	give	VERB
cusj-6360	115	4	finite	finite	ADJ
cusj-6360	115	5	variance	variance	NOUN
cusj-6360	115	6	,	,	PUNCT
cusj-6360	115	7	that	that	ADV
cusj-6360	115	8	is	is	ADV
cusj-6360	115	9	,	,	PUNCT
cusj-6360	115	10	σ2	σ2	PROPN
cusj-6360	115	11	<	<	X
cusj-6360	115	12	∞	∞	PROPN
cusj-6360	115	13	,	,	PUNCT
cusj-6360	115	14	so	so	ADV
cusj-6360	115	15	by	by	ADP
cusj-6360	115	16	d.c.t	d.c.t	NOUN
cusj-6360	115	17	.	.	PUNCT
cusj-6360	116	1	(	(	PUNCT
cusj-6360	116	2	dominated	dominate	VERB
cusj-6360	116	3	convergence	convergence	NOUN
cusj-6360	116	4	theorem	theorem	VERB
cusj-6360	116	5	)	)	PUNCT
cusj-6360	116	6	,	,	PUNCT
cusj-6360	116	7	we	we	PRON
cusj-6360	116	8	have	have	VERB
cusj-6360	116	9	p	p	NOUN
cusj-6360	116	10	(	(	PUNCT
cusj-6360	116	11	max	max	PROPN
cusj-6360	116	12	1≤m≤2tµ	1≤m≤2tµ	NUM
cusj-6360	117	1	ym	ym	INTJ
cusj-6360	117	2	>	>	X
cusj-6360	117	3	ε	ε	PROPN
cusj-6360	117	4	√	√	PROPN
cusj-6360	117	5	t	t	PROPN
cusj-6360	117	6	)	)	PUNCT
cusj-6360	118	1	=	=	PUNCT
cusj-6360	118	2	2	2	NUM
cusj-6360	118	3	t	t	NOUN
cusj-6360	118	4	µ	µ	X
cusj-6360	118	5	p	p	X
cusj-6360	118	6	(	(	PUNCT
cusj-6360	118	7	y1	y1	INTJ
cusj-6360	118	8	>	>	X
cusj-6360	118	9	ε	ε	PROPN
cusj-6360	118	10	√	√	PROPN
cusj-6360	118	11	t	t	PROPN
cusj-6360	118	12	)	)	PUNCT
cusj-6360	118	13	=	=	SYM
cusj-6360	118	14	2	2	NUM
cusj-6360	118	15	µε2e(y	µε2e(y	NUM
cusj-6360	118	16	2	2	NUM
cusj-6360	118	17	1	1	NUM
cusj-6360	118	18	;	;	PUNCT
cusj-6360	118	19	y1	y1	INTJ
cusj-6360	118	20	>	>	X
cusj-6360	118	21	ε	ε	PROPN
cusj-6360	118	22	√	√	NUM
cusj-6360	118	23	t)→	t)→	NOUN
cusj-6360	118	24	0	0	NUM
cusj-6360	118	25	which	which	PRON
cusj-6360	118	26	proves	prove	VERB
cusj-6360	118	27	that	that	SCONJ
cusj-6360	118	28	(	(	PUNCT
cusj-6360	118	29	sn	sn	INTJ
cusj-6360	118	30	−	−	PROPN
cusj-6360	118	31	t)/	t)/	PROPN
cusj-6360	119	1	√	√	PROPN
cusj-6360	119	2	t	t	PROPN
cusj-6360	119	3	→	→	SYM
cusj-6360	119	4	0	0	NUM
cusj-6360	119	5	is	be	AUX
cusj-6360	119	6	true	true	ADJ
cusj-6360	119	7	.	.	PUNCT
cusj-6360	120	1	hence	hence	ADV
cusj-6360	120	2	,	,	PUNCT
cusj-6360	120	3	this	this	PRON
cusj-6360	120	4	completes	complete	VERB
cusj-6360	120	5	the	the	DET
cusj-6360	120	6	proof	proof	NOUN
cusj-6360	120	7	.	.	PUNCT
cusj-6360	121	1	remark	remark	VERB
cusj-6360	121	2	5.4.1	5.4.1	NUM
cusj-6360	121	3	.	.	PUNCT
cusj-6360	122	1	this	this	PRON
cusj-6360	122	2	is	be	AUX
cusj-6360	122	3	because	because	SCONJ
cusj-6360	122	4	of	of	ADP
cusj-6360	122	5	the	the	DET
cusj-6360	122	6	converging	converge	VERB
cusj-6360	122	7	together	together	ADV
cusj-6360	122	8	lemma	lemma	PROPN
cusj-6360	122	9	stated	state	VERB
cusj-6360	122	10	weak	weak	ADJ
cusj-6360	122	11	convergence	convergence	NOUN
cusj-6360	122	12	.	.	PUNCT
cusj-6360	123	1	please	please	INTJ
cusj-6360	123	2	see	see	VERB
cusj-6360	123	3	remark	remark	NOUN
cusj-6360	123	4	5.3.1	5.3.1	PROPN
cusj-6360	123	5	.	.	PUNCT
cusj-6360	124	1	q.e.d	q.e.d	PROPN
cusj-6360	124	2	.	.	PUNCT
cusj-6360	125	1	page	page	NOUN
cusj-6360	125	2	3	3	NUM
cusj-6360	125	3	buy	buy	VERB
cusj-6360	125	4	signal	signal	NOUN
cusj-6360	125	5	from	from	ADP
cusj-6360	125	6	limit	limit	NOUN
cusj-6360	125	7	theorem	theorem	ADJ
cusj-6360	125	8	[	[	PUNCT
cusj-6360	125	9	by	by	ADP
cusj-6360	125	10	yiqiao	yiqiao	PROPN
cusj-6360	125	11	yin	yin	PROPN
cusj-6360	125	12	]	]	PUNCT
cusj-6360	125	13	§	§	PROPN
cusj-6360	125	14	5	5	NUM
cusj-6360	125	15	references	reference	NOUN
cusj-6360	125	16	[	[	X
cusj-6360	125	17	1	1	NUM
cusj-6360	125	18	]	]	PUNCT
cusj-6360	125	19	durrett	durrett	PROPN
cusj-6360	125	20	,	,	PUNCT
cusj-6360	125	21	rick	rick	PROPN
cusj-6360	125	22	,	,	PUNCT
cusj-6360	125	23	“	"	PUNCT
cusj-6360	125	24	probability	probability	NOUN
cusj-6360	125	25	:	:	PUNCT
cusj-6360	125	26	theory	theory	NOUN
cusj-6360	125	27	and	and	CCONJ
cusj-6360	125	28	examples	example	NOUN
cusj-6360	125	29	”	"	PUNCT
cusj-6360	125	30	,	,	PUNCT
cusj-6360	125	31	4e	4e	NOUN
cusj-6360	125	32	.	.	PUNCT
cusj-6360	126	1	[	[	X
cusj-6360	126	2	2	2	NUM
cusj-6360	126	3	]	]	PUNCT
cusj-6360	126	4	fama	fama	PROPN
cusj-6360	126	5	,	,	PUNCT
cusj-6360	126	6	eugene	eugene	PROPN
cusj-6360	126	7	f.	f.	PROPN
cusj-6360	126	8	(	(	PUNCT
cusj-6360	126	9	1992	1992	NUM
cusj-6360	126	10	)	)	PUNCT
cusj-6360	126	11	,	,	PUNCT
cusj-6360	126	12	“	"	PUNCT
cusj-6360	126	13	the	the	DET
cusj-6360	126	14	cross	cross	NOUN
cusj-6360	126	15	-	-	NOUN
cusj-6360	126	16	section	section	NOUN
cusj-6360	126	17	of	of	ADP
cusj-6360	126	18	expected	expect	VERB
cusj-6360	126	19	stock	stock	NOUN
cusj-6360	126	20	returns	return	NOUN
cusj-6360	126	21	,	,	PUNCT
cusj-6360	126	22	”	"	PUNCT
cusj-6360	126	23	journal	journal	NOUN
cusj-6360	126	24	of	of	ADP
cusj-6360	126	25	finance	finance	NOUN
cusj-6360	126	26	,	,	PUNCT
cusj-6360	126	27	47	47	NUM
cusj-6360	126	28	,	,	PUNCT
cusj-6360	126	29	427	427	NUM
cusj-6360	126	30	-	-	SYM
cusj-6360	126	31	465	465	NUM
cusj-6360	126	32	.	.	PUNCT
cusj-6360	127	1	[	[	X
cusj-6360	127	2	3	3	NUM
cusj-6360	127	3	]	]	PUNCT
cusj-6360	127	4	fama	fama	PROPN
cusj-6360	127	5	,	,	PUNCT
cusj-6360	127	6	eugene	eugene	PROPN
cusj-6360	127	7	f.	f.	PROPN
cusj-6360	127	8	(	(	PUNCT
cusj-6360	127	9	1993	1993	NUM
cusj-6360	127	10	)	)	PUNCT
cusj-6360	127	11	,	,	PUNCT
cusj-6360	127	12	“	"	PUNCT
cusj-6360	127	13	common	common	ADJ
cusj-6360	127	14	risk	risk	NOUN
cusj-6360	127	15	factors	factor	NOUN
cusj-6360	127	16	in	in	ADP
cusj-6360	127	17	the	the	DET
cusj-6360	127	18	returns	return	NOUN
cusj-6360	127	19	on	on	ADP
cusj-6360	127	20	stocks	stock	NOUN
cusj-6360	127	21	and	and	CCONJ
cusj-6360	127	22	bonds	bond	NOUN
cusj-6360	127	23	,	,	PUNCT
cusj-6360	127	24	”	"	PUNCT
cusj-6360	127	25	journal	journal	NOUN
cusj-6360	127	26	of	of	ADP
cusj-6360	127	27	financial	financial	ADJ
cusj-6360	127	28	economics	economic	NOUN
cusj-6360	127	29	,	,	PUNCT
cusj-6360	127	30	33	33	NUM
cusj-6360	127	31	,	,	PUNCT
cusj-6360	127	32	3	3	NUM
cusj-6360	127	33	-	-	SYM
cusj-6360	127	34	56	56	NUM
cusj-6360	127	35	.	.	PUNCT
cusj-6360	128	1	[	[	X
cusj-6360	128	2	4	4	NUM
cusj-6360	128	3	]	]	X
cusj-6360	128	4	fama	fama	PROPN
cusj-6360	128	5	,	,	PUNCT
cusj-6360	128	6	eugene	eugene	PROPN
cusj-6360	128	7	f.	f.	PROPN
cusj-6360	128	8	(	(	PUNCT
cusj-6360	128	9	1996	1996	NUM
cusj-6360	128	10	)	)	PUNCT
cusj-6360	128	11	,	,	PUNCT
cusj-6360	128	12	“	"	PUNCT
cusj-6360	128	13	multifactor	multifactor	NOUN
cusj-6360	128	14	portfolio	portfolio	NOUN
cusj-6360	128	15	efficiency	efficiency	NOUN
cusj-6360	128	16	and	and	CCONJ
cusj-6360	128	17	multifactor	multifactor	NOUN
cusj-6360	128	18	asset	asset	NOUN
cusj-6360	128	19	pricing	pricing	NOUN
cusj-6360	128	20	,	,	PUNCT
cusj-6360	128	21	”	"	PUNCT
cusj-6360	128	22	journal	journal	NOUN
cusj-6360	128	23	of	of	ADP
cusj-6360	128	24	financial	financial	ADJ
cusj-6360	128	25	and	and	CCONJ
cusj-6360	128	26	quantitative	quantitative	ADJ
cusj-6360	128	27	analysis	analysis	NOUN
cusj-6360	128	28	,	,	PUNCT
cusj-6360	128	29	31	31	NUM
cusj-6360	128	30	,	,	PUNCT
cusj-6360	128	31	441465	441465	NUM
cusj-6360	128	32	.	.	PUNCT
cusj-6360	129	1	[	[	X
cusj-6360	129	2	5	5	NUM
cusj-6360	129	3	]	]	PUNCT
cusj-6360	129	4	fama	fama	PROPN
cusj-6360	129	5	,	,	PUNCT
cusj-6360	129	6	eugene	eugene	PROPN
cusj-6360	129	7	f.	f.	PROPN
cusj-6360	129	8	(	(	PUNCT
cusj-6360	129	9	2006	2006	NUM
cusj-6360	129	10	)	)	PUNCT
cusj-6360	129	11	,	,	PUNCT
cusj-6360	129	12	“	"	PUNCT
cusj-6360	129	13	profitability	profitability	NOUN
cusj-6360	129	14	,	,	PUNCT
cusj-6360	129	15	investment	investment	NOUN
cusj-6360	129	16	,	,	PUNCT
cusj-6360	129	17	and	and	CCONJ
cusj-6360	129	18	average	average	ADJ
cusj-6360	129	19	returns	return	NOUN
cusj-6360	129	20	,	,	PUNCT
cusj-6360	129	21	”	"	PUNCT
cusj-6360	129	22	,	,	PUNCT
cusj-6360	129	23	journal	journal	NOUN
cusj-6360	129	24	of	of	ADP
cusj-6360	129	25	financial	financial	ADJ
cusj-6360	129	26	economics	economic	NOUN
cusj-6360	129	27	,	,	PUNCT
cusj-6360	129	28	82	82	NUM
cusj-6360	129	29	,	,	PUNCT
cusj-6360	129	30	491	491	NUM
cusj-6360	129	31	-	-	SYM
cusj-6360	129	32	518	518	NUM
cusj-6360	129	33	.	.	PUNCT
cusj-6360	130	1	[	[	X
cusj-6360	130	2	6	6	NUM
cusj-6360	130	3	]	]	X
cusj-6360	130	4	malkiel	malkiel	PROPN
cusj-6360	130	5	,	,	PUNCT
cusj-6360	130	6	burton	burton	PROPN
cusj-6360	130	7	g.	g.	PROPN
cusj-6360	130	8	(	(	PUNCT
cusj-6360	130	9	2007	2007	NUM
cusj-6360	130	10	)	)	PUNCT
cusj-6360	130	11	,	,	PUNCT
cusj-6360	130	12	“	"	PUNCT
cusj-6360	130	13	reflections	reflection	NOUN
cusj-6360	130	14	on	on	ADP
cusj-6360	130	15	the	the	DET
cusj-6360	130	16	efficient	efficient	ADJ
cusj-6360	130	17	market	market	NOUN
cusj-6360	130	18	hypothesis	hypothesis	NOUN
cusj-6360	130	19	:	:	PUNCT
cusj-6360	130	20	30	30	NUM
cusj-6360	130	21	years	year	NOUN
cusj-6360	130	22	later	later	ADV
cusj-6360	130	23	,	,	PUNCT
cusj-6360	130	24	”	"	PUNCT
cusj-6360	130	25	the	the	DET
cusj-6360	130	26	financial	financial	ADJ
cusj-6360	130	27	review	review	NOUN
cusj-6360	130	28	,	,	PUNCT
cusj-6360	130	29	40	40	NUM
cusj-6360	130	30	,	,	PUNCT
cusj-6360	130	31	1	1	NUM
cusj-6360	130	32	-	-	SYM
cusj-6360	130	33	9	9	NUM
cusj-6360	130	34	.	.	PUNCT
cusj-6360	131	1	[	[	X
cusj-6360	131	2	7	7	NUM
cusj-6360	131	3	]	]	X
cusj-6360	131	4	yin	yin	NOUN
cusj-6360	131	5	,	,	PUNCT
cusj-6360	131	6	yiqiao	yiqiao	PROPN
cusj-6360	131	7	(	(	PUNCT
cusj-6360	131	8	2017	2017	NUM
cusj-6360	131	9	)	)	PUNCT
cusj-6360	131	10	,	,	PUNCT
cusj-6360	131	11	“	"	PUNCT
cusj-6360	131	12	anomaly	anomaly	NOUN
cusj-6360	131	13	correction	correction	NOUN
cusj-6360	131	14	by	by	ADP
cusj-6360	131	15	optimal	optimal	ADJ
cusj-6360	131	16	trading	trading	NOUN
cusj-6360	131	17	frequency	frequency	NOUN
cusj-6360	131	18	”	"	PUNCT
cusj-6360	131	19	,	,	PUNCT
cusj-6360	131	20	cusj	cusj	NOUN
cusj-6360	131	21	,	,	PUNCT
cusj-6360	131	22	page	page	NOUN
cusj-6360	131	23	4	4	NUM
cusj-6360	131	24	introduction	introduction	NOUN
cusj-6360	131	25	theoretical	theoretical	ADJ
cusj-6360	131	26	framework	framework	NOUN
cusj-6360	131	27	architecture	architecture	NOUN
cusj-6360	131	28	theories	theory	NOUN
cusj-6360	131	29	algorithms	algorithm	VERB
cusj-6360	131	30	conclusion	conclusion	NOUN
cusj-6360	131	31	appendix	appendix	VERB
cusj-6360	131	32	proof	proof	NOUN
cusj-6360	131	33	of	of	ADP
cusj-6360	131	34	theorem	theorem	ADJ
cusj-6360	131	35	2.2.1	2.2.1	NUM
cusj-6360	131	36	proof	proof	NOUN
cusj-6360	131	37	of	of	ADP
cusj-6360	131	38	theorem	theorem	ADJ
cusj-6360	131	39	2.2.2	2.2.2	NUM
cusj-6360	131	40	proof	proof	NOUN
cusj-6360	131	41	of	of	ADP
cusj-6360	131	42	theorem	theorem	ADJ
cusj-6360	131	43	2.2.3	2.2.3	NUM
cusj-6360	131	44	proof	proof	NOUN
cusj-6360	131	45	of	of	ADP
cusj-6360	131	46	theorem	theorem	ADJ
cusj-6360	131	47	2.2.3	2.2.3	NUM