id sid tid token lemma pos dem-8574 1 1 dem_2015_27to48 dem_2015_27to48 X dem-8574 1 2 © © PROPN dem-8574 1 3 2015 2015 NUM dem-8574 1 4 nicolaus nicolaus PROPN dem-8574 1 5 copernicus copernicus PROPN dem-8574 1 6 university university PROPN dem-8574 1 7 press press NOUN dem-8574 1 8 . . PUNCT dem-8574 2 1 all all DET dem-8574 2 2 rights right NOUN dem-8574 2 3 reserved reserve VERB dem-8574 2 4 . . PUNCT dem-8574 3 1 http://www.dem.umk.pl/dem http://www.dem.umk.pl/dem PROPN dem-8574 4 1 d d PUNCT dem-8574 4 2 y y PROPN dem-8574 4 3 n n PROPN dem-8574 4 4 a a PRON dem-8574 4 5 m m VERB dem-8574 5 1 i i NOUN dem-8574 5 2 c c NOUN dem-8574 5 3 e e NOUN dem-8574 5 4 c c NOUN dem-8574 5 5 o o X dem-8574 6 1 n n INTJ dem-8574 6 2 o o NOUN dem-8574 6 3 m m VERB dem-8574 7 1 e e NOUN dem-8574 7 2 t t NOUN dem-8574 7 3 r r NOUN dem-8574 7 4 i i NOUN dem-8574 7 5 c c NOUN dem-8574 7 6 m m VERB dem-8574 7 7 o o NOUN dem-8574 7 8 d d X dem-8574 7 9 e e X dem-8574 7 10 l l NOUN dem-8574 7 11 s s X dem-8574 7 12 doi doi NOUN dem-8574 7 13 : : PUNCT dem-8574 7 14 http://dx.doi.org/10.12775/dem.2015.002 http://dx.doi.org/10.12775/dem.2015.002 NOUN dem-8574 7 15 vol vol NOUN dem-8574 7 16 . . PROPN dem-8574 7 17 15 15 NUM dem-8574 7 18 ( ( PUNCT dem-8574 7 19 2015 2015 NUM dem-8574 7 20 ) ) PUNCT dem-8574 7 21 27−47 27−47 PROPN dem-8574 7 22 submitted submit VERB dem-8574 7 23 october october PROPN dem-8574 7 24 25 25 NUM dem-8574 7 25 , , PUNCT dem-8574 7 26 2015 2015 NUM dem-8574 7 27 issn issn X dem-8574 7 28 ( ( PUNCT dem-8574 7 29 online online ADJ dem-8574 7 30 ) ) PUNCT dem-8574 7 31 2450 2450 NUM dem-8574 7 32 - - SYM dem-8574 7 33 7067 7067 NUM dem-8574 7 34 accepted accept VERB dem-8574 7 35 december december PROPN dem-8574 7 36 15 15 NUM dem-8574 7 37 , , PUNCT dem-8574 7 38 2015 2015 NUM dem-8574 7 39 issn issn X dem-8574 7 40 ( ( PUNCT dem-8574 7 41 print print NOUN dem-8574 7 42 ) ) PUNCT dem-8574 7 43 1234 1234 NUM dem-8574 7 44 - - SYM dem-8574 7 45 3862 3862 NUM dem-8574 7 46 łukasz łukasz NOUN dem-8574 7 47 lenart lenart ADJ dem-8574 7 48 * * PUNCT dem-8574 7 49 discrete discrete ADJ dem-8574 7 50 spectral spectral ADJ dem-8574 7 51 analysis analysis NOUN dem-8574 7 52 . . PUNCT dem-8574 8 1 the the DET dem-8574 8 2 case case NOUN dem-8574 8 3 of of ADP dem-8574 8 4 industrial industrial ADJ dem-8574 8 5 production production NOUN dem-8574 8 6 in in ADP dem-8574 8 7 selected select VERB dem-8574 8 8 european european ADJ dem-8574 8 9 countries∗∗ countries∗∗ PROPN dem-8574 8 10 a a DET dem-8574 8 11 b b PROPN dem-8574 8 12 s s ADP dem-8574 8 13 t t PROPN dem-8574 8 14 r r NOUN dem-8574 8 15 a a DET dem-8574 8 16 c c NOUN dem-8574 8 17 t. t. NOUN dem-8574 8 18 the the DET dem-8574 8 19 aim aim NOUN dem-8574 8 20 of of ADP dem-8574 8 21 this this DET dem-8574 8 22 paper paper NOUN dem-8574 8 23 is be AUX dem-8574 8 24 to to PART dem-8574 8 25 show show VERB dem-8574 8 26 the the DET dem-8574 8 27 usefulness usefulness NOUN dem-8574 8 28 the the DET dem-8574 8 29 discrete discrete ADJ dem-8574 8 30 spectral spectral ADJ dem-8574 8 31 analysis analysis NOUN dem-8574 8 32 in in ADP dem-8574 8 33 identification identification NOUN dem-8574 8 34 cyclical cyclical ADJ dem-8574 8 35 fluctuations fluctuation NOUN dem-8574 8 36 . . PUNCT dem-8574 9 1 the the DET dem-8574 9 2 subsampling subsample VERB dem-8574 9 3 procedure procedure NOUN dem-8574 9 4 was be AUX dem-8574 9 5 applied apply VERB dem-8574 9 6 to to PART dem-8574 9 7 construct construct VERB dem-8574 9 8 the the DET dem-8574 9 9 asymptotically asymptotically ADV dem-8574 9 10 consistent consistent ADJ dem-8574 9 11 test test NOUN dem-8574 9 12 for for ADP dem-8574 9 13 fourier fourier ADJ dem-8574 9 14 coefficient coefficient NOUN dem-8574 9 15 and and CCONJ dem-8574 9 16 frequency frequency NOUN dem-8574 9 17 significance significance NOUN dem-8574 9 18 . . PUNCT dem-8574 10 1 the the DET dem-8574 10 2 case case NOUN dem-8574 10 3 of of ADP dem-8574 10 4 monthly monthly ADJ dem-8574 10 5 production production NOUN dem-8574 10 6 in in ADP dem-8574 10 7 industry industry NOUN dem-8574 10 8 in in ADP dem-8574 10 9 european european ADJ dem-8574 10 10 countries country NOUN dem-8574 10 11 ( ( PUNCT dem-8574 10 12 thirty thirty NUM dem-8574 10 13 countries country NOUN dem-8574 10 14 ) ) PUNCT dem-8574 10 15 was be AUX dem-8574 10 16 considered consider VERB dem-8574 10 17 . . PUNCT dem-8574 11 1 using use VERB dem-8574 11 2 proposed propose VERB dem-8574 11 3 approach approach NOUN dem-8574 11 4 the the DET dem-8574 11 5 frequencies frequency NOUN dem-8574 11 6 concerning concern VERB dem-8574 11 7 business business NOUN dem-8574 11 8 fluctuations fluctuation NOUN dem-8574 11 9 , , PUNCT dem-8574 11 10 seasonal seasonal ADJ dem-8574 11 11 fluctuations fluctuation NOUN dem-8574 11 12 and and CCONJ dem-8574 11 13 trading trading NOUN dem-8574 11 14 - - PUNCT dem-8574 11 15 day day NOUN dem-8574 11 16 effects effect NOUN dem-8574 11 17 fluctuations fluctuation NOUN dem-8574 11 18 were be AUX dem-8574 11 19 recognized recognize VERB dem-8574 11 20 in in ADP dem-8574 11 21 considered consider VERB dem-8574 11 22 data data NOUN dem-8574 11 23 sets set NOUN dem-8574 11 24 . . PUNCT dem-8574 12 1 the the DET dem-8574 12 2 comparison comparison NOUN dem-8574 12 3 with with ADP dem-8574 12 4 existing exist VERB dem-8574 12 5 procedures procedure NOUN dem-8574 12 6 was be AUX dem-8574 12 7 shown show VERB dem-8574 12 8 . . PUNCT dem-8574 13 1 k k PROPN dem-8574 13 2 e e PROPN dem-8574 13 3 y y PROPN dem-8574 13 4 w w NOUN dem-8574 13 5 o o NOUN dem-8574 13 6 r r NOUN dem-8574 13 7 d d NOUN dem-8574 13 8 s s X dem-8574 13 9 : : PUNCT dem-8574 13 10 discrete discrete ADJ dem-8574 13 11 spectral spectral ADJ dem-8574 13 12 analysis analysis NOUN dem-8574 13 13 , , PUNCT dem-8574 13 14 almost almost ADV dem-8574 13 15 periodic periodic ADJ dem-8574 13 16 function function NOUN dem-8574 13 17 , , PUNCT dem-8574 13 18 frequency frequency NOUN dem-8574 13 19 identification identification NOUN dem-8574 13 20 , , PUNCT dem-8574 13 21 graphical graphical ADJ dem-8574 13 22 test test NOUN dem-8574 13 23 . . PUNCT dem-8574 14 1 j j PROPN dem-8574 14 2 e e PROPN dem-8574 14 3 l l PROPN dem-8574 14 4 classification classification NOUN dem-8574 14 5 : : PUNCT dem-8574 14 6 c14 c14 NOUN dem-8574 14 7 , , PUNCT dem-8574 14 8 c46 c46 NOUN dem-8574 14 9 , , PUNCT dem-8574 14 10 e32 e32 PROPN dem-8574 14 11 . . PUNCT dem-8574 15 1 introduction introduction NOUN dem-8574 15 2 the the DET dem-8574 15 3 main main ADJ dem-8574 15 4 part part NOUN dem-8574 15 5 of of ADP dem-8574 15 6 monthly monthly ADJ dem-8574 15 7 or or CCONJ dem-8574 15 8 quarterly quarterly ADJ dem-8574 15 9 macroeconomic macroeconomic ADJ dem-8574 15 10 time time NOUN dem-8574 15 11 series series NOUN dem-8574 15 12 concerning concern VERB dem-8574 15 13 industry industry NOUN dem-8574 15 14 , , PUNCT dem-8574 15 15 trade trade NOUN dem-8574 15 16 , , PUNCT dem-8574 15 17 service service NOUN dem-8574 15 18 , , PUNCT dem-8574 15 19 national national ADJ dem-8574 15 20 accounts account NOUN dem-8574 15 21 , , PUNCT dem-8574 15 22 prices price NOUN dem-8574 15 23 , , PUNCT dem-8574 15 24 etc etc X dem-8574 15 25 . . X dem-8574 15 26 exhibit exhibit VERB dem-8574 15 27 both both PRON dem-8574 15 28 : : PUNCT dem-8574 15 29 seasonal seasonal ADJ dem-8574 15 30 fluctuations fluctuation NOUN dem-8574 15 31 and and CCONJ dem-8574 15 32 business business NOUN dem-8574 15 33 cycle cycle NOUN dem-8574 15 34 fluctuations fluctuation NOUN dem-8574 15 35 . . PUNCT dem-8574 16 1 the the DET dem-8574 16 2 problem problem NOUN dem-8574 16 3 of of ADP dem-8574 16 4 analysing analyse VERB dem-8574 16 5 these these DET dem-8574 16 6 cyclical cyclical ADJ dem-8574 16 7 fluctuations fluctuation NOUN dem-8574 16 8 is be AUX dem-8574 16 9 widely widely ADV dem-8574 16 10 considered consider VERB dem-8574 16 11 in in ADP dem-8574 16 12 the the DET dem-8574 16 13 literature literature NOUN dem-8574 16 14 using use VERB dem-8574 16 15 different different ADJ dem-8574 16 16 statistical statistical ADJ dem-8574 16 17 tools tool NOUN dem-8574 16 18 . . PUNCT dem-8574 17 1 one one NUM dem-8574 17 2 popular popular ADJ dem-8574 17 3 nonparametric nonparametric NOUN dem-8574 17 4 approach approach NOUN dem-8574 17 5 is be AUX dem-8574 17 6 based base VERB dem-8574 17 7 on on ADP dem-8574 17 8 a a DET dem-8574 17 9 spectral spectral ADJ dem-8574 17 10 analysis analysis NOUN dem-8574 17 11 . . PUNCT dem-8574 18 1 * * PUNCT dem-8574 18 2 correspondence correspondence NOUN dem-8574 18 3 to to PART dem-8574 18 4 łukasz łukasz VERB dem-8574 18 5 lenart lenart PROPN dem-8574 18 6 , , PUNCT dem-8574 18 7 cracow cracow PROPN dem-8574 18 8 university university PROPN dem-8574 18 9 of of ADP dem-8574 18 10 economics economic NOUN dem-8574 18 11 , , PUNCT dem-8574 18 12 department department NOUN dem-8574 18 13 of of ADP dem-8574 18 14 mathematics mathematic NOUN dem-8574 18 15 , , PUNCT dem-8574 18 16 e e NOUN dem-8574 18 17 - - NOUN dem-8574 18 18 mail mail NOUN dem-8574 18 19 : : PUNCT dem-8574 18 20 lenartl@uek.krakow.pl lenartl@uek.krakow.pl PROPN dem-8574 18 21 ∗∗ ∗∗ PROPN dem-8574 19 1 this this DET dem-8574 19 2 research research NOUN dem-8574 19 3 was be AUX dem-8574 19 4 supported support VERB dem-8574 19 5 by by ADP dem-8574 19 6 research research NOUN dem-8574 19 7 grant grant NOUN dem-8574 19 8 dec-2013/09 dec-2013/09 PROPN dem-8574 19 9 / / SYM dem-8574 19 10 b b PROPN dem-8574 19 11 / / SYM dem-8574 19 12 hs4/01945 hs4/01945 NUM dem-8574 19 13 from from ADP dem-8574 19 14 the the DET dem-8574 19 15 national national PROPN dem-8574 19 16 science science PROPN dem-8574 19 17 centre centre PROPN dem-8574 19 18 łukasz łukasz VERB dem-8574 19 19 lenart lenart ADJ dem-8574 19 20 dynamic dynamic ADJ dem-8574 19 21 econometric econometric ADJ dem-8574 19 22 models model NOUN dem-8574 19 23 15 15 NUM dem-8574 19 24 ( ( PUNCT dem-8574 19 25 2015 2015 NUM dem-8574 19 26 ) ) PUNCT dem-8574 19 27 27–47 27–47 NUM dem-8574 19 28 28 28 NUM dem-8574 19 29 the the DET dem-8574 19 30 spectral spectral ADJ dem-8574 19 31 analysis analysis NOUN dem-8574 19 32 of of ADP dem-8574 19 33 macroeconomic macroeconomic ADJ dem-8574 19 34 time time NOUN dem-8574 19 35 series series NOUN dem-8574 19 36 is be AUX dem-8574 19 37 considered consider VERB dem-8574 19 38 mainly mainly ADV dem-8574 19 39 in in ADP dem-8574 19 40 continuous continuous ADJ dem-8574 19 41 counterpart counterpart NOUN dem-8574 19 42 ( ( PUNCT dem-8574 19 43 see see INTJ dem-8574 19 44 ftiti ftiti NOUN dem-8574 19 45 , , PUNCT dem-8574 19 46 2010 2010 NUM dem-8574 19 47 ; ; PUNCT dem-8574 19 48 metz metz PROPN dem-8574 19 49 , , PUNCT dem-8574 19 50 2009 2009 NUM dem-8574 19 51 ; ; PUNCT dem-8574 19 52 orlov orlov PROPN dem-8574 19 53 , , PUNCT dem-8574 19 54 2006 2006 NUM dem-8574 19 55 ; ; PUNCT dem-8574 19 56 orlov orlov PROPN dem-8574 19 57 , , PUNCT dem-8574 19 58 2009 2009 NUM dem-8574 19 59 ; ; PUNCT dem-8574 19 60 pakko pakko NOUN dem-8574 19 61 , , PUNCT dem-8574 19 62 2004 2004 NUM dem-8574 19 63 ; ; PUNCT dem-8574 19 64 mcadam mcadam PROPN dem-8574 19 65 and and CCONJ dem-8574 19 66 mestre mestre PROPN dem-8574 19 67 , , PUNCT dem-8574 19 68 2008 2008 NUM dem-8574 19 69 ; ; PUNCT dem-8574 19 70 uebele uebele PROPN dem-8574 19 71 and and CCONJ dem-8574 19 72 ritschl ritschl PROPN dem-8574 19 73 , , PUNCT dem-8574 19 74 2009 2009 NUM dem-8574 19 75 ) ) PUNCT dem-8574 19 76 . . PUNCT dem-8574 20 1 under under ADP dem-8574 20 2 stationarity stationarity NOUN dem-8574 20 3 assumption assumption NOUN dem-8574 20 4 the the DET dem-8574 20 5 continuous continuous ADJ dem-8574 20 6 function function NOUN dem-8574 20 7 called call VERB dem-8574 20 8 spectral spectral ADJ dem-8574 20 9 density density NOUN dem-8574 20 10 function function NOUN dem-8574 20 11 is be AUX dem-8574 20 12 defined define VERB dem-8574 20 13 . . PUNCT dem-8574 21 1 based base VERB dem-8574 21 2 on on ADP dem-8574 21 3 spectral spectral ADJ dem-8574 21 4 density density NOUN dem-8574 21 5 function function NOUN dem-8574 21 6 ( ( PUNCT dem-8574 21 7 and and CCONJ dem-8574 21 8 the the DET dem-8574 21 9 definition definition NOUN dem-8574 21 10 of of ADP dem-8574 21 11 harmonizable harmonizable ADJ dem-8574 21 12 time time NOUN dem-8574 21 13 series series PROPN dem-8574 21 14 ) ) PUNCT dem-8574 21 15 the the DET dem-8574 21 16 popular popular ADJ dem-8574 21 17 spectral spectral ADJ dem-8574 21 18 characteristics characteristic NOUN dem-8574 21 19 are be AUX dem-8574 21 20 defined define VERB dem-8574 21 21 : : PUNCT dem-8574 21 22 modulus modulus NOUN dem-8574 21 23 of of ADP dem-8574 21 24 coherency coherency NOUN dem-8574 21 25 function function NOUN dem-8574 21 26 , , PUNCT dem-8574 21 27 dynamic dynamic ADJ dem-8574 21 28 correlation correlation NOUN dem-8574 21 29 , , PUNCT dem-8574 21 30 dynamic dynamic ADJ dem-8574 21 31 correlation correlation NOUN dem-8574 21 32 on on ADP dem-8574 21 33 a a DET dem-8574 21 34 frequency frequency NOUN dem-8574 21 35 band band NOUN dem-8574 21 36 , , PUNCT dem-8574 21 37 cohesion cohesion NOUN dem-8574 21 38 , , PUNCT dem-8574 21 39 cohesion cohesion NOUN dem-8574 21 40 within within ADP dem-8574 21 41 the the DET dem-8574 21 42 frequency frequency NOUN dem-8574 21 43 band band NOUN dem-8574 21 44 , , PUNCT dem-8574 21 45 phase phase NOUN dem-8574 21 46 shift shift NOUN dem-8574 21 47 ( ( PUNCT dem-8574 21 48 see see VERB dem-8574 21 49 priestley priestley NOUN dem-8574 21 50 , , PUNCT dem-8574 21 51 1981 1981 NUM dem-8574 21 52 ; ; PUNCT dem-8574 21 53 hamilton hamilton PROPN dem-8574 21 54 , , PUNCT dem-8574 21 55 1994 1994 NUM dem-8574 21 56 ; ; PUNCT dem-8574 21 57 croux croux VERB dem-8574 21 58 , , PUNCT dem-8574 21 59 2001 2001 NUM dem-8574 21 60 for for ADP dem-8574 21 61 more more ADJ dem-8574 21 62 details detail NOUN dem-8574 21 63 ) ) PUNCT dem-8574 21 64 . . PUNCT dem-8574 22 1 these these DET dem-8574 22 2 measures measure NOUN dem-8574 22 3 are be AUX dem-8574 22 4 broadly broadly ADV dem-8574 22 5 used use VERB dem-8574 22 6 in in ADP dem-8574 22 7 analysing analyse VERB dem-8574 22 8 the the DET dem-8574 22 9 business business NOUN dem-8574 22 10 cycle cycle NOUN dem-8574 22 11 fluctuations fluctuation NOUN dem-8574 22 12 . . PUNCT dem-8574 23 1 they they PRON dem-8574 23 2 are be AUX dem-8574 23 3 estimated estimate VERB dem-8574 23 4 under under ADP dem-8574 23 5 fundamental fundamental ADJ dem-8574 23 6 assumption assumption NOUN dem-8574 23 7 that that SCONJ dem-8574 23 8 time time NOUN dem-8574 23 9 series series PROPN dem-8574 23 10 is be AUX dem-8574 23 11 zero zero NUM dem-8574 23 12 mean mean NOUN dem-8574 23 13 . . PUNCT dem-8574 24 1 but but CCONJ dem-8574 24 2 this this DET dem-8574 24 3 assumption assumption NOUN dem-8574 24 4 is be AUX dem-8574 24 5 not not PART dem-8574 24 6 supported support VERB dem-8574 24 7 by by ADP dem-8574 24 8 any any DET dem-8574 24 9 formal formal ADJ dem-8574 24 10 statistical statistical ADJ dem-8574 24 11 test test NOUN dem-8574 24 12 in in ADP dem-8574 24 13 most most ADV dem-8574 24 14 empirical empirical ADJ dem-8574 24 15 macroeconomic macroeconomic ADJ dem-8574 24 16 real real ADJ dem-8574 24 17 data datum NOUN dem-8574 24 18 analysis analysis NOUN dem-8574 24 19 . . PUNCT dem-8574 25 1 in in ADP dem-8574 25 2 this this DET dem-8574 25 3 paper paper NOUN dem-8574 25 4 the the DET dem-8574 25 5 more more ADV dem-8574 25 6 general general ADJ dem-8574 25 7 assumption assumption NOUN dem-8574 25 8 is be AUX dem-8574 25 9 formulated formulate VERB dem-8574 25 10 concerning concern VERB dem-8574 25 11 nontrivial nontrivial ADJ dem-8574 25 12 mean mean NOUN dem-8574 25 13 function function NOUN dem-8574 25 14 . . PUNCT dem-8574 26 1 this this DET dem-8574 26 2 general general ADJ dem-8574 26 3 assumption assumption NOUN dem-8574 26 4 was be AUX dem-8574 26 5 considered consider VERB dem-8574 26 6 in in ADP dem-8574 26 7 lenart lenart ADJ dem-8574 26 8 , , PUNCT dem-8574 26 9 2011 2011 NUM dem-8574 26 10 ; ; PUNCT dem-8574 26 11 lenart lenart ADJ dem-8574 26 12 and and CCONJ dem-8574 26 13 pipień pipień NOUN dem-8574 26 14 , , PUNCT dem-8574 26 15 2013a 2013a NUM dem-8574 26 16 ; ; PUNCT dem-8574 26 17 lenart lenart ADJ dem-8574 26 18 and and CCONJ dem-8574 26 19 pipień pipień NOUN dem-8574 26 20 , , PUNCT dem-8574 26 21 2013b 2013b NUM dem-8574 26 22 ( ( PUNCT dem-8574 26 23 in in ADP dem-8574 26 24 univariate univariate ADJ dem-8574 26 25 case case NOUN dem-8574 26 26 ) ) PUNCT dem-8574 26 27 and and CCONJ dem-8574 26 28 recently recently ADV dem-8574 26 29 in in ADP dem-8574 26 30 lenart lenart ADJ dem-8574 26 31 and and CCONJ dem-8574 26 32 pipień pipień NOUN dem-8574 26 33 , , PUNCT dem-8574 26 34 2015 2015 NUM dem-8574 26 35 ( ( PUNCT dem-8574 26 36 in in ADP dem-8574 26 37 multivariate multivariate NOUN dem-8574 26 38 case case NOUN dem-8574 26 39 ) ) PUNCT dem-8574 26 40 with with ADP dem-8574 26 41 application application NOUN dem-8574 26 42 to to ADP dem-8574 26 43 macroeconomic macroeconomic ADJ dem-8574 26 44 time time NOUN dem-8574 26 45 series series NOUN dem-8574 26 46 . . PUNCT dem-8574 27 1 in in ADP dem-8574 27 2 this this DET dem-8574 27 3 paper paper NOUN dem-8574 27 4 we we PRON dem-8574 27 5 show show VERB dem-8574 27 6 that that SCONJ dem-8574 27 7 the the DET dem-8574 27 8 parameters parameter NOUN dem-8574 27 9 of of ADP dem-8574 27 10 the the DET dem-8574 27 11 discrete discrete ADJ dem-8574 27 12 spectrum spectrum NOUN dem-8574 27 13 can can AUX dem-8574 27 14 be be AUX dem-8574 27 15 identified identify VERB dem-8574 27 16 not not PART dem-8574 27 17 only only ADV dem-8574 27 18 with with ADP dem-8574 27 19 the the DET dem-8574 27 20 seasonal seasonal ADJ dem-8574 27 21 and and CCONJ dem-8574 27 22 business business NOUN dem-8574 27 23 cycle cycle NOUN dem-8574 27 24 fluctuations fluctuation NOUN dem-8574 27 25 but but CCONJ dem-8574 27 26 additionally additionally ADV dem-8574 27 27 with with ADP dem-8574 27 28 the the DET dem-8574 27 29 trading trading NOUN dem-8574 27 30 - - PUNCT dem-8574 27 31 day day NOUN dem-8574 27 32 effect effect NOUN dem-8574 27 33 . . PUNCT dem-8574 28 1 in in ADP dem-8574 28 2 the the DET dem-8574 28 3 section section NOUN dem-8574 28 4 2 2 NUM dem-8574 28 5 , , PUNCT dem-8574 28 6 based base VERB dem-8574 28 7 on on ADP dem-8574 28 8 lenart lenart ADJ dem-8574 28 9 and and CCONJ dem-8574 28 10 pipień pipień NOUN dem-8574 28 11 , , PUNCT dem-8574 28 12 2013a 2013a NUM dem-8574 28 13 and and CCONJ dem-8574 28 14 lenart lenart ADJ dem-8574 28 15 and and CCONJ dem-8574 28 16 pipień pipień NOUN dem-8574 28 17 , , PUNCT dem-8574 28 18 2015 2015 NUM dem-8574 28 19 the the DET dem-8574 28 20 model model NOUN dem-8574 28 21 was be AUX dem-8574 28 22 formulated formulate VERB dem-8574 28 23 and and CCONJ dem-8574 28 24 illustrative illustrative ADJ dem-8574 28 25 example example NOUN dem-8574 28 26 was be AUX dem-8574 28 27 presented present VERB dem-8574 28 28 . . PUNCT dem-8574 29 1 in in ADP dem-8574 29 2 the the DET dem-8574 29 3 next next ADJ dem-8574 29 4 part part NOUN dem-8574 29 5 the the DET dem-8574 29 6 empirical empirical ADJ dem-8574 29 7 analysis analysis NOUN dem-8574 29 8 was be AUX dem-8574 29 9 presented present VERB dem-8574 29 10 . . PUNCT dem-8574 30 1 the the DET dem-8574 30 2 production production NOUN dem-8574 30 3 in in ADP dem-8574 30 4 industry industry NOUN dem-8574 30 5 – – PUNCT dem-8574 30 6 monthly monthly ADJ dem-8574 30 7 data datum NOUN dem-8574 30 8 ( ( PUNCT dem-8574 30 9 mining mining NOUN dem-8574 30 10 and and CCONJ dem-8574 30 11 quarrying quarrying NOUN dem-8574 30 12 ; ; PUNCT dem-8574 30 13 manufacturing manufacturing NOUN dem-8574 30 14 ; ; PUNCT dem-8574 30 15 electricity electricity NOUN dem-8574 30 16 , , PUNCT dem-8574 30 17 gas gas NOUN dem-8574 30 18 , , PUNCT dem-8574 30 19 steam steam NOUN dem-8574 30 20 and and CCONJ dem-8574 30 21 air air NOUN dem-8574 30 22 conditioning conditioning NOUN dem-8574 30 23 supply supply NOUN dem-8574 30 24 ) ) PUNCT dem-8574 30 25 from from ADP dem-8574 30 26 feb feb PROPN dem-8574 30 27 . . PROPN dem-8574 30 28 2000 2000 NUM dem-8574 30 29 to to ADP dem-8574 30 30 dec dec PROPN dem-8574 30 31 . . PROPN dem-8574 30 32 2014 2014 NUM dem-8574 30 33 was be AUX dem-8574 30 34 considered consider VERB dem-8574 30 35 . . PUNCT dem-8574 31 1 in in ADP dem-8574 31 2 the the DET dem-8574 31 3 first first ADJ dem-8574 31 4 subsection subsection NOUN dem-8574 31 5 the the DET dem-8574 31 6 graphical graphical ADJ dem-8574 31 7 methods method NOUN dem-8574 31 8 to to PART dem-8574 31 9 identify identify VERB dem-8574 31 10 / / SYM dem-8574 31 11 recognize recognize VERB dem-8574 31 12 the the DET dem-8574 31 13 frequency frequency NOUN dem-8574 31 14 ( ( PUNCT dem-8574 31 15 concerning concern VERB dem-8574 31 16 to to ADP dem-8574 31 17 business business NOUN dem-8574 31 18 fluctuations fluctuation NOUN dem-8574 31 19 , , PUNCT dem-8574 31 20 seasonal seasonal ADJ dem-8574 31 21 fluctuations fluctuation NOUN dem-8574 31 22 and and CCONJ dem-8574 31 23 trading trading NOUN dem-8574 31 24 - - PUNCT dem-8574 31 25 day day NOUN dem-8574 31 26 effect effect NOUN dem-8574 31 27 fluctuations fluctuation NOUN dem-8574 31 28 ) ) PUNCT dem-8574 31 29 was be AUX dem-8574 31 30 presented present VERB dem-8574 31 31 . . PUNCT dem-8574 32 1 such such ADJ dem-8574 32 2 graphical graphical ADJ dem-8574 32 3 methods method NOUN dem-8574 32 4 to to PART dem-8574 32 5 identify identify VERB dem-8574 32 6 ’ ' PUNCT dem-8574 32 7 periodic periodic ADJ dem-8574 32 8 phenomena phenomenon NOUN dem-8574 32 9 ’ ' PUNCT dem-8574 32 10 in in ADP dem-8574 32 11 the the DET dem-8574 32 12 autocovariance autocovariance NOUN dem-8574 32 13 function function NOUN dem-8574 32 14 in in ADP dem-8574 32 15 class class NOUN dem-8574 32 16 of of ADP dem-8574 32 17 almost almost ADV dem-8574 32 18 periodically periodically ADV dem-8574 32 19 correlated correlate VERB dem-8574 32 20 time time NOUN dem-8574 32 21 series series PROPN dem-8574 32 22 were be AUX dem-8574 32 23 presented present VERB dem-8574 32 24 in in ADP dem-8574 32 25 hurd hurd PROPN dem-8574 32 26 and and CCONJ dem-8574 32 27 gerr gerr PROPN dem-8574 32 28 , , PUNCT dem-8574 32 29 1991 1991 NUM dem-8574 32 30 and and CCONJ dem-8574 32 31 recently recently ADV dem-8574 32 32 in in ADP dem-8574 32 33 lenart lenart ADJ dem-8574 32 34 , , PUNCT dem-8574 32 35 2011 2011 NUM dem-8574 32 36 . . PUNCT dem-8574 33 1 finally finally ADV dem-8574 33 2 in in ADP dem-8574 33 3 the the DET dem-8574 33 4 second second ADJ dem-8574 33 5 subsection subsection NOUN dem-8574 33 6 formal formal ADJ dem-8574 33 7 statistical statistical ADJ dem-8574 33 8 test test NOUN dem-8574 33 9 for for ADP dem-8574 33 10 frequency frequency NOUN dem-8574 33 11 significance significance NOUN dem-8574 33 12 was be AUX dem-8574 33 13 applied apply VERB dem-8574 33 14 to to ADP dem-8574 33 15 data datum NOUN dem-8574 33 16 sets set NOUN dem-8574 33 17 . . PUNCT dem-8574 34 1 1 1 X dem-8574 34 2 . . X dem-8574 34 3 model model NOUN dem-8574 34 4 specification specification NOUN dem-8574 34 5 let let VERB dem-8574 34 6 ty ty PRON dem-8574 34 7 be be AUX dem-8574 34 8 macroeconomic macroeconomic ADJ dem-8574 34 9 time time NOUN dem-8574 34 10 series series PROPN dem-8574 34 11 ( ( PUNCT dem-8574 34 12 index index NOUN dem-8574 34 13 , , PUNCT dem-8574 34 14 gross gross ADJ dem-8574 34 15 data datum NOUN dem-8574 34 16 ) ) PUNCT dem-8574 34 17 with with ADP dem-8574 34 18 possible possible ADJ dem-8574 34 19 : : PUNCT dem-8574 34 20 seasonal seasonal ADJ dem-8574 34 21 fluctuations fluctuation NOUN dem-8574 34 22 with with ADP dem-8574 34 23 period period NOUN dem-8574 34 24 t t NOUN dem-8574 34 25 , , PUNCT dem-8574 34 26 business business NOUN dem-8574 34 27 fluctuations fluctuation NOUN dem-8574 34 28 and and CCONJ dem-8574 34 29 trading trading NOUN dem-8574 34 30 - - PUNCT dem-8574 34 31 day day NOUN dem-8574 34 32 discrete discrete ADJ dem-8574 34 33 spectral spectral ADJ dem-8574 34 34 analysis analysis NOUN dem-8574 34 35 . . PUNCT dem-8574 35 1 the the DET dem-8574 35 2 case case NOUN dem-8574 35 3 of of ADP dem-8574 35 4 industrial industrial ADJ dem-8574 35 5 production production NOUN dem-8574 35 6 … … PUNCT dem-8574 35 7 dynamic dynamic ADJ dem-8574 35 8 econometric econometric ADJ dem-8574 35 9 models model NOUN dem-8574 35 10 15 15 NUM dem-8574 35 11 ( ( PUNCT dem-8574 35 12 2015 2015 NUM dem-8574 35 13 ) ) PUNCT dem-8574 35 14 27–47 27–47 NUM dem-8574 35 15 29 29 NUM dem-8574 35 16 fluctuations fluctuation NOUN dem-8574 35 17 . . PUNCT dem-8574 36 1 let let VERB dem-8574 36 2 us we PRON dem-8574 36 3 denote denote VERB dem-8574 36 4 the the DET dem-8574 36 5 natural natural ADJ dem-8574 36 6 logarithm logarithm NOUN dem-8574 36 7 : : PUNCT dem-8574 36 8 ) ) PUNCT dem-8574 36 9 ( ( PUNCT dem-8574 36 10 ln= ln= NOUN dem-8574 36 11 ~ ~ PUNCT dem-8574 36 12 tt tt PROPN dem-8574 36 13 yy yy PROPN dem-8574 36 14 . . PUNCT dem-8574 37 1 based base VERB dem-8574 37 2 on on ADP dem-8574 37 3 lenart lenart ADJ dem-8574 37 4 and and CCONJ dem-8574 37 5 pipień pipień NOUN dem-8574 37 6 , , PUNCT dem-8574 37 7 2013a 2013a NUM dem-8574 37 8 we we PRON dem-8574 37 9 assume assume VERB dem-8574 37 10 that that SCONJ dem-8574 37 11 ) ) PUNCT dem-8574 37 12 , , PUNCT dem-8574 37 13 ( ( PUNCT dem-8574 37 14 ) ) PUNCT dem-8574 37 15 , , PUNCT dem-8574 37 16 (= (= ADV dem-8574 37 17 ) ) PUNCT dem-8574 37 18 ~ ~ PUNCT dem-8574 37 19 ( ( PUNCT dem-8574 37 20 ttfye ttfye VERB dem-8574 37 21 t t PROPN dem-8574 37 22 µβ µβ INTJ dem-8574 37 23 + + CCONJ dem-8574 37 24 ( ( PUNCT dem-8574 37 25 1 1 X dem-8574 37 26 ) ) PUNCT dem-8574 37 27 where where SCONJ dem-8574 37 28 ) ) PUNCT dem-8574 37 29 ( ( PUNCT dem-8574 37 30 tµ tµ NOUN dem-8574 37 31 is be AUX dem-8574 37 32 almost almost ADV dem-8574 37 33 periodic periodic ADJ dem-8574 37 34 function function NOUN dem-8574 37 35 ( ( PUNCT dem-8574 37 36 ap ap PROPN dem-8574 37 37 in in ADP dem-8574 37 38 short short ADJ dem-8574 37 39 ) ) PUNCT dem-8574 37 40 of of ADP dem-8574 37 41 the the DET dem-8574 37 42 form form NOUN dem-8574 37 43 tiemt tiemt PROPN dem-8574 37 44 ψ ψ X dem-8574 37 45 ψ ψ NOUN dem-8574 37 46 ψµ ψµ NOUN dem-8574 37 47 ) ) PUNCT dem-8574 37 48 ( ( PUNCT dem-8574 37 49 =) =) X dem-8574 37 50 ( ( PUNCT dem-8574 37 51 ∑ ∑ ADV dem-8574 37 52 ψ∈ ψ∈ VERB dem-8574 37 53 , , PUNCT dem-8574 37 54 where where SCONJ dem-8574 37 55 . . PUNCT dem-8574 37 56 ) ) PUNCT dem-8574 37 57 ( ( PUNCT dem-8574 37 58 1 1 NUM dem-8574 37 59 lim= lim= NOUN dem-8574 37 60 ) ) PUNCT dem-8574 37 61 ( ( PUNCT dem-8574 37 62 1= 1= X dem-8574 37 63 ti ti X dem-8574 37 64 n n PRON dem-8574 37 65 tn tn NOUN dem-8574 37 66 et et AUX dem-8574 37 67 n n CCONJ dem-8574 37 68 m m AUX dem-8574 37 69 ψµψ ψµψ VERB dem-8574 37 70 − − PROPN dem-8574 37 71 →∞ →∞ X dem-8574 37 72 ∑ ∑ PUNCT dem-8574 37 73 we we PRON dem-8574 37 74 assume assume VERB dem-8574 37 75 that that SCONJ dem-8574 37 76 the the DET dem-8574 37 77 set set NOUN dem-8574 37 78 of of ADP dem-8574 37 79 frequencies frequency NOUN dem-8574 37 80 0}=|)(:|)[0,2{= 0}=|)(:|)[0,2{= PROPN dem-8574 37 81 /∈ψ /∈ψ PUNCT dem-8574 37 82 ψπψ ψπψ NOUN dem-8574 37 83 m m VERB dem-8574 37 84 is be AUX dem-8574 37 85 finite finite ADJ dem-8574 37 86 and and CCONJ dem-8574 37 87 unknown unknown ADJ dem-8574 37 88 . . PUNCT dem-8574 38 1 this this DET dem-8574 38 2 set set NOUN dem-8574 38 3 ψ ψ NOUN dem-8574 38 4 can can AUX dem-8574 38 5 be be AUX dem-8574 38 6 decompose decompose VERB dem-8574 38 7 in in ADP dem-8574 38 8 natural natural ADJ dem-8574 38 9 way way NOUN dem-8574 38 10 via via ADP dem-8574 38 11 : : PUNCT dem-8574 38 12 321= 321= NOUN dem-8574 39 1 ψ∪ψ∪ψψ ψ∪ψ∪ψψ PROPN dem-8574 39 2 , , PUNCT dem-8574 39 3 where where SCONJ dem-8574 39 4 1ψ 1ψ NUM dem-8574 39 5 corresponds correspond VERB dem-8574 39 6 to to ADP dem-8574 39 7 business business NOUN dem-8574 39 8 fluctuations fluctuation NOUN dem-8574 39 9 , , PUNCT dem-8574 39 10 1}0,1,=,/{22 1}0,1,=,/{22 NUM dem-8574 39 11 −⊂ψ −⊂ψ ADP dem-8574 39 12 tktkπ tktkπ NOUN dem-8574 39 13 corresponds correspond NOUN dem-8574 39 14 to to ADP dem-8574 39 15 seasonal seasonal ADJ dem-8574 39 16 fluctuations fluctuation NOUN dem-8574 39 17 and and CCONJ dem-8574 39 18 3ψ 3ψ NUM dem-8574 39 19 is be AUX dem-8574 39 20 a a DET dem-8574 39 21 set set NOUN dem-8574 39 22 of of ADP dem-8574 39 23 remaining remain VERB dem-8574 39 24 frequencies frequency NOUN dem-8574 39 25 ( ( PUNCT dem-8574 39 26 corresponding correspond VERB dem-8574 39 27 to to ADP dem-8574 39 28 interaction interaction NOUN dem-8574 39 29 between between ADP dem-8574 39 30 seasonal seasonal ADJ dem-8574 39 31 and and CCONJ dem-8574 39 32 business business NOUN dem-8574 39 33 fluctuations fluctuation NOUN dem-8574 39 34 and and CCONJ dem-8574 39 35 frequencies frequency NOUN dem-8574 39 36 corresponding correspond VERB dem-8574 39 37 to to ADP dem-8574 39 38 trading trading NOUN dem-8574 39 39 - - PUNCT dem-8574 39 40 day day NOUN dem-8574 39 41 effects effect NOUN dem-8574 39 42 ) ) PUNCT dem-8574 39 43 . . PUNCT dem-8574 40 1 equivalently equivalently ADV dem-8574 40 2 , , PUNCT dem-8574 40 3 the the DET dem-8574 40 4 model model NOUN dem-8574 40 5 ( ( PUNCT dem-8574 40 6 1 1 X dem-8574 40 7 ) ) PUNCT dem-8574 40 8 can can AUX dem-8574 40 9 be be AUX dem-8574 40 10 written write VERB dem-8574 40 11 via via ADP dem-8574 40 12 : : PUNCT dem-8574 40 13 ) ) PUNCT dem-8574 40 14 , , PUNCT dem-8574 40 15 ( ( PUNCT dem-8574 40 16 ) ) PUNCT dem-8574 40 17 ( ( PUNCT dem-8574 40 18 ) ) PUNCT dem-8574 40 19 , , PUNCT dem-8574 40 20 (= (= ADV dem-8574 40 21 ) ) PUNCT dem-8574 40 22 ~ ~ PUNCT dem-8574 40 23 ( ( PUNCT dem-8574 40 24 21 21 NUM dem-8574 40 25 tttfye tttfye NOUN dem-8574 40 26 t t NOUN dem-8574 40 27 µµβ µµβ NOUN dem-8574 41 1 + + NOUN dem-8574 41 2 + + NUM dem-8574 41 3 ( ( PUNCT dem-8574 41 4 2 2 NUM dem-8574 41 5 ) ) PUNCT dem-8574 41 6 where where SCONJ dem-8574 41 7 ) ) PUNCT dem-8574 41 8 ( ( PUNCT dem-8574 41 9 1 1 NUM dem-8574 41 10 tµ tµ NOUN dem-8574 41 11 is be AUX dem-8574 41 12 a a DET dem-8574 41 13 periodic periodic ADJ dem-8574 41 14 function function NOUN dem-8574 41 15 with with ADP dem-8574 41 16 period period NOUN dem-8574 41 17 t t NOUN dem-8574 41 18 which which PRON dem-8574 41 19 represents represent VERB dem-8574 41 20 the the DET dem-8574 41 21 seasonal seasonal ADJ dem-8574 41 22 fluctuations fluctuation NOUN dem-8574 41 23 and and CCONJ dem-8574 41 24 tiemt tiemt NOUN dem-8574 41 25 ψ ψ X dem-8574 41 26 ψ ψ NOUN dem-8574 41 27 ψµ ψµ NOUN dem-8574 41 28 ) ) PUNCT dem-8574 41 29 ( ( PUNCT dem-8574 41 30 =) =) X dem-8574 41 31 ( ( PUNCT dem-8574 41 32 2\ 2\ NUM dem-8574 41 33 2 2 NUM dem-8574 41 34 ∑ ∑ NOUN dem-8574 41 35 ψψ∈ ψψ∈ NOUN dem-8574 41 36 . . PUNCT dem-8574 42 1 the the DET dem-8574 42 2 function function NOUN dem-8574 42 3 ) ) PUNCT dem-8574 42 4 ( ( PUNCT dem-8574 42 5 1 1 NUM dem-8574 42 6 tµ tµ NOUN dem-8574 42 7 can can AUX dem-8574 42 8 be be AUX dem-8574 42 9 equivalently equivalently ADV dem-8574 42 10 represented represent VERB dem-8574 42 11 by by ADP dem-8574 42 12 the the DET dem-8574 42 13 vector vector NOUN dem-8574 42 14 ( ( PUNCT dem-8574 42 15 sequence sequence NOUN dem-8574 42 16 of of ADP dem-8574 42 17 seasonal seasonal ADJ dem-8574 42 18 values value NOUN dem-8574 42 19 ) ) PUNCT dem-8574 42 20 ' ' PUNCT dem-8574 42 21 121 121 NUM dem-8574 42 22 ] ] PUNCT dem-8574 43 1 [= [= X dem-8574 43 2 −tµµµ −tµµµ VERB dem-8574 43 3 kµ kµ NOUN dem-8574 43 4 , , PUNCT dem-8574 43 5 and and CCONJ dem-8574 43 6 ) ) PUNCT dem-8574 43 7 (= (= ADP dem-8574 43 8 121 121 NUM dem-8574 43 9 −+++− −+++− NOUN dem-8574 43 10 tt tt PROPN dem-8574 43 11 µµµµ µµµµ NOUN dem-8574 43 12 k k PROPN dem-8574 43 13 . . PUNCT dem-8574 44 1 the the DET dem-8574 44 2 sequence sequence NOUN dem-8574 44 3 1 1 NUM dem-8574 44 4 ~~ ~~ NUM dem-8574 44 5 = = PUNCT dem-8574 44 6 −− −− PROPN dem-8574 44 7 ttt ttt PROPN dem-8574 44 8 yyx yyx PROPN dem-8574 44 9 represents represent VERB dem-8574 44 10 the the DET dem-8574 44 11 monthly monthly ADJ dem-8574 44 12 log log NOUN dem-8574 44 13 growth growth NOUN dem-8574 44 14 rate rate NOUN dem-8574 44 15 . . PUNCT dem-8574 45 1 if if SCONJ dem-8574 45 2 ) ) PUNCT dem-8574 45 3 , , PUNCT dem-8574 45 4 ( ( PUNCT dem-8574 45 5 βtf βtf NOUN dem-8574 45 6 is be AUX dem-8574 45 7 a a DET dem-8574 45 8 polynomial polynomial NOUN dem-8574 45 9 of of ADP dem-8574 45 10 order order NOUN dem-8574 45 11 one one NUM dem-8574 45 12 then then ADV dem-8574 45 13 ) ) PUNCT dem-8574 45 14 , , PUNCT dem-8574 45 15 ( ( PUNCT dem-8574 45 16 ~)(~= ~)(~= NUM dem-8574 45 17 ) ) PUNCT dem-8574 45 18 ( ( PUNCT dem-8574 45 19 21 21 NUM dem-8574 45 20 ttxe ttxe NOUN dem-8574 45 21 t t PROPN dem-8574 46 1 µµ µµ NOUN dem-8574 46 2 + + CCONJ dem-8574 46 3 ( ( PUNCT dem-8574 46 4 3 3 NUM dem-8574 46 5 ) ) PUNCT dem-8574 46 6 where where SCONJ dem-8574 46 7 1)()(=)(~ 1)()(=)(~ PROPN dem-8574 46 8 111 111 NUM dem-8574 46 9 −− −− PROPN dem-8574 46 10 ttt ttt PROPN dem-8574 46 11 µµµ µµµ NOUN dem-8574 46 12 is be AUX dem-8574 46 13 periodic periodic ADJ dem-8574 46 14 function function NOUN dem-8574 46 15 that that PRON dem-8574 46 16 corresponds correspond VERB dem-8574 46 17 to to ADP dem-8574 46 18 seasonal seasonal ADJ dem-8574 46 19 pattern pattern NOUN dem-8574 46 20 and and CCONJ dem-8574 46 21 tiemttt tiemttt NOUN dem-8574 46 22 ψ ψ X dem-8574 46 23 ψ ψ X dem-8574 46 24 ψµµµ ψµµµ NOUN dem-8574 46 25 ) ) PUNCT dem-8574 47 1 ( ( PUNCT dem-8574 47 2 ~=1)()(=)(~ ~=1)()(=)(~ NUM dem-8574 47 3 2\ 2\ NUM dem-8574 47 4 222 222 NUM dem-8574 47 5 ∑ ∑ NOUN dem-8574 47 6 ψψ∈ ψψ∈ VERB dem-8574 47 7 −− −− NOUN dem-8574 47 8 . . PUNCT dem-8574 48 1 the the DET dem-8574 48 2 sequence sequence NOUN dem-8574 48 3 1 1 NUM dem-8574 48 4 ~~ ~~ NUM dem-8574 48 5 = = X dem-8574 48 6 ' ' PART dem-8574 48 7 −− −− PROPN dem-8574 48 8 ttt ttt PROPN dem-8574 48 9 yyx yyx PROPN dem-8574 48 10 represents represent VERB dem-8574 48 11 the the DET dem-8574 48 12 annual annual ADJ dem-8574 48 13 log log NOUN dem-8574 48 14 growth growth NOUN dem-8574 48 15 rate rate NOUN dem-8574 48 16 . . PUNCT dem-8574 49 1 if if SCONJ dem-8574 49 2 ) ) PUNCT dem-8574 49 3 , , PUNCT dem-8574 49 4 ( ( PUNCT dem-8574 49 5 βtf βtf NOUN dem-8574 49 6 is be AUX dem-8574 49 7 a a DET dem-8574 49 8 polynomial polynomial NOUN dem-8574 49 9 of of ADP dem-8574 49 10 order order NOUN dem-8574 49 11 one one NUM dem-8574 49 12 then then ADV dem-8574 49 13 ) ) PUNCT dem-8574 49 14 , , PUNCT dem-8574 49 15 ( ( PUNCT dem-8574 49 16 ' ' PUNCT dem-8574 49 17 ~= ~= NOUN dem-8574 49 18 ) ) PUNCT dem-8574 49 19 ' ' PUNCT dem-8574 49 20 ( ( PUNCT dem-8574 49 21 2 2 NUM dem-8574 49 22 txe txe NOUN dem-8574 49 23 t t PROPN dem-8574 49 24 µ µ X dem-8574 49 25 ( ( PUNCT dem-8574 49 26 3 3 NUM dem-8574 49 27 ) ) PUNCT dem-8574 49 28 łukasz łukasz VERB dem-8574 49 29 lenart lenart ADJ dem-8574 49 30 dynamic dynamic ADJ dem-8574 49 31 econometric econometric ADJ dem-8574 49 32 models model NOUN dem-8574 49 33 15 15 NUM dem-8574 49 34 ( ( PUNCT dem-8574 49 35 2015 2015 NUM dem-8574 49 36 ) ) PUNCT dem-8574 49 37 27–47 27–47 NUM dem-8574 49 38 30 30 NUM dem-8574 49 39 where where SCONJ dem-8574 49 40 tiemttt tiemttt NOUN dem-8574 49 41 ψ ψ X dem-8574 49 42 ψ ψ X dem-8574 49 43 ψµµµ ψµµµ NOUN dem-8574 49 44 ) ) PUNCT dem-8574 49 45 ( ( PUNCT dem-8574 49 46 ' ' NUM dem-8574 49 47 ~=12)()(=)('~ ~=12)()(=)('~ PUNCT dem-8574 50 1 2\ 2\ NUM dem-8574 50 2 222 222 NUM dem-8574 50 3 ∑ ∑ NOUN dem-8574 50 4 ψψ∈ ψψ∈ VERB dem-8574 50 5 −− −− NOUN dem-8574 50 6 . . PUNCT dem-8574 51 1 in in ADP dem-8574 51 2 future future ADJ dem-8574 51 3 work work NOUN dem-8574 51 4 we we PRON dem-8574 51 5 assume assume VERB dem-8574 51 6 that that SCONJ dem-8574 51 7 the the DET dem-8574 51 8 autocovariance autocovariance NOUN dem-8574 51 9 function function NOUN dem-8574 51 10 of of ADP dem-8574 51 11 the the DET dem-8574 51 12 time time NOUN dem-8574 51 13 series series NOUN dem-8574 51 14 } } PUNCT dem-8574 51 15 : : PUNCT dem-8574 51 16 { { PUNCT dem-8574 51 17 z∈txt z∈txt PROPN dem-8574 51 18 ( ( PUNCT dem-8574 51 19 or or CCONJ dem-8574 51 20 } } PUNCT dem-8574 51 21 : : PUNCT dem-8574 51 22 ' ' PUNCT dem-8574 51 23 { { PUNCT dem-8574 51 24 z∈tx z∈tx PROPN dem-8574 51 25 t t PROPN dem-8574 51 26 ) ) PUNCT dem-8574 51 27 is be AUX dem-8574 51 28 a a DET dem-8574 51 29 periodic periodic ADJ dem-8574 51 30 function function NOUN dem-8574 51 31 with with ADP dem-8574 51 32 the the DET dem-8574 51 33 same same ADJ dem-8574 51 34 periodt periodt NOUN dem-8574 51 35 . . PUNCT dem-8574 52 1 this this PRON dem-8574 52 2 is be AUX dem-8574 52 3 a a DET dem-8574 52 4 natural natural ADJ dem-8574 52 5 generalization generalization NOUN dem-8574 52 6 of of ADP dem-8574 52 7 the the DET dem-8574 52 8 assumption assumption NOUN dem-8574 52 9 concerning concern VERB dem-8574 52 10 second second ADJ dem-8574 52 11 order order NOUN dem-8574 52 12 stationarity stationarity NOUN dem-8574 52 13 . . PUNCT dem-8574 53 1 this this DET dem-8574 53 2 assumption assumption NOUN dem-8574 53 3 follows follow VERB dem-8574 53 4 from from ADP dem-8574 53 5 the the DET dem-8574 53 6 natural natural ADJ dem-8574 53 7 hypothesis hypothesis NOUN dem-8574 53 8 that that PRON dem-8574 53 9 for for ADP dem-8574 53 10 monthly monthly ADJ dem-8574 53 11 data datum NOUN dem-8574 53 12 at at ADP dem-8574 53 13 some some DET dem-8574 53 14 months month NOUN dem-8574 53 15 the the DET dem-8574 53 16 variability variability NOUN dem-8574 53 17 can can AUX dem-8574 53 18 be be AUX dem-8574 53 19 higher high ADJ dem-8574 53 20 than than ADP dem-8574 53 21 at at ADP dem-8574 53 22 another another DET dem-8574 53 23 month month NOUN dem-8574 53 24 . . PUNCT dem-8574 54 1 with with ADP dem-8574 54 2 no no DET dem-8574 54 3 loss loss NOUN dem-8574 54 4 of of ADP dem-8574 54 5 generality generality NOUN dem-8574 54 6 we we PRON dem-8574 54 7 assume assume VERB dem-8574 54 8 that that PRON dem-8574 54 9 exists exist VERB dem-8574 54 10 natural natural ADJ dem-8574 54 11 m m VERB dem-8574 54 12 such such ADJ dem-8574 54 13 that that DET dem-8574 54 14 msn msn NOUN dem-8574 54 15 = = PUNCT dem-8574 54 16 . . PUNCT dem-8574 55 1 then then ADV dem-8574 55 2 the the DET dem-8574 55 3 time time NOUN dem-8574 55 4 series series PROPN dem-8574 55 5 } } PUNCT dem-8574 55 6 : : PUNCT dem-8574 55 7 { { PUNCT dem-8574 55 8 z∈txt z∈txt PROPN dem-8574 55 9 can can AUX dem-8574 55 10 be be AUX dem-8574 55 11 represented represent VERB dem-8574 55 12 as as ADP dem-8574 55 13 a a DET dem-8574 55 14 second second ADJ dem-8574 55 15 order order NOUN dem-8574 55 16 stationary stationary PROPN dem-8574 55 17 t t PROPN dem-8574 55 18 -valued -value VERB dem-8574 55 19 time time NOUN dem-8574 55 20 series series NOUN dem-8574 55 21 with with ADP dem-8574 55 22 almost almost ADV dem-8574 55 23 periodic periodic ADJ dem-8574 55 24 mean mean NOUN dem-8574 55 25 function function NOUN dem-8574 55 26 . . PUNCT dem-8574 56 1 more more ADV dem-8574 56 2 precisely precisely ADV dem-8574 56 3 the the DET dem-8574 56 4 time time NOUN dem-8574 56 5 series series PROPN dem-8574 56 6 t t PROPN dem-8574 56 7 tsststt tsststt NOUN dem-8574 56 8 xxxy xxxy PROPN dem-8574 56 9 ] ] X dem-8574 57 1 [= [= X dem-8574 57 2 1)(21)(1 1)(21)(1 NOUN dem-8574 57 3 k−+−+ k−+−+ NOUN dem-8574 57 4 is be AUX dem-8574 57 5 t t PROPN dem-8574 57 6 values value NOUN dem-8574 57 7 second second ADJ dem-8574 57 8 order order NOUN dem-8574 57 9 stationary stationary ADJ dem-8574 57 10 time time NOUN dem-8574 57 11 series series NOUN dem-8574 57 12 with with ADP dem-8574 57 13 almost almost ADV dem-8574 57 14 periodic periodic ADJ dem-8574 57 15 mean mean NOUN dem-8574 57 16 function function NOUN dem-8574 57 17 . . PUNCT dem-8574 58 1 this this DET dem-8574 58 2 mean mean NOUN dem-8574 58 3 function function NOUN dem-8574 58 4 can can AUX dem-8574 58 5 be be AUX dem-8574 58 6 decomposed decompose VERB dem-8574 58 7 ( ( PUNCT dem-8574 58 8 in in ADP dem-8574 58 9 natural natural ADJ dem-8574 58 10 way way NOUN dem-8574 58 11 ) ) PUNCT dem-8574 58 12 to to ADP dem-8574 58 13 two two NUM dem-8574 58 14 main main ADJ dem-8574 58 15 parts part NOUN dem-8574 58 16 : : PUNCT dem-8574 58 17 periodic periodic ADJ dem-8574 58 18 function function NOUN dem-8574 58 19 ( ( PUNCT dem-8574 58 20 that that PRON dem-8574 58 21 corresponds correspond VERB dem-8574 58 22 to to ADP dem-8574 58 23 seasonal seasonal ADJ dem-8574 58 24 frequencies frequency NOUN dem-8574 58 25 2ψ 2ψ NOUN dem-8574 58 26 ) ) PUNCT dem-8574 58 27 and and CCONJ dem-8574 58 28 almost almost ADV dem-8574 58 29 periodic periodic ADJ dem-8574 58 30 function function NOUN dem-8574 58 31 ( ( PUNCT dem-8574 58 32 that that PRON dem-8574 58 33 corresponds correspond VERB dem-8574 58 34 to to ADP dem-8574 58 35 frequencies frequency NOUN dem-8574 58 36 31 31 NUM dem-8574 58 37 ψ∪ψ ψ∪ψ NOUN dem-8574 58 38 ) ) PUNCT dem-8574 58 39 the the DET dem-8574 58 40 natural natural ADJ dem-8574 58 41 estimator estimator NOUN dem-8574 58 42 of of ADP dem-8574 58 43 kµ kµ PROPN dem-8574 58 44 ( ( PUNCT dem-8574 58 45 k=1,2, k=1,2, PROPN dem-8574 58 46 ... ... PUNCT dem-8574 58 47 ,t–1 ,t–1 PUNCT dem-8574 58 48 ) ) PUNCT dem-8574 58 49 based base VERB dem-8574 58 50 on on ADP dem-8574 58 51 sample sample NOUN dem-8574 58 52 } } PUNCT dem-8574 58 53 , , PUNCT dem-8574 58 54 , , PUNCT dem-8574 58 55 , , PUNCT dem-8574 58 56 { { PUNCT dem-8574 58 57 21 21 NUM dem-8574 58 58 nxxx nxxx PROPN dem-8574 58 59 k k PROPN dem-8574 58 60 where where SCONJ dem-8574 58 61 mtn mtn PROPN dem-8574 58 62 = = PUNCT dem-8574 58 63 has have VERB dem-8574 58 64 the the DET dem-8574 58 65 following follow VERB dem-8574 58 66 form form NOUN dem-8574 58 67 . . PUNCT dem-8574 59 1 1 1 NUM dem-8574 60 1 = = NOUN dem-8574 60 2 ˆ ˆ NOUN dem-8574 60 3 1 1 NUM dem-8574 60 4 ) ) PUNCT dem-8574 60 5 ( ( PUNCT dem-8574 60 6 1= 1= X dem-8574 60 7 , , PUNCT dem-8574 60 8 tjk tjk PROPN dem-8574 60 9 m m NOUN dem-8574 60 10 j j PROPN dem-8574 60 11 nk nk NOUN dem-8574 60 12 x x VERB dem-8574 60 13 m m VERB dem-8574 60 14 −+∑µ −+∑µ ADV dem-8574 60 15 ( ( PUNCT dem-8574 60 16 4 4 X dem-8574 60 17 ) ) PUNCT dem-8574 60 18 the the DET dem-8574 60 19 estimator estimator NOUN dem-8574 60 20 ' ' PART dem-8574 60 21 1,2,1 1,2,1 NUM dem-8574 60 22 , , PUNCT dem-8574 60 23 ] ] PUNCT dem-8574 60 24 ˆˆˆ[=ˆ ˆˆˆ[=ˆ PROPN dem-8574 60 25 ntnnn ntnnn VERB dem-8574 60 26 −µµµ −µµµ NOUN dem-8574 60 27 kµ kµ NOUN dem-8574 60 28 is be AUX dem-8574 60 29 asymptotically asymptotically ADV dem-8574 60 30 normally normally ADV dem-8574 60 31 distributed distribute VERB dem-8574 60 32 with with ADP dem-8574 60 33 known know VERB dem-8574 60 34 variance variance NOUN dem-8574 60 35 covariance covariance NOUN dem-8574 60 36 matrix matrix NOUN dem-8574 60 37 . . PUNCT dem-8574 61 1 theorem theorem VERB dem-8574 61 2 2.1 2.1 NUM dem-8574 61 3 assume assume VERB dem-8574 61 4 that that SCONJ dem-8574 61 5 there there PRON dem-8574 61 6 exist exist VERB dem-8574 61 7 constants constant NOUN dem-8574 61 8 0 0 NUM dem-8574 61 9 > > SYM dem-8574 61 10 δ δ PROPN dem-8574 61 11 , , PUNCT dem-8574 61 12 ∞∆ ∞∆ X dem-8574 61 13 < < X dem-8574 61 14 and and CCONJ dem-8574 61 15 ∞