Short-term and Long-term trends, seasonal adjustment, and the business cycle

126 Pages·2012·3.57 MB·English

SHORT-TERM
AND LONG-TERM
TRENDS, SEASONAL
ADJUSTMENT,
AND THE BUSINESS
CYCLE
Regina Kaiser and Agustín Maravall
Banco de España - Servicio de Estudios
Documento de Trabajo nº 9918
SHORT-TERM
ANDL ONG-TERM
TRENDS, SEASONAL
ADJUSTMENT,
ANDT HE BUSINESS
CYCLE
RegKiania(s *e)r
anAdg usMtairna( v*a*l)l
(*)U niversiCdaardl IoIsI M,a drid.
(. ). BandceoE spanMaa,d rid.
BancdoeE spa-nSae rvidceEi sot udios
DocumednetT or abna'j9 o91 8
Inp ublishtihnigss e ritehse B ancod eE spanase ektso d isseminate
studioefsi nterethsatwt i lhle lpa cquairneta debrest ter
witht heS panisehc onomy.
Thea nalysoepsi,n ioannsd fi ndingosft hespea perrse present
thev iewosf t heiaru thortsh;e ya ren otn ecessatrihloys e
oft heB ancod eE spana.
TheB ancod eE spandai sseminaittpesr si ncirpeaplo rts
ande conomiicn dicatvoiraIs N TERNEanTd I NFOviA.PatL:U S
http://www.bde.es
ISSN0:2 13-2710
ISBN:8 4-7793-682-X
Dep6sitloe gaMl.: 3 6426-1999
lmprentdae lB ancod eE spana
ABSTRACT
Int himso nografpihr,ws eta ,n alyiznde e tasiolm eo ft hmea jolri mitaotfti hoen s
standparrodc edtuore es timbautsei nceyscsl weist thh eH odrick-P(rHePs)co tt
filtBeyri .n corportaitmsieen rgi aensa lytseicsh niqiutie sss ,e enh ows ome
intuiatnidrv eel atsiivmeplmlyoe d ificattoti hoefn isl ctaenir m prosvieg nificantly
itpse rformainnpc aer,t iciuntl earrmo sfc leannoefts hsse i gnsamla,l lreerv ision,
stabiolfei ntdy- peersitoidm aatnodrd se,t ectoifto unr npionign ts.
Thenw,e s hohwo wt hmeo diffiieldct aenbr e s eeans t heex acsto lutoifao w ne ll­
definsetda tisptriocballen ma,m eloyp,t im(amli nimmuema ns quareerdr or)
estimaotfci oomnp oneinnat s st anduanrodb served-commopdoenwleh,ne trt eh e
observseedr iiesds e compoisnetdao t renadc ,y claes ,e asonaanlda, n i rregular
componeTnhti.ps r obliesms traightftoosr owlavwreid t Kha lmaonr W iener­
Kolmogofrioltvte ecrh niqTuheem so.d eflostr h ceo mponeinntcso rposroamtee- a­
priofreia tutrheasrt,e fltehceat d -hnoact uorfet hHeP filatenrds, o mes eries­
dependfeenatt utrheaset,n sutrhea tth aeg gregAaRtIeM mAo deilm plibeytd h e
componeinset xsa ctthlpyea rsimonAiRoIuMsAm odeild entidfiireedco tntl hye
observseedri Ieitsss . h owhno wt hmeo del-biansteedr pregtraetafitaolcnyi litates
diagnosatnidc isn ferentchee,r efbayc ilitsaytsitnegm aatniacl ysainsd
improvemTehnept r.o cediustr rei viimapllleym enwtietadhl reaadvya ilfarbelee
software.

Contents
Preface
9
Introduction
1 13
TheH odrick-PrfielstceWorit:et n er-
2
Kolmogodreorvi vation
16
Revisions
3 20
3.P1r eliemsitniamorafeyt n pidoo inan ntrdse vi.s ions 20
3.A2n e xample . . . . 2.4
Spuriroeussu lts
4 34
4.S1p urciroousss correlation 35
4.S2p uraiuotuosc ioorcnra;el liabtration 38
4.3 Spuricoyuc.sl e.p er.i odic 40
4.3W.h1i tei-nnpo.ui tse 40
4.3R.a2n domi-nwpa.ul tk 43
4.3S.p3e ccthracartlae roifts htceiy ccsslp eu;r iroeucsonne-ss
sidered 46
ImprovinHgo drtihcek -Prfielstceort t
5 52
5.R1e durceivnigs. i ons 52
5.2I mprotvhcieyn cgls iicganla l 56
Hodrick-Pfirletsecrowitinttg ha im no debla seadp proach
6 69
6.A1s immpoldee l-ablagsoerdi th.m.... . ... . .69. .
6.A2 commpoldeetle-m beatsheodd 72
6.S3o mceo mmeonnmt osd el-dbiaasgenadon sidtn ifcesr en8c8e
6.M4M SeEs timoaftt hcieyo cnlp ea:r aad ox 100
Reefrences
103
AppendAi x
108
A.1W ienelrm-oKgvooerroosvfti ohRneo driecskcfi-olPttrte r1 08
A.2T hael gorithm 110
A.A3n ootnec omputation 111
Appendix
B 113
B.A1R IAM-modeld-ebcaosmepodofa st iitsmieeor ni es 113
.
B.E2q uivoatfl hefenuR cJoeId ricka-nPAdrR eIsMcAo-tbta sed ap-
proa.c he.s . . . . .. .. ... .... 1 .1. 6 .. .
B.C3o mpulneotbes ceormvpeodn enftot rh m4eso edreoilfte h se
exam.p le. . . . . . .1 20

Preface
Thimso nographt hapedr dorbelmseesmae ssou efrc ionngco ymci(lcae lss o
calbluesdi cnyecsilsnme a sc)r oectoinmsoeemr iIicne sdt.eh ceta hdfeao tl ­
lowtehdGe r eDaetp reescsoinoondm,ei vsetlasoni p netde rtehpseot s siinb le
exist(emnocorerle e sosyfss tecmyactilinec se)t c hoen soemfeyoe,jrx ample,
Habe(r91l4eo4rr) Shu(m1p9e3It9btee) rc. a ampep atrheaintnot rdteor
idenetciofnyco ymci,olc ne es thora edm ofvreot mhs ee rsieeassfl ouncatlu a­
tioansss,o ciated bweihtahav nistdohh rloe,or ntg--stteeecrrutmmlr aern d,
assocmioastwteildttye h c hnoplrooggiBrcuearsalnsn sM.d i tc(h91e4lp6lr) o ­
vidpeedr htahfipers ms atir ne feproeifnnocmtreu cohtf h peo streersie.oa rr ch
Statimsetasiucraeolmft e hncety cwlaes broaasdc layp tsuterhveieann r gi ­
atiotnh seeo frw iietsah r iann gfeer qouifee nascf,tt ehrse e rhiaebsse en
seasoanjdaulsaltnyedd de tre(nBdueardnn.Mds i tcshueglglea rs atneogdfe
ferqueansscoiceiswa ittehd cyclebse twwi6eta ehn3n d2 a qepurearsri.to)d
Stactaimles tthiwoedrdsee vitsoee sdt icmyactlverai icaatalni tdoh neg,sr ea d­
ualelvyo ltvoewdam redtshf oudnsd ambeanstoeantdl h alepy p liocmfao tvi­on
inagv erfialgtteeo r sste hresi eeese,;x afmoBprrl ayen ,Bd o sc(h1a9nT7 h1e) .
la2s0yt e ahrasv e wimtetnheosdsoreledos egoaintrc wcabohlr ofaordn tTsh.e
firfsrto dnetaw littf uhr tdheevre loopftm hemeno tvsiv negr-taaygpoefea p­
pro;at chshee cfornowdna ttsh dee veloopfmm oercneot m pslteaxt iaps­tical
prohaeEcsx.a moprfle esse iabnro cdthih r eccatbnie o nfsoS uinm(d9s1 7 i7n) ,
LahainrMdio o(r1e9 S9t1oa)cn,kWd a sto(n1 9a9n3Hd)a mi(l1to9An9l 4­).
thotuhgfehi arpsptr iosa ckhtn opor wens enlti mseirttiahotneuie sow nasn,d
more sopmheitshtdoeidvcsea ltioentpd hse eed c aopnpdr (omaocnshot t ably,
multiavnandro inalteiexn teeanras riaeota nnes a)rs ltyaa gned, have proved
stuinlrle ldiiasbpllpeao,yob iren hgaw vhiemonor v ianwgafy r otmh e sample
periAosBd a.x atneKdri n(g1 9p9o5io)nu twt e,s tfialcaletp restehnet
same qbuaess"itacis o nd id MBiutrcfnhiseyf letalyaan rgdsoh :os wh ould
onies otlhacety ec lciocmaploo nfae nen cto intocim msee rIinep sa?r ticular,
hoswh oounlsede pabruastien eeslse-mcfeyrncostlmlse o e wvloyl sveicnugl ar
treanndrdsa ,p viadrlyysi enagso orin rarle cgoumlpaosrn? e"n t
Bet haasit m ta yii,ta s f atchtma eta su(risinon mwgea yt)hb eu sicnyecslse
iasn a ctpuraels nseieondfeg c onoimnpi asrttsio,cft u hloraserel attote hde
fnuctioopfno ilnigc ya-gmeanakcinindeg si nstiotfu taippolnise,d amnadc roe­
conormeisce. La arcckhapi rnagc atnirdce allia albtelirevmn eoa,vt ivnegr-aage
methaortdehs e aocnteuusas letldoy, the epcooinnaotgm ceitinc(he sasut c h
9
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ast hOeE CDt,hIe n ternMaotnieotFnauarnloyd r t, h Eeu ropCeeannt ral
Banokf)th eanvi en terrunloaerrls e commentdoma etaiseoucnrosen coym­ic
clesa rtMehA a-tt myepteh oOdncsea. sn a tyh avte,rb yr oawdiltyth,hi en
seotfa pplbiuesdi neasnsa-lctyyhscethlrsaebe,s e eacn o nvertogweanrcdes
whacto ublecd a l"lHedodr irceks-cP(oHtPfit)l"t earm ientgh,o dporloo­gy
posbeyHd o draincPdkr e s(c1o9ts8te0a e)l ;Ks yod laannPddr es(c18o92t)t
anPdr etstc(o1T9h8ee6m )e.rg oetfnh HcePef ilatsape arr ahdaipsgr,mo ba­
blbye,ef sont ebryee cdo ngolmoibca lainEzdua rtoiipoennat tnei gowrnhai,c h
has rearq euliarhteiidlgv ehevo lefmyle thodohloomgoigceiannole r idtteoyr
compcaoruen tArnui neasv.o ciodnasbelqietus he anttcose, o mdee grtehee,
proceedvuernetiu osafe tlnul syea sda blbaocxk.
Acadecmriicto ifc itshfimel thHeapPrso inotusetod m see rdiroauwsb .a cks
But, tbheceyr ointdni ocmtiu scemhff, oh rabtse esnp enatd dornet shseisneg
shortcAonmi imnpgosre.tx acnetpi tsB iaoxantn eKdri n(g1 9w9h5e)ar,ne
alter(nraetlifiavltete edr) ist hiapmtrp orpsoomvsoeeosdt ,oh ftn heeess st i­
matofortrsh cee nyteraa,brl us atv oeisdtsi maatbt oiteohxn t retmhees of
ser(iiensc loufcd oiuncrgus,re r,e rnetc peaenonrtddi s S.y)s teimmaoptvriec­
menotf tfhielp teerrf orhmabasen eccnle e haarmlpyeb ryie tadsd -nhaotcu re
antdh lea ocfk uannd ersltyaitnimgso tdwieiclata p hlr edceifisneoi ftt hieo n
compo(nsefenoeter,sx amHpalrev1,e9 y8a,5n C,dr tasLf,e ybaunrMdni el ls,
1989).
Int hmiosn opghfr,ia ,rw seat naliyndz eets aoimolef mtahjelo irm itations
ofH Pfi lteBryi nign.c otripmsoeer raaitneiasnlt gye scihsn mioqsudteels­y,
veloopveedrl at2sh0te yaesaa nr tsea rfmoaftt hhee x plionst hieo n use of
ARIMtAy-pmeo de(lBsoa xnJ de nk1i9n7si0,t)s ,ei ehsno s wo mien tuitive
anrde lastiimvmepolldyei fitcota htfeii olntsie mrp rcsoaivnge n ifiitcsa ntly
perfaonrcimenp, a rtiictnu elroamfcrs l eaonfn estsihsge sn maallr,le evri sion,
staboiefln idt-ype esrtiiromsada,n td doe teocftt uironni ng points.
Thewnes, h ohwo twh meo dififiletcdea brne s eent heaexs a scotl uotfi on
aw ell-sdteafitniepsdrt oibnclaaemlme o,lp yt,i( mmailn immeuasmnq uared
erreosrt)i moafct oimopno innaes nttasn udnaorbds ervedm-ocdoemlp,o nent
whetrheoe b sesrevreiiddsee sc omipnoatst oer de anc dy,ca ls ee,a saonnda l,
ani rrecgoumlpao.rnT ehniptsr obilsse tmr aighttosf oolwrviwetat rhhd e
well-KkanlomowarWnn i ener-Koflilmttoeegcroh rn(oisvqfe uoeeer,xs a mple,
Harv1e9y8o,9rM , a raal1vl9,9 T5h)me.o dfeoltrshc eo mpoinnecnotrsp orate
somae- prfaeitourrie rse,fl tethcahetda -tnh aotcou fr eHt Ph efi ltseorm,e and
series-fdeeuaprteetnshd,eaa ntns ttu hrtaeht a eg greAgRaItMmeAo dieml-
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plibeytd hc eo mpoinesex nattcsht pleay r simAoRnIiMmoAou dse l identified
direocntt holeby s esrreivee·Fsd u. hretsru,m mtihntegr endt hcaeyn ctdlh ee,
stantdraerndd /-s ceyacs/loienr arledgeucloamrp oofs iBtui(ro18mn90ao )nr
HillamnTedir a( o1 9i8os2b )t aAinn eodb.v iouostf hmaedo vdaenlt-abgaes ed
interpirtseh tiaagtttr ieoafncat illyi dtiaatgenason sidtn ifcesrt ehnecree,b y
fcailistyastttieianmcnga a laynisdmi psr onvte.m lelFiyiit,nss ha ohwontw h e
procetdruirveii maiplsll eymw eintthe daa lvlaraiebfalrdseeyoe f tware.
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