VAR MODELİN DAYANIKLI TAHMİNİ: İKTİSADİ BÜYÜME - ENFLASYON İLİŞKİSİ ÜZERİNE BİR İNCELEME

Marmara Üniversitesi øø%)'HUJLVL YIL 2010&ø/7;;,;, SAYI II, S. 539-553 9$502'(/ø1'$<$1,./,7$+0ø1ø ø.7ø6$'ø%h<h0(-ENFLASYON ø/øù.ø6øh=(5ø1(%ø5 ø1&(/(0( Özlem YORULMAZ* .DUXQ1(0/ø2ö/8** Özet 8\JXODPDODUGD ]DPDQ VHULOHULQLQ JHQHO \DSÕVÕQÕQ GÕúÕQGD VHULGHNL J|]OHPOHULQoR÷XQOX÷XQGDQIDUNOÕ\DSÕVHUJLOH\HQG]HQVL]J|]OHPOHUOH\]OHúLOPHVL RODVÕGÕU %X WU J|]OHPOHU D\NÕUÕ RODUDN LVLPOHQGLULOLU D\NÕUÕ J|]OHPOHULQ DQDOL] ]HULQGH \DQÕOWÕFÕ LVWHQPH\HQ YH ROXPVX] HWNLOHUL RODELOLU %X DoÕGDQ D\NÕUÕ J|]OHPOHUGHQ HWNLOHQPH\HQ GLUHQoOL \DSÕGDNL GD\DQÕNOÕ WDKPLQFLOHULQ NXOODQÕPÕ |QHULOLU  dDOÕúPDGD $50$ YH 9$50$ PRGHOOHULQGH NDUúÕODúÕODQ D\NÕUÕ J|]OHP WUOHULQH EXQODUÕQ WHúKLVLQH 9$5 PRGHOLQLQ GD\DQÕNOÕ WDKPLQLQH GH÷LQLOPLú YH GD\DQÕNOÕ 9$5 PRGHOL LOH - \ÕOODUÕ DUDVÕQGDNL 7UNL\H¶GHNL E\PH RUDQÕ YHHQIODV\RQLOLúNLVLLOLúNLVLLQFHOHQPLúWLU Anahtar Kelimeler: (..'D\DQÕNOÕ9$50/76D\NÕUÕJ|]OHPOHU ROBUST ESTIMATION OF THE VECTOR AUTOREGRESSIVE MODEL: AN INVESTIGATION OF THE RELATIONSHIP BETWEEN ECONOMIC GROWTH AND INFLATION Abstract In applications it is probable to confront irregular observations which are different from the majority of the time series data and do not conform the general pattern. These observations are named as outliers. Outliers may have undesiriable, damaging and misleading effects on statistical analyses. Hence, it is purposed to use * 'UøVWDQEXOhQLYHUVLWHVLøNWLVDW)DNOWHVL(NRQRPHWUL%|OPøVWDWLVWLN$QDELOLP'DOÕ ** 3URI'UøVWDQEXOhQLYHUVLWHVLøNWLVDW)DNOWHVL(NRQRPHWUL%|OPøVWDWLVWLN$QDELOLP 'DOÕNDUXQ#LVWDQEXOHGXWU 539 $UDú*|Ug]OHP<258/0$= 3URI'U.DUXQ1(0/ø2ö/8 robust estimators that are outlier resistant. In the study, outlier types which may be encountered in ARMA and VARMA models, outlier detection approaches, robust estimation of VAR model were touched on and besides the relationship between the economic growth rate and inflation in Turkey between years of 1950-2006 was investigated. Key Words: OLS, Robust VAR, MLTS, outliers *LULú øNWLVDGL oDOÕúPDODUD LOLúNLQ LVWDWLVWLNVHO PRGHOOHPH YH oÕNDUVDPD \DSÕODELOPHVL DQFDN EHOOL YDUVD\ÕPODUÕQ VD÷ODQPDVÕ\OD PPNQGU %X YDUVD\ÕPODUGDQ HQ ELOLQHQL YH VÕNOÕNOD NXOODQÕODQÕ YHULQLQ QRUPDO GD÷ÕOPDVÕ ]HULQH ROPDNOD EHUDEHU X\JXODPDGD YHUL\L ROXúWXUDQ J|]OHPOHULQ oR÷XQOX÷XQXQ EX YDUVD\ÕPÕ WHPVLO HGHELOPHVLQLQ \DQÕVÕUD ED]Õ J|]OHPOHULQ oR÷XQOXNWDQ IDUNOÕ VÕUD GÕúÕ ELU \DSÕ VHUJLOHGL÷L ELOLQPHNWHGLU %X úHNLOGH IDUNOÕ YHULQLQ oR÷XQOX÷XQGDQ DQODPOÕELoLPGHVDSPDJ|VWHUHQYHULQLQoR÷XQOX÷XQXQL]OHGL÷LLVWDWLVWLNVHOGD÷ÕOÕPÕ izlemeyen gözlemler genelliNOH OLWHUDWUGH µD\NÕUÕ¶ RODUDN LVLPOHQGLULOLU 9HULQLQ DQDOL] VUHFLQGH D\NÕUÕ J|]OHPOHULQ YDUOÕ÷ÕQÕQ GLNNDWH DOÕQPD\DUDN QRUPDOOLN YDUVD\ÕPÕQÕQ GLNNDWH DOÕQPDVÕ (Q dRN 2ODELOLUOLN (d2  \|QWHPLQH \D GD (Q .oN.DUHOHU (.. \|QWHPLQHGD\DOÕWDKPLQOHULQ \DSÕOPDVÕHWNLQROPD\DQ\DQOÕ RODQWDKPLQOHUOHNDUúÕNDUúÕ\DNDOÕQPDVÕQDQHGHQROXU%XDoÕGDQEXWUJ|]OHPOHULQ GLNNDWH DOÕQDUDN PRGHOOHPH \DSÕOPDVÕ \DGD EX WU J|]OHPOHUGHQ HWNLOHQPH\HQ WDKPLQ\|QWHPOHULQLQNXOODQÕOPDVÕJHUHNLU $\NÕUÕ J|]OHPOHULQ WHúKLV HGLOPHVL YH HWNLOHULQLQ EHOLUOHQLS NRQWURO DOWÕQD DOÕQPDVՁ]HULQH\DSÕOPÕúID]ODVD\ÕGDDUDúWÕUPDROPDNODEHUDEHUEXNRQXGD\DSÕODQ oDOÕúPDODUÕQVD\ÕVÕDODQODUÕQDJ|UHRUDQODQGÕ÷ÕQGDLNWLVDGL]DPDQVHULOHULQLQID]OD\HU WXWPDGÕ÷Õ V|\OHQHELOLU =DPDQ VHULOHULQLQ DNÕúÕ D\NÕUÕ J|]OHP ya da müdahaleler EDúOÕ÷Õ DOWÕQGD GH÷HUOHQGLULOHQ JHQHO G]HQL ER]DQ ROD\ODU \]QGHQ ]DPDQ ]DPDQ GH÷LúHELOLU*HQHOG]HQLER]DFDNROD\ODUWDWLOOHUJUHYVDWÕúSURPRV\RQODUÕSROLWLND GH÷LúLPOHULHNRQRPLNNUL]OHUEHNOHQPH\HQVÕFDN\DGDVR÷XNKDYDGDOJDODUÕVDYDú GR÷DODIHWOHUUHNODPODUYVúHNOLQGHVÕUDODQDELOHFH÷L JLEL |OoP \DGD ND\ÕW KDWDVÕ ND\QDNOÕGDRODELOLU Gerek ARMA gibi WHN GH÷LúNHQOL JHUHNVH 9$50$ JLEL oRN GH÷LúNHQOL zaman serisi modellerinin tahmininde özellikle EKK ve EÇO gibi tahmin PHWRGODUÕQÕQ NXOODQÕOPDVÕ D\NÕUÕ J|]OHPOHULQ YDUOÕ÷ÕQGD ]DPDQ VHULOHULQLQ DQDOL] VUHFLQLQKHPHQKHPHQWP DGÕPODUÕQÕROXPVX]HWNLOHU /LWHUDWUGHEX PRGHOOHULQ SDUDPHWUH WDKPLQLQGH NXOODQÕODQ WHNQLNOHULQ D\NÕUÕ J|]OHP NDUúÕVÕQGD GLUHQoVL] ROGX÷XEX\]GHQGD\DQÕNOÕWDKPLQ\|QWHPOHULQHEDúYXUXOPDVÕJHUHNWL÷LYXUJXODQÕU dDOÕúPDGD $50$ YH 9$50$ PRGHOOHULQGH NDUúÕODúÕODELOHQ D\NÕUÕ J|]OHP WUOHUL EXQODUÕQWHúKLVOHULYH9$50$PRGHOLQLQGD\DQÕNOÕWDKPLQLQGHQV|]HGLOPLúWLU6RQ E|OPGHLVHE\PHRUDQÕYHHQIODV\RQDUDVÕQGDNLLOLúNL9$50$PRGHOLQLQNODVLN YH GD\DQÕNOÕ WDKPLQOHUL\OH D\UÕ D\UÕ LQFHOHQPLú YH EX VHULOHUGHNL D\NÕUÕ J|]OHPOHU EHOLUOHQPLúWLU 540 2. $\NÕUÕ*|]OHP7UOHUL =DPDQ VHULOHULQGH D\NÕUÕ J|]OHP NRQXVXQX LON NH] )R[ HOH DOPÕúWÕU 2WRUHJUHVLI PRGHOOHUH GD\DOÕ ]DPDQ VHULOHULQGH NDUúÕODúÕODELOHFHN D\NÕUÕ J|]OHP WUOHULQLLNLVÕQÕIDD\ÕUPÕúI. tür (additive-AO) ve II. tür (innovational-IO) olarak LVLPOHQGLUPLúWLU /LWHUDWUH 7VD\¶ÕQ |QHUGL÷L o IDUNOÕ D\NÕUÕ J|]OHP WU GDKD HNOHQHQH NDGDU  X]XQFD  ELU VUH VDGHFH $2 YH ,2 WU D\NÕUÕ J|]OHPOHU \HU WXWPXúWXU 7VD\¶ÕQ EX oDOÕúPDGD |QHUGL÷L D\NÕUÕ J|]OHPOHU Level Shift-LS (seviye GH÷LúLPL  7HPSRUDU\ &KDQJH-7& JHoLFL GH÷LúLP  YH 9DULDQFH &KDQJH-VC YDU\DQVGH÷LúLPL ¶GÕU6HYL\HYHYDU\DQVGH÷LúLPLNLPL\D]DUODUWDUDIÕQGDQD\NÕUÕ J|]OHPRODUDNVÕQÕIODQGÕUÕOPDN\HULQH\DSÕVDOGH÷LúLPRODUDNHOHDOÕQÕUYHEXGH÷LúLP NDOÕFÕ RODUDN GH÷HUOHQGLULOLU. $\NÕUÕ J|]OHPOHULQ GLNNDWH DOÕQPDPDVÕ KDOLQGH oÕNDUVDPDODUÕQ GR÷UXOX÷X JYHQLOLUOL÷L HWNLOHQHELOLU YH DUDúWÕUPDFÕ \DQOÕú PRGHO VHoLPL\DQOÕWDKPLQYH|QJ|UOHUOH\]OHúHELOLU $50$0RGHOOHUGH.DUúÕODúÕODQ$\NÕUÕ*|]OHPOHU9H7HúKLVL øOJLOHQLOHQ yt zaman serisi için p ve q GHUHFHOL $50$ PRGHOL DúD÷ÕGDNL JLELLIDGHHGLPHN]HUHD\NÕUÕJ|]OHPWUOHULEX\DSÕ\DED÷OÕNDODUDNDoÕNODQPÕúWÕU ( yt  P )  I1 ( yt 1  P )  ...  I p ( yt  p  P ) T1ut 1  ...  T q ut  q  ut (2.1) 2 Burada ut VÕIÕU RUWDODPDOÕ YH VDELW V u YDU\DQVOÕ úRNKDWD WHULPLGLU %X HúLWOLNJHFLNPHLúOHPFLVLNXOODQÕODUDNNDSDOÕELoLPGHDúD÷ÕGDNLJLEL\D]ÕOÕU I ( B)( yt  P ) T ( B)ut <XNDUÕGDNL HúLWOLNWH \HU DODQ ‘B’ JHFLNPH LúOHPFLVL RODUDN ELOLQLU Byt yt 1 úHNOLQGH J|VWHULOLU YH \LQH D\QÕ HúLWOLNWH \HU DODQ I ( B) ile T ( B) úHNOLQGH  SROLQRPLDO JHFLNPH LúOHPFLOHULQH NDUúÕOÕN JHOLU %X LúOHPFLOHULQ DoÕOÕPÕ úöyledir: I ( B) 1  I1 B  I2 B 2  ...  I p B p T ( B) 1  T1 B  T 2 B 2  ...  T q B q Orijinal seri y t ve gözlenen seri z t iken ve yt VHULVL \XNDUÕGDNL ARMA(p,q) modeli ile ifade edilmek üzere, Zt Yt  Z L( B ) I t (2.2) 541 $UDú*|Ug]OHP<258/0$= 3URI'U.DUXQ1(0/ø2ö/8 (T) PRGHOL]HULQGHQD\NÕUÕJ|]OHPOHUDúD÷ÕGDNLWDQÕPODQ (...truncated)