VAR Modelin Dayanıklı Tahmini: İktisadi Büyüme - Enflasyon İlişkisi Üzerine Bir İnceleme

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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

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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

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Pedro Galeano, Daniel Pena, Ruey S. Tsay, “Outlier Detection in Multivariate Time Series By Projection Pursuit”, Journal of the American Statistical Association, 101, 474, 2006, s. 655-660.

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y

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t t k t k t

y

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B y

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(3.1)

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B

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B

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(8)

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Christophe Croux, Kristel Joossens, “Robust Estimation of the Vector Autoregressive Model by a Least Trimmed Squares procedure”, COMPSTAT 2008, Physica-Verlag HD, 2008, s. 489.

(9)

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(10)

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(3.7) ifadesinde yeralan

l

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log(2 )

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6

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(11)

1954 IO 1981 LS 1994 LS 1999 IO 2001 LS $\NÕUÕJ|]OHPRODUDNEHOLUOHQHQEXJ|]OHPOHULQNDUúÕOÕNJHOGL÷LWDULKVHOROD\ODUú|\OH VÕUDODQPÕúWÕU

1954 IO (NRQRPLN NUL] LKUDFDW RUDQÕQÕQ D]DOPDVÕ HQIODV\RQ RUDQÕQÕQ_{¶OHUGHQ¶OHUHoÕNÕúÕ}

1981 LS (NRQRPLN YH VL\DVL NUL] HQIODV\RQ YH LúVVL]OLN RUDQÕQGD FLGGL_DUWÕúODU 1994 LS Ekonomik kriz, dövize olan talep, Türk LLUDVÕQÕQGH÷HUND\EÕ 1999 IO $V\DNUL]LQLQHWNLVLGHSUHPOHUEDQNDFÕOÕNVHNW|UQGHNLNUL] 2001 LS 6L\DVL NUL] HWNLVL ,0)¶QLQ o|NHQ SURJUDPÕ LúVL]OLN RUDQÕ YH_{G|YL]NXUXQGDUHNRUDUWÕú}

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(12)

Tablo 4.1: EKK tahmin yöntemiyle elde edilen VAR parametre tahminleri Büyüme Enflasyon C 5.4453 (0.8873) [6.1369] -0.0265(0.0216) [ -1.2269] Büyüme(-1) -0.1665 (0.1399) [-1.1901] 0.0058(0.0034) [1.7059] Enflasyon(-1) -6.0707 (5.7562) [-1.0546] 0.0485(0.1399) [0.3467] 7DEORGDVÕUDVÕ\OD>@LoLQGHNLGH÷HUOHUVWDQGDUWKDWD\ÕYHWWHVWVNRUXQX göstermektedir. .DWVD\ÕODUDLOLúNLQWWHVWLVNRUODUÕQDEDNÕOGÕ÷ÕQGDDQODPOÕOÕNG]H\LQGH HQIODV\RQYHE\PHRUDQÕDUDVÕQGDLOLúNL\RNWXU)DNDW0/76VRQXoODUÕLOHWDKPLQ HGLOHQNDWVD\ÕODUÕQD\QÕDQODPOÕOÕNG]H\LQGHGH÷HUOHQGLULOPHVL\OHHOGHHGLOHQVRQXo fDUNOÕGÕU

Tablo 4.2: MLTS tahmin yöntemiyle elde edilen VAR parametre tahminleri Büyüme Enflasyon C 6.2735(0.3700) [16.95] 0.0115(0.0571) [0.2014] Büyüme(-1) -0.0710 (0.0583) [ -1.2178] 0.0003(0.0090) [0.0333] Enflasyon(-1)-18.6179(2.4006)[ -7.7555] 0.1685(0.3707) [0.4545] 7DEORGDVÕUDVÕ\OD>@LoLQGHNLGH÷HUOHUVWDQGDUWKDWD\ÕYHWWHVWVNRUXQX göstermektedir. %XQDJ|UHHQIODV\RQXQJHFLNPHOLGH÷HULE\PHRUDQÕ]HULQGHHWNLOLGLU

5. Sonuç

Enflasyon YHE\PHRUDQODUÕVHULOHULQGHD\NÕUÕJ|]OHPRODUDNDGODQGÕUÕODQ oHúLWOL VL\DVL YH HNRQRPLN NUL] G|QHPOHUL\OH NDUúÕODúPDN NDoÕQÕOPD]GÕU $\NÕUÕ J|]OHPOHULQ YDUOÕ÷ÕQÕQ WDKPLQ YH oHúLWOL WHVW VUHoOHUL ]HULQGHNL HWNLOHUL J|]|QQH DOÕQGÕ÷ÕQGD \DEXD\NÕUÕ Jözlem etkilerini dikkate alan modelleme yapma yada bu D\NÕUÕJ|]OHPOHUGHQHWNLOHQPH\HQWDKPLQVUHoOHULLOHPRGHOOHPH\DSPDJHUHNOLOL÷L RUWD\D oÕNDU %XUDGD - \ÕOODUÕ DUDVÕQGDNL HQIODV\RQ YH E\PH RUDQODUÕ DUDVÕQGDNL LOLúNL LQFHOHQLUNHQ |QFH VHULOHU ]HULQGHNL D\NÕUÕ J|]OHPOHU WHVSLW HGLOPLúWLU6RQUDVÕQGD&URX[WDUDIÕQGDQ|QHULOHQD\NÕUÕJ|]OHPOHUGHQHWNLOHQPH\HQ GD\DQÕNOÕ 0/76 WDKPLQFLVL LOH 9$5 PRGHOL SDUHPHWUHOHUL WDKPLQ HGLOPLúWLU 'D\DQÕNOÕ WDKPLQ VRQXFXQD GD\DOÕ RODUDN GH÷HUOHQGLULOHQ LOLúNL (..¶\D GD\DOÕ RODUDN HOGH HGLOHQGHQ IDUNOÕGÕU (..¶\D GD\DOÕ RODUDN HOGH HGLOHQ VRQXFD J|UH E\PH RUDQÕ YH HQIODV\RQ DUDVÕQGD LOLúNL \RNWXU IDNDW 0/76¶\H GD\DOÕ WDKPLQ VRQXoODUÕ HQIODV\RQXQ JHFLNPHOL GH÷HUL LOH E\PH RUDQÕ DUDVÕQGD LOLúNL\H GLNNDW çekmektedir.

(13)

6. Kaynakça

AGULLO, Jose, Christophe CROUX, Stefan VAN AELST: “The Multivariate Least-Trimmed Squares Estimator”, Journal of Multivariate Analysis, Vol. 99, 2008, s.311-318.

BALKE, N. S., T. S. FOMBY: “Large Shocks, Small Shocks, and Economic Fluctuations: Outliers in Macroeconomic Time Series”, Journal of Applied Econometrics, 9, 1994, s.181–200.

%(5%(5 0HWLQ 6H\IHWWLQ $57$1 ³(QIODV\RQ YH (NRQRPLN %\PH øOLúNLVL 7UNL\H gUQH÷L ´ Turkish Economic Association, Discussion Paper, 2004-21

CHANG, I, G. TIAO, C.CHEN: “Estimation Of Time Series Parameters In The Presence Of Outliers”, Technometrics, 30, 1988, s. 193–204.

CHEN, C., L. M. LIU: “Forecasting Time Series With Outliers”, Journal Of Forecasting, 12, 1993, s.13–35.

CROUX, C, A. RUIZ-GAZEN: “High Breakdown Estimators for Principal Components: The Projection-Pursuit Approach Revisited”, Journal of Multivariate Analysis.,95, 2005, s. 206-226.

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FRANSES, Philip,H., 'LFN 9$1 'ø-. Non-Linear Time Series Models in Empirical Finance, Cambridge University Press, 2002.

3(1$ 'DQLHO *HRUJH 7ø$2 5XH\ 76$< A Course in Time Series Analysis, New York, Wiley, 2001.

REBER, John C., Jeff T. TERPSTRA, Xianzhe CHEN: “Weighted L1-estimates for a VAR(p) Time Series Model”, Journal of Nonparametric Statistics, 20, 5, 2008, s.395–411.

RICARDO, A., R. MARONNA, M.DOUGLAS, Y. J. VICTOR: Robust Statistics, New York, John Wiley & Sons, 2006.

ROUSSEEUW, P.J., A. M. LEROY: Robust Regression and Outlier Detection, New York, Wiley, 1987.

WILLIAM, Wei: Time Series Analysis: Univariate and Multivariate Methods, 2.Bs, USA, Pearson Addison Wesley, 2006.

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