M-GARCH Modellerinin Karşılaştırmalı Analizi

Year 2009, Issue: 18, 126 - 145, 01.12.2009

Hilal Bozkurt

Abstract

Tek bir değişken için zamanla değişen varyans kavramını ele alan ARCH modeli, çok sayıda içeren modeller için genişletilmiştir. Bu modellerde en önemli problem, çok sayıda parametrenin tahmin ediliyor olmasıdır. Bu çalışma Diagonal VEC, Sabit Koşullu Korelasyon (CCC) ve Diagonal BEKK gibi M-GARCH modellerini, Frobenius, Eigenvalue ve Foerstner Metric gibi metrik uzaklık teknikleri açısından karşılaştırmaktadır. Diagonal VEC, benchmark olarak düşünülmüştür. Temel bulgu, Diagonal BEKK tahminlerinin CCC modeline göre benchmark modelinin sonuçlarına daha yakın sonuçlar verdiği yönündedir

Keywords

M-GARCH, metrik uzaklık

The Comparative Analysis Of M-GARCH Models

Abstract

The ARCH model in capturing time-varying variance of economic data in the
univariate case has been extended to the multivariate case. An important problem with
these models is the a large number of parameters that have to be estimated. This paper
compares different M-GARCH type models, namely The Diagonal VEC, Constant Conditional
Correlation (CCC) and Diagonal BEKK in terms of their matrix distance metrics. apply
three distance metrics, namely Frobenius, Eigenvalue ve Foerstner Metric. The Diagonal
VEC is considered as the bencmark. The main finding is that Diagonal BEKK estimation
gives more close results with the bencmark than CCC.

Keywords

M-GARCH, metric distance

References

• Alexander, C. (2001) “Orthogonal GARCH” in Mastering Risk Volume 2, FT Prentice Hall, pp. 21-38.
• Alexander, C. (2002) “Principal component Models for Generating Large GARCH Covariance Matrices”, Economic Notes, 31(2), pp. 337-359.
• Bauwens, L. (2003), “Multivariate GARCH models”, Université catholique de Louvain, yayınlanmamış ders notu http://zonecours.hec.ca/documents/A2004-1- 190733.mgarch-slides-LB-print.pdf (21.04.2004)
• Bollerslev, T., 1986. Generalised autoregressive conditional heteroscedasticity. Journal of Econometrics 31, 307–327.
• Bollerslev, T., 1990. Modelling the coherence in short-run nominal exchange rate: a multivariate generalized ARCH approach. Review of Economics and Statistics 72, 498–505.
• Bollerslev, T., Engle, R. F., Wooldridge, J. M. (1988). A capital asset p
• ricing model withtime varying covariance. Journal of Political Economy, 96, 116–131.
• Bollerslev, Tim, 1987. A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return. The Review of Economics and Statistics 23, 542-547.
• Burns, Patrick, 2005. Multivariate GARCH with only univariate estimation., March- 2005, 1-5.
• Chiang, Alpha, C.(1986), “Matematiksel İktisadın Temel Yöntemleri”,Çev:Ergun Kip, Muzaffer Sarımeşeli, Osman aydoğuş, Teori Yayınları, Ankara.
• Drost, Feike C. and Nijman, Theo E.1991. Temporal aggregation of GARCH processes”, Econometrica 61/4, 909-1027.
• Engle, R.F. and Sheppard, K. 2001. Therotical and empirical properties of dynamic conditional correlation multivariate GARCH. Discussion Paper, September 2001- 15.
• Engle, R.F., Kroner, K.F., 1995. Multivariate simultaneous generalized ARCH. Econometric Theory 11, 122–150.
• Engle, R.F., 1982. Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50, 987–1007.
• Engle, R.F. 2000. Dynamic conditional correlation –a simple class of multivarıate garch models. Discussion Paper, May, 09.
• Engle, R.F.,1983. Estimates of the variance of U.S. inflation based upon the ARCH model. Journal of Money, Credit and Banking 15, 286-301.
• Engle, R.F. (ed.)1995. ARCH. Selected Readings. Oxford University Pres, Oxford.
• Laurent, S. J.V.K. Rombouts, Annastiina Silvennoinen and Francesco Violante (2006), “Comparıng And Rankıng Covarıance Structures Of M-Garch Volatılıty Models”, Ox-Metrics News Programme, October 4, 2006, London.
• Li, W.K., McLeod, A.I. (1981). Distribution of the residual autocorrelations in multivariate ARMA time series models. Journal of the Royal Statistical Society. Series B (Methodological), 43,2, 231-239.
• Milhoj, Anders, 1987. A conditional variance model for daily deviations of an exchange rate. Journal of Business and Economic Statistics 5, 1, 99-103.
• Silvennoinen, A., Terasvista, T., 2008, Multivariate GARCH models. SSE/EFI Working Paper Series in Economics and Finance, 669.
• Tse, Y.K., Tsui, A.K.C., 2002.A multivariate generalized autoregressive conditional eteroscedasticity model with time-varying correlations. Journal of Business and Economic Statistics 20, 351–362.
• Tse, Y.K. 2000. A test for constant correlations in a multivariate GARCH model. Journal of Econometrics, 98, 107-127.
• Weide, Van Der R., 2002. GO-GARCH:A multivariate generalized orthogonal GARCH model. Journal of Applied Econometrics 17, 549-564.