Sains Malaysiana 38(1): 109-118(2009)

Comparing the Accuracy of Density Forecasts

from Competing GARCH Models

(Perbandingan Ketepatan Ramalan Ketumpatan

Antara Model-Model GARCH)

Abu Hassan Shaari Mohd Nor*

School of Economics Studies, Faculty of Economics and Business

Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor

Malaysia

Ahmad Shamiri & Zaidi Isa

Faculty of Science and Technology, Universiti Kebangsaan Malaysia

43600 UKM Bangi, Selangor

Malaysia

Received:   20 January 2008 / Accepted:   12 May 2008

ABSTRACT

In this research we introduce an analyzing procedure using the Kullback-Leibler information criteria (KLIC) as a statistical tool to evaluate and compare the predictive abilities of possibly misspecified density forecast models. The main advantage of this statistical tool is that we use the censored likelihood functions to compute the tail minimum of the KLIC, to compare the performance of a density forecast models in the tails. Use of KLIC is practically attractive as well as convenient, given its equivalent of the widely used LR test. We include an illustrative simulation to compare a set of distributions, including symmetric and asymmetric distribution, and a family of GARCH volatility models. Our results on simulated data show that the choice of the conditional distribution appears to be a more dominant factor in determining the adequacy and accuracy (quality) of density forecasts than the choice of volatility model.

Keywords: Conditional distribution; density; forecast accuracy; GARCH; Kullback-Leibler information criteria

ABSTRAK

Kajian ini memperkenalkan prosedur kriteria maklumat Kullback-Leibler (KLIC) sebagai alat statistik untuk menilai dan membandingkan kemampuan model peramalan ketumpatan yang mengalami kesilapan spesifikasi.  Kelebihan utama kaedah ini ialah penggunaan fungsi kebolehjadian terpangkas untuk mendapatkan nilai hujung minimum KLIC  dan membandingkan prestasi peramalan ketumpatan tersebut. Penggunaan kaedah KLIC ini adalah sangat sesuai dan mudah serta mempunyai persamaan dengan ujian LR. Pendekatan simulasi untuk menjana data telah digunakan untuk membandingkan prestasi peramalan ketumpatan untuk berbagai-bagai-bagai jenis taburan termasuk taburan simetri, tidak simetri dan model-model daripada keluarga GARCH. Hasil analisis terhadap data simulasi menunjukkan bahawa pemilihan  jenis taburan bersyarat adalah faktor yang lebih dominan dalam menentukan ketepatan dan kualiti peramalan ketumpatan  berbanding dengan jenis model kemeruapan yang digunakan.

Kata kunci: Ketumpatan; ketepatan ramalan; GARCH; kriteria maklumat Kullback-Leibler; taburan bersyarat

REFERENCES/RUJUKAN

Bao, Y. Lee, T. H. & Saltoglu, B. 2006. Comparing density forecast models. Journal of Forecasting 26(3): 203-225.

Berkowitz, J. 2001. Testing density forecasts with applications to risk management. Journal of Business and Economic Statistics 19(4): 465-474.

Bollerslev, T. 1986. Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31(3): 307–327.

Corradi, V. & Swanson, N. R. 2004. Predictive density evaluation in the handbook of economic forecasting. Amsterdam: North Holland Press.

D'Agostino, R. B. & Stephens, M. A. 1986. Goodness-of-fit-techniques. New York: Marcel Dekker.

Dawid, A. P. 1984. Present position and potential developments: some personal views: statistical theory: The prequential approach. Journal of the Royal Statistical Society Series (A) 147(2): 278-292.

Diebold, F. X. Gunther, T. A. & Tay, A. S. 1998.  Evaluating density forecasts with applications to financial risk management. International Economic Review 39(4): 863-883.

Diebold, F. X. & Mariano, R. S. 1995. Comparing predictive accuracy. Journal of Business & Economic Statistics 13(3): 253-263.

Diebold, F. X. Tay, A. S. & Wallis, K. 1999. Evaluating density forecasts of inflation: the survey of professional forecasts. Oxford: Oxford University Press.

Fernández-Villaverde, J. & Rubio-Ramírez, J. 2004. Comparing dynamic equilibrium models to Ddata: a Bayesian approach. Journal of Econometrics 123(1): 153–187.

Granger, C. W. & Pesaran, M. H. 1996. A decision-theoretic approach to forecast evaluation. Cambridge: University of Cambridge Press.

Hamill, T. M. 2000. Interpretation of rank histograms for verifying ensemble forecasts. Monthly Weather Review 129(3): 550-560.

Hansen, P. R. 2001. An unbiased and powerful test for superior predictive ability. Working paper, Brown University.

Kullback, S. & Leibler, R. A. 1951. On information and sufficiency. The Annals of Mathematical Statistics 22(1): 79-86.

Li, F. & Tkacz, G. 2001. Evaluating linear and non-linear time-varying forecast-combination methods. Ottawa: Bank of Canada.

Noceti, P. Smith, J. & Hodges, S. 2003. An evaluation of tests of distributional forecasts. Journal of Forecasting 22(7): 447-455.

Poon, S. H. & Granger, C. W. 2003. Forecasting financial market volatility. Journal of Economic Literature 41(2): 478-539.

Rosenblatt, M. 1952. Remarks on a multivariate transformation. The Annals of Mathematical Statistics 23(3): 470-472.

Sarno, L. & Valente, G. 2004. Comparing the accuracy of density forecasts from competing models. Journal of Forecasting 23(8): 541-557.

Vuong, Q. H. 1989. Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica 57(2): 307-333.

West, K. D. 1996. Asymptotic inference about predictive ability. Econometrica 64(5): 1067-1084.

West, K. D. Edison, H. J. & Cho, D. 1993. A utility-based comparison of some models of exchange rate volatility. Journal of International Economics 35(1-2): 23–46.

White, H. 2000. A reality check for data snooping. Econometrica 68(5): 1097-1126.

*Pengarang untuk surat menyurat