Browse > Article

Estimation of nonlinear GARCH-M model  

Shim, Joo-Yong (Department of Applied Statistics, Catholic University of Daegu)
Lee, Jang-Taek (Department of Statistics, Dankook University)
Publication Information
Journal of the Korean Data and Information Science Society / v.21, no.5, 2010 , pp. 831-839 More about this Journal
Abstract
Least squares support vector machine (LS-SVM) is a kernel trick gaining a lot of popularities in the regression and classification problems. We use LS-SVM to propose a iterative algorithm for a nonlinear generalized autoregressive conditional heteroscedasticity model in the mean (GARCH-M) model to estimate the mean and the conditional volatility of stock market returns. The proposed method combines a weighted LS-SVM for the mean and unweighted LS-SVM for the conditional volatility. In this paper, we show that nonlinear GARCH-M models have a higher performance than the linear GARCH model and the linear GARCH-M model via real data estimations.
Keywords
Generalized autoregressive conditional heteroscedasticity model; generalized autoregressive conditional heteroscedasticity model in the mean model; generalized cross validation; least squares support vector machine; weighted least squares support vector machine;
Citations & Related Records
Times Cited By KSCI : 4  (Citation Analysis)
연도 인용수 순위
1 Najand, M. and Yung, K. (1991). A GARCH examination of the relationship between volume and price variability in futures markets. The Journal of Futures Markets, 11, 613-621.   DOI
2 Perez Cruz, F., Afonso Rodriguez, J. A. and Giner, J. (2003). Estimating GARCH models using support vector machines. Quantitative Finance, 3, 163-172.   DOI   ScienceOn
3 Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31, 307-327.   DOI   ScienceOn
4 Domowitz, I. and Hakkio, C. S. (1985). Conditional variance and the riskpremium in the foreign exchange market. Journal of International Economics, 18, 47-66.
5 Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50, 987-1007.   DOI   ScienceOn
6 Hwang, C. (2007). Kernel machine for Poisson regression. Journal of Korean Data & Information Science Society, 18, 767-772.   과학기술학회마을
7 Hwang, C. and Shin, S. (2010). Estimating GARCH models using kernel machine learning. Journal of Korean Data & Information Science Society, 21, 419-425.   과학기술학회마을
8 Kimeldorf, G. S. and Wahba, G. (1971). Some results on Tchebycheffian spline functions. Journal of Mathematical Analysis and its Applications, 33, 82-95.   DOI
9 Kuhn, H. W. and Tucker, A. W. (1951). Nonlinear programming. Proceedings of 2nd Berkeley Symposium, University of California Press, Berkeley, 481-492.
10 Suykens, J. A. K., De Brabanter, J., Lukas, L. and Vandewalle, J. (2002). Weighted least squares support vector machines: Robustness and sparse approximation. Neurocomputing, 66, 85-105
11 Vapnik, V. N. (1998). Statistical Learning Theory, John Wiley, New York.
12 Shim, J. and Hwang, C. (2003). Prediction intervals for LS-SVM regression using the bootstrap. Journal of Korean Data & Information Science Society, 14, 337-343.   과학기술학회마을
13 Mercer, J. (1909). Function of positive and negative type and their connection with theory of integral equations. Philosophical Transactions of Royal Society, A, 415-446.
14 Shim, J. and Lee, J. T. (2009). Kernel method for autoregressive data. Journal of Korean Data & Information Science Society, 20, 467-472.   과학기술학회마을
15 Suykens, J. A. K. and Vanderwalle, J. (1999). Least square support vector machine classifier. Neural Processing Letters, 9, 293-300.   DOI   ScienceOn