Predicting the volatility of the S&P-500 stock index via GARCH models: the role of asymmetries

In this paper, we examine the relative out of sample predictive ability of different GARCH models, with particular emphasis on the predictive content of the asymmetric component. First, we perforin pairwise comparisons of various models against the GARCH(l, 1) model. For the case of nonnested models, this is accomplished by constructing the [Diebold, FX, & Mariano, R.S. 1995. Comparing predictive accuracy. Journal of Business and Economic Statistics, 13, 253-263 test statistic]. For the case of nested models, this is accomplished via the out of sample encompassing tests of [Clark, T.E., & McCracken, M.W., 2001. Tests for equal forecast accuracy and encompassing for nested models. Journal of Econometrics, 105, 85-110]. Finally, a joint comparison of all models against the GARCH(l, 1) model is performed along the lines of the reality check of [White, H., 2000, A reality check for data snooping. Econometrica, 68, 1097-1126]. Our findings can be summarized as follows: for the case of one-step ahead pairwise comparison, the GARCH(l, I) is beaten by the asymmetric GARCH models. The same finding applies to different longer forecast horizons, although the predictive superiority of asymmetric models is not as striking as in the one-step ahead case. In the multiple comparison case, the GARCH(l, 1) model is beaten when compared against the class of asymmetric GARCH, while it is not beaten when compared against other GARCH models that do not allow for asymmetries. (C) 2004 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.