Comparison of Specification Tests for GARCH Models

In this paper, using simulations, we compare specification procedures for testing the null hypothesis of a Gaussian distribution for the innovations of GARCH models. More precisely, Cramer-von Mises and Kolmogorov-Smirnov type statistics are computed for empirical processes based on the standardized residuals and their squares. For computing P-values, we use the parametric bootstrap method and the multipliers method. We also use the so-called Khmaladze's transform to obtain an approximated Brownian motion under the null hypothesis, for which we compute also Cramer-von Mises and Kolmogorov-Smirnov type statistics, using both the standardized residuals and their squares