Comparison of specification tests for GARCH models

Specification procedures for testing the null hypothesis of a Gaussian distribution for the innovations of GARCH models are compared using simulations. More precisely, Cramér-von Mises and Kolmogorov-Smirnov type statistics are computed for empirical processes based on the standardized residuals and their squares. For calculating P-values, the parametric bootstrap method and the multipliers method are used. In addition, the Khmaladze transform is also applied to obtain an approximate Brownian motion under the null hypothesis, for which Cramér-von Mises and Kolmogorov-Smirnov type statistics are computed, using both the standardized residuals and their squares.