Diagnostics for conditional heteroscedasticity models: some simulation results

In this paper, we study the size and power of various diagnostic statistics for univariate conditional heteroscedasticity models. These test statistics include the residual-based tests recently derived by Tse, Li and Mak, and Wooldridge, respectively. Monte-Carlo experiments with 1000 replications are conducted to generate conditional variances which follow the autoregressive conditional heteroscedasticity (ARCH)/GARCH processes. We use quasi-maximum likelihood estimation (MLE) method to obtain estimates of parameters under different ARCH/ generalized ARCH (GARCH) models. It is found that the Tse and Li–Mak diagnostics are more powerful.