Diagnostics for GARCH-Type Models under Symmetric and Asymmetric Errors

Abstract

In this paper, the size and power of Ljung-Box and Li-Mak diagnostic tests for univariate autoregressive conditional heteroscedastic models were studied under both symmetric and asymmetric distributions for errors. Monte Carlo simulations with 1000 independent replications are conducted to generate conditional variances with standard normal, Students-t and Skewed-t distributions. It was found that though the Li-Mak test has higher empirical size than the nominal size of 5% but can be considered a better alternative to the Ljung-Box test in case of asymmetric errors. The empirical power of the Li-Mak test was also found slightly better for asymmetric heavy-tailed data.