Diagnostic test for GARCH models based on absolute residual autocorrelations

In this paper the asymptotic distribution of the absolute residual autocorrelations from generalized autoregressive conditional heteroscedastic (garch) models is derived. the correct asymptotic standard errors for the absolute residual autocorrelations are also obtained and based on these results,a diagnostic test for checking the adequacy of garch-type models are developed. our results do not depend on the existence of higher moments and is therefore robust under heavy-tailed distributions.