Residual-based diagnostics for conditional heteroscedasticity models

Abstract: We examine the residual-based diagnostics for univariate and multivari-ate conditional heteroscedasticity models. The tests involve the parameter estimates of an autoregression with the squared standardised residuals and the cross products of the standardised residuals as dependent variables. Noting that the regression in-volves estimated regressors and the standard distribution theories of the ordinary least squares estimates do not apply, we derive the asymptotic variance of the regression estimates. Diagnostic statistics, which are asymptotically distributed as Â2; are con-structed. We conduct a Monte Carlo experiment to investigate the ¯nite sample proper-ties of the residual-based tests for both univariate and multivariate models. The results are favourable to the residual-based diagnostics compared to the portmanteau statistics used in the literature