Application and Diagnostic Checking of Univariate and Multivariate GARCH Models in Serbian Financial Market

The goal of this article is to give theoretical and empirical review for diagnostic checking of multivariate volatility processes. In theoretical part we presented three categories diagnostics for conditional heteroscedasticity models: portmanteau tests of the Ljung-Box type, residual-based diagnostics (RB) and Lagrange Multiplier (LM) tests. In our empirical analysis we used the Ljung-Box statistics (Q-test) of standardized residuals, those of its squared, as well as of the cross product of standardized residuals to check the model adequacy. Our results showed that the residual-based diagnostics provide a useful check for model adequacy. Overall result is that models perform statistically well.