Diagnostic analytics for a GARCH model under skew-normal distributions

In this paper, a generalized autoregressive conditional heteroskedasticity model under skew-normal distributions is studied. A maximum likelihood approach is taken and the parameters in the model are estimated based on the expectation-maximization algorithm. The statistical diagnostics is made through the local influence technique, with the normal curvature and diagnostics results established for the model under four perturbation schemes in identifying possible influential observations. A simulation study is conducted to evaluate the performance of our proposed method and a real-world application is presented as an illustrative example.