This paper proposes a convenient and generally applicable diognostic m-test for checking the distributional specification of parametric conditional heteroscedasticity models for financial data such as customary student t GARCH model. The proposed test is based on the moments of probability integral transform of the innovations of the assumed model. Monte-carlo evidence indicates that our suggested test performs well both in terms of size and power.
Lejeune, B. (2002). A diagnostic m-test for distributional specification of parametric conditional heteroscedasticity models for financial data (CORE Discussion Papers 2002/24). https://hdl.handle.net/2078.5/128349