Misspecification tests for periodic long memory GARCH models

Distributional theory for Quasi-Maximum Likelihood estimators in long memory conditional heteroskedastic models is not formally defined, even asymptotically. Because of that, this paper analyses the real size and power of the likelihood ratio and the Lagrange multiplier misspecification tests when periodic long memory GARCH models are involved. The performance of these tests is studied by means of Monte Carlo simulations with respect to the class of generalized long memory GARCH models. For this class of models, analytical derivatives are developed. An application to the USD/JPY exchange rate is also provided.