Misspecification Tests for Periodic Long Memory GARCH Models

Abstract

Distributional theory for Quasi-Maximum Likelihood estimators in long memory conditional heteroskedastic models is not formally defined, even asymptotically. Because of that, this paper analyzes the performance of the Likelihood Ratio and the Lagrange Multiplier misspecification tests for Periodic Long Memory GARCH models. The real size and power of these tests are studied by means of Monte Carlo simulations with respect to the class of Generalized Long Memory GARCH models. An application to the USD/JPY exchange rate is also provided.

Keywords: Long Memory, Generalized Long Memory GARCH models, PLM- GARCH models, misspecification tests