Asymptotic Normality of the Encompassing Test Associated to the linear Parametric Modelling and the Kernel Method for α-Mixing Processes

Abstract

This paper contributes on model selection between parametric and nonparametric methods through the use of encompassing test. We provide asymptotic normality of encompassing statistic associated to the encompassing hypothesis for parametric and nonparametric regression methods. We develop various results on this test for more general processes satisfying several dependence structures.