Generalized empirical likelihood M testing for semiparametric models with time series data

The problem of testing for the correct specification of semiparametric models with time series data is considered. Two general classes of M test statistics that are based on the generalized empirical likelihood method are proposed. A test for omitted covariates in a semiparametric time series regression model is then used to showcase the results. Monte Carlo experiments show that the tests have reasonable size and power properties in finite samples. An application to the demand of electricity in Ontario (Canada) illustrates their usefulness in practice.