Consistent model specification tests for time series econometric models

In this paper we consider general hypothesis testing problems for nonparametric and semiparametric time-series econometric models. We apply the general methodology to construct a consistent test for omitted variables and a consistent test for a partially linear model. The proposed tests are shown to have asymptotic normal distributions under their respective null hypotheses. We also discuss the problems of testing portfolio conditional mean-variance efficiency and testing a semiparametric single index model. Monte Carlo simulations are conducted to examine the finite sample performances of the nonparametric omitted variable test and the test for a partially linear specification.