Nonparametric and semiparametric regression model selection

It is known that semiparametric time series regression is often used without checking its suitability and compactness. In theory, this may result in dealing with an unnecessarily complicated model. In practice, one may encounter the computational difficulty caused by the spareness of the data. This is partly because the curse of dimensionality problem may still arise from using a semiparametric time series regression model. This paper suggests that in order to provide more precise predictions we need to choose the most significant regressors for both the parametric and nonparametric time series components. We develop a novel cross-validation based model selection procedure for the choice of both the parametric and nonparametric time series components in semiparametric time series regression, and then establish some asymptotic properties of the proposed model selection procedure. In addition, we demonstrate how to implement the model selection procedure in practice through using both simulated and real examples. Our empirical studies show that the proposed cross-validation selection procedure works well numerically.