Semiparametric non-linear time series model selection

Summary.  Semiparametric time series regression is often used without checking its suitability, resulting in an unnecessarily complicated model. In practice, one may encounter computational difficulties caused by the curse of dimensionality. The paper suggests that to provide more precise predictions we need to choose the most significant regressors for both the parametric and the nonparametric time series components. We develop a novel cross-validation-based model selection procedure for the simultaneous choice of both the parametric and the nonparametric time series components, and we establish some asymptotic properties of the model selection procedure proposed. In addition, we demonstrate how to implement it by using both simulated and real examples. Our empirical studies show that the procedure works well.