Data-Driven Bandwidth Selection for Nonstationary Semiparametric Models

This article extends the asymptotic results of the traditional least squares cross-validatory (CV) bandwidth selection method to semiparametric regression models with nonstationary data. Two main findings are that (a) the CV-selected bandwidth is stochastic even asymptotically and (b) the selected bandwidth based on the local constant method converges to 0 at a different speed than that based on the local linear method. Both findings are in sharp contrast to existing results when working with weakly dependent or independent data. Monte Carlo simulations confirm our theoretical results and show that the automatic data-driven method works well.