Cross-validatory bandwidth selections for regression estimation based on dependent data

We suggest a simple and fast method to determine the bandwidth in kernel regression. The method can be viewed as a generalized cross-validation. We have proved asymptotic optimality of the proposed bandwidth selector under the assumption that the observations are strictly stationary and rho-mixing. Simulation has been conducted to compare the performance of various cross-validation bandwidth selectors applied to dependent data, which shows that the ordinary cross-validation method is quite stable in regression estimation with random design even when the data are highly correlated.