Bandwidth selection for kernel regression with long-range dependent errors

Abstract

We investigate the effect of long-range dependence on bandwidth selection for kernel regression with the plug-in method of Herrmann, Gasser & Kneip (1992). A new bandwidth estimator is proposed to allow for long-range dependence. Properties of the proposed estimator are investigated theoretically and via simulation. We find that the proposed estimator performs well in terms of integrated squared error of the estimated trend, allowing us to incorporate both deterministic nonlinear features having an unknown structure and long-range dependence into a single model. The method is illustrated using biweekly measurements of the volume of the Great Salt Lake.