On bandwidth choice in nonparametric regression with both short- and long-range dependent errors

Abstract

We analyse methods based on the block bootstrap and leave out cross validation, for choosing the bandwidth in nonparametric regression when errors have an almost arbitrarily long range of dependence. A novel analytical device for modelling the dependence structure of errors is introduced. This allows a concise theoretical description of the way in which the range of dependence affects optimal bandwidth choice. It is shown that, provided block length or leave out number, respectively, are chosen appropriately, both techniques produce first order optimal bandwidths. Nevertheless, the block bootstrap has far better empirical properties, particularly under long range dependence