Block length selection in the bootstrap for time series

Abstract

The blockwise bootstrap is a modification of Efron's bootstrap designed to give correct results for dependent stationary observations. One drawback of the method is that it depends critically on a block length which has to be chosen by the user. Here we propose a fully data-driven method to select this block length. It is based on the equivalence of the blockwise bootstrap variance to a lag weight estimator of a spectral density at the origin. The relevant spectral density is the one of the process given by the influence function of the statistic to be bootstrapped. In this equivalence the block length is the inverse of the bandwidth. We thus apply a recently developed local bandwidth selection procedure to the time series given by the estimated influence function. Simulations show that this procedure gives good results in a wide range of situations.