Optimal choice of bootstrap block length for periodically correlated time series

Abstract

This paper discusses the problem of choosing the optimal block length for two block bootstrap methods designed for periodically correlated processes. These are the Generalized Seasonal Block Bootstrap and the Extension of Moving Block Bootstrap. Two estimation problems are considered: the overall mean and the seasonal means. In both cases, the optimal block length is obtained by minimizing the mean squared error of the corresponding bootstrap variance estimator and in all cases it is proportional to the cube root of the sample size and should be a multiple of the period length plus one observation to avoid some bias. Finally, the results of the performed simulation are presented, in which optimal blocks lengths are estimated for several periodically correlated time series.