Abstract

We will discuss 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 will be 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. In addition, a second approach to obtaining the optimal block length using the jackknife variance estimator will be discussed. Finally, the results of the performed simulation will be presented, in which optimal block lengths were estimated for several periodically correlated time series.