A Generalized Block Bootstrap for Seasonal Time Series

Abstract

When time‐series data contain a periodic/seasonal component, the usual block bootstrap procedures are not directly applicable. We propose a modification of the block bootstrap – the generalized seasonal block bootstrap (GSBB) – and show its asymptotic consistency without undue restrictions on the relative size of the period and block size. Notably, it is exactly such restrictions that limit the applicability of other proposals of block bootstrap methods for time series with periodicities. The finite‐sample performance of the GSBB is also illustrated by means of a small simulation experiment.

Keywords: Periodic time series, resampling, seasonality