Bootstraps for Time Series

Abstract

We review and compare block, sieve and local bootstraps for time series and thereby illuminate theoretical aspects of the procedures as well as their performance on finite-sample data. Our view is selective with the intention of providing a new and fair picture of some particular aspects of bootstrapping time series.

The generality of the block bootstrap is contrasted with sieve bootstraps. We discuss implementational advantages and disadvantages. We argue that two types of sieve often outperform the block method, each of them in its own important niche, namely linear and categorical processes. Local bootstraps, designed for nonparametric smoothing problems, are easy to use and implement but exhibit in some cases low performance.