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.