Sieve bootstrap for time series

Abstract

We study a bootstrap method which is based on the method of sieves. A linear process is approximated by a sequence of autoregressive processes of order p=p(n), where p(n)→∞, p(n)=o(n) as the sample size n→∞. For given data, we then estimate such an AR(p(n)) model and generate a bootstrap sample by resampling from the residuals. This sieve bootstrap enjoys a nice nonparametric property, being model-free within a class of linear processes.