SIEVE BOOTSTRAP FOR TIME-SERIES

We study a bootstrap method which is based on the method of sieves. A linear process is approximated by a sequence of autoregressive process es of order p = p(n), where p(n) --> infinity, p(n)= o(n) as the sampl e size n --> infinity. For given data, we then estimate such an AR(p(n )) model and generate a bootstrap sample by resampling from the residu als. This sieve bootstrap enjoys a nice nonparametric property, being model-free within a class of linear processes. We show its consistency for a class of nonlinear estimators and compare the procedure with th e blockwise bootstrap, which has been proposed by Kunsch in 1989. In p articular, the sieve bootstrap variance of the mean is shown to have a better rate of convergence if the dependence between separated values of the underlying process decreases sufficiently fast with growing se paration. Finally, a simulation study helps to illustrate the advantag es and disadvantages of the sieve compared to the blockwise bootstrap.