Asymptotic properties of sieve bootstrap prediction intervals for FARIMA processes

The sieve bootstrap is a resampling technique that uses autoregressive approximations of order p to model invertible linear time series, where p is allowed to go to infinity with sample size n. The asymptotic properties of sieve bootstrap prediction intervals for stationary invertible linear processes with short memory have been established in the past. In this paper, we extend these results to long memory (FARIMA) processes. We show that under certain regularity conditions the sieve bootstrap provides consistent estimators of the conditional distribution of future values of FARIMA processes, given the observed data.