Properties of the Sieve Bootstrap for Fractionally Integrated and Non-Invertible Processes
D. S. Poskitt
In this paper we will investigate the consequences of applying
the sieve bootstrap under regularity conditions that are sufficiently general
to encompass both fractionally integrated and non-invertible processes. The
sieve bootstrap is obtained by approximating the data generating process by
an autoregression whose order h increases with the sample size T.
The sieve bootstrap may be particularly useful in the analysis of fractionally
integrated processes since the statistics of interest can often be non-pivotal
with distributions that depend on the fractional index d. The validity
of the sieve bootstrap is established and it is shown that when the sieve
bootstrap is used to approximate the distribution of a general class of statistics
admitting an Edgeworth expansion then the error rate achieved is of order
O(T β+d-1), for any β > 0. Practical
implementation of the sieve bootstrap is considered and the results are illustrated
using a canonical example.
