Properties of the Sieve Bootstrap for Fractionally Integrated and Non-Invertible Processes

In this article, we 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 for |d|<1/2 and it is shown that when the sieve bootstrap is used to approximate the distribution of a general class of statistics then the error rate will be of an order smaller than , &bgr;>0. Practical implementation of the sieve bootstrap is considered and the results are illustrated using a canonical example. Copyright 2007 The Author