Abstract
Abstract. 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 , β>0. Practical implementation of the sieve bootstrap is considered and the results are illustrated using a canonical example.
Highlights
It is well known that, under a variety of conditions that hold in many econometric applications, improvements in the accuracy of first order large sample approximations can be obtained using bootstrap techniques. Such improvements require that the bootstrap re-sampling be conducted in such a way as to capture the essential features of the data generating process and in the context of time series analysis there are two basic methods that can be employed, the block bootstrap (Kunsch, 1989) and the sieve bootstrap (Buhlmann, 1997)
The error in the coverage probability of a one sided confidence interval is O(T −3/4) for the block bootstrap, for example, compared to the O(T −1) rate achieved with simple random samples, where here, as in what follows, T is used to denote sample size
The relatively poor performance of the block bootstrap has lead to the search for other ways to implement the bootstrap with dependent data and to the development of adaptations designed to increase the asymptotic refinement of the block bootstrap, see the recent contributions of Horowitz (2003) and Andrews (2004) and the references contained therein, for example
Summary
It is well known that, under a variety of conditions that hold in many econometric applications, improvements in the accuracy of first order large sample approximations can be obtained using bootstrap techniques Such improvements require that the bootstrap re-sampling be conducted in such a way as to capture the essential features of the data generating process and in the context of time series analysis there are two basic methods that can be employed, the block bootstrap (Kunsch, 1989) and the sieve bootstrap (Buhlmann, 1997).
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