Higher-order improvements of the sieve bootstrap for fractionally integrated processes

Donald Poskitt, Simone D. Grose and Gael M. Martin

Journal of Econometrics, 2015, vol. 188, issue 1, 94-110

Abstract: This paper investigates the accuracy of bootstrap-based inference in the case of long memory fractionally integrated processes. The re-sampling method is based on the semi-parametric sieve, whereby the dynamics in the process used to produce the bootstrap draws are captured by an autoregressive approximation. Application of the sieve method to data pre-filtered by a semi-parametric estimate of the long memory parameter is also explored. Higher-order improvements yielded by both forms of re-sampling are demonstrated using Edgeworth expansions for a broad class of statistics that includes first- and second-order moments, the discrete Fourier transform and regression coefficients. The methods are then applied to the problem of estimating the sampling distributions of the sample mean and of selected sample autocorrelation coefficients, in experimental settings. In the case of the sample mean, the pre-filtered version of the bootstrap is shown to avoid the distinct underestimation of the sampling variance of the mean which the raw sieve method demonstrates in finite samples, higher-order accuracy of the latter notwithstanding. Pre-filtering also produces gains in terms of the accuracy with which the sampling distributions of the sample autocorrelations are reproduced, most notably in the part of the parameter space in which asymptotic normality does not obtain.

Keywords: Long memory; ARFIMA; Sieve bootstrap; Bootstrap-based inference; Edgeworth expansion; Sampling distribution (search for similar items in EconPapers)
JEL-codes: C18 C22 C52 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Related works:
Working Paper: Higher-Order Improvements of the Sieve Bootstrap for Fractionally Integrated Processes (2013)
Working Paper: Higher Order Improvements of the Sieve Bootstrap for Fractionally Integrated Processes (2012)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:188:y:2015:i:1:p:94-110

DOI: 10.1016/j.jeconom.2015.03.045

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