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Higher-Order Improvements of the Sieve Bootstrap for Fractionally Integrated Processes

Donald Poskitt, Simone D. Grose () and Gael Martin

No 25/13, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

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 approach, 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. Most importantly, the sieve bootstrap is shown to reproduce the (empirically infeasible) Edgeworth expansion of the sampling distribution of the autocorrelation coefficients, in the part of the parameter space in which the expansion is valid.

Keywords: Long memory; ARFIMA; sieve bootstrap; bootstrap-based inference; Edgeworth expansion; sampling distribution. (search for similar items in EconPapers)
Date: 2013
New Economics Papers: this item is included in nep-ets
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Citations: View citations in EconPapers (4)

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Related works:
Journal Article: Higher-order improvements of the sieve bootstrap for fractionally integrated processes (2015) Downloads
Working Paper: Higher Order Improvements of the Sieve Bootstrap for Fractionally Integrated Processes (2012) Downloads
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