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BIAS CORRECTION OF SEMIPARAMETRIC LONG MEMORY PARAMETER ESTIMATORS VIA THE PREFILTERED SIEVE BOOTSTRAP

Published online by Cambridge University Press:  18 March 2016

D. S. Poskitt ,
Gael M. Martin  and
Simone D. Grose
D. S. Poskitt
Affiliation:
Monash University
Gael M. Martin*
Affiliation:
Monash University
Simone D. Grose
Affiliation:
Monash University
*
*Address correspondence to Gael Martin, Department of Econometrics and Business Statistics, Monash University, Victoria 3800, Australia; e-mail: gael.martin@monash.edu.
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Abstract

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This paper investigates bootstrap-based bias correction of semiparametric estimators of the long memory parameter, d, in fractionally integrated processes. The re-sampling method involves the application of the sieve bootstrap to data prefiltered by a preliminary semiparametric estimate of the long memory parameter. Theoretical justification for using the bootstrap technique to bias adjust log periodogram and semiparametric local Whittle estimators of the memory parameter is provided in the case where the true value of d lies in the range 0 ≤ d < 0.5. That the bootstrap method provides confidence intervals with the correct asymptotic coverage is also proven, with the intervals shown to adjust explicitly for bias, as estimated via the bootstrap. Simulation evidence comparing the performance of the bootstrap bias correction with analytical bias-correction techniques is presented. The bootstrap method is shown to produce notable bias reductions, in particular when applied to an estimator for which some degree of bias reduction has already been accomplished by analytical means.

Type
ARTICLES
Information
Econometric Theory , Volume 33 , Issue 3 , June 2017 , pp. 578 - 609
Copyright
Copyright © Cambridge University Press 2016 

Footnotes

This research has been supported by Australian Research Council (ARC) Discovery Grant DP120102344. The authors would like to thank the Editor, a co-editor and two referees for very detailed and constructive comments on earlier drafts of the paper.

References

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