Nadarajah, K., Martin, G.M. and Poskitt, D.S. (2021) Optimal bias correction of the log-periodogram estimator of the fractional parameter: a jackknife approach. Journal of Statistical Planning and Inference, 211. pp. 41-79. ISSN 0378-3758
Abstract
We use the jackknife to bias correct the log-periodogram regression (LPR) estimator of the fractional parameter in a stationary fractionally integrated model. The weights for the jackknife estimator are chosen in such a way that bias reduction is achieved without the usual increase in asymptotic variance, with the estimator viewed as ‘optimal’ in this sense. The theoretical results are valid under both the non-overlapping and moving-block sub-sampling schemes that can be used in the jackknife technique, and do not require the assumption of Gaussianity for the data generating process. A Monte Carlo study explores the finite sample performance of different versions of the jackknife estimator, under a variety of scenarios. The simulation experiments reveal that when the weights are constructed using the parameter values of the true data generating process, a version of the optimal jackknife estimator almost always out-performs alternative semi-parametric bias-corrected estimators. A feasible version of the jackknife estimator, in which the weights are constructed using estimates of the unknown parameters, whilst not dominant overall, is still the least biased estimator in some cases. Even when misspecified short run dynamics are assumed in the construction of the weights, the feasible jackknife estimator still shows significant reduction in bias under certain designs. As is not surprising, parametric maximum likelihood estimation out-performs all semi-parametric methods when the true values of the short memory parameters are known, but is dominated by the semi-parametric methods (in terms of bias) when the short memory parameters need to be estimated, and in particular when the model is misspecified.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020 Elsevier B.V. This is an author produced version of a paper subsequently published in Journal of Statistical Planning and Inference. Uploaded in accordance with the publisher's self-archiving policy. Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/). |
Keywords: | Long memory; bias adjustment; cumulants; discrete Fourier transform; periodograms; log-periodogram regression |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Social Sciences (Sheffield) > Department of Economics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 02 Apr 2020 10:29 |
Last Modified: | 11 May 2021 00:38 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.jspi.2020.04.010 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:159002 |