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Optimal Bias Correction of the Log-periodogram Estimator of the Fractional Parameter: A Jackknife Approach

Kanchana Nadarajah (), Gael Martin () and Donald Poskitt

No 7/19, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

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 Önite sample performance of di§erent versions of the optimal jackknife estimator under a variety of fractional data generating processes. The simulations reveal that when the weights are constructed using the true parameter values, a version of the optimal jackknife estimator almost always out-performs alternative bias-corrected estimators. A feasible version of the jackknife estimator, in which the weights are constructed using consistent estimators of the unknown parameters, whilst not dominant overall, is still the least biased estimator in some cases.

Keywords: Long memory; bias adjustment; cumulants; discrete Fourier transform; periodograms; log-periodogram regression. (search for similar items in EconPapers)
JEL-codes: C18 C22 C52 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
Date: 2019
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