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

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.