Bias Correction of Semiparametric Long Memory Parameter Estimators via the Pre-filtered Sieve Bootstrap

TL;DR

This paper introduces a bootstrap-based bias correction method for semiparametric estimators of the long memory parameter in fractionally integrated processes, providing theoretical justification and demonstrating improved bias reduction through simulations.

Contribution

It proposes a novel pre-filtered sieve bootstrap approach for bias correction of long memory estimators, with theoretical validation and empirical performance comparison.

Findings

Bootstrap bias correction reduces estimator bias significantly.

The method achieves correct asymptotic coverage for confidence intervals.

It outperforms analytical bias correction techniques in simulations.

Abstract

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 pre-filtered 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 $0\leq d<0.5$. 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.