Bias Correction of Long-memory Estimator of Functional Time Series via the Prefiltered Sieve Bootstrap

2026-07-30

AI Summary

This study addresses the substantial bias that can afflict long-memory parameter estimation in the presence of strong short-range autocorrelation. To mitigate this issue, the authors propose a bias-correction approach that integrates pre-filtering with sieve bootstrap techniques. The method first obtains an initial estimate using a local polynomial Whittle estimator adapted for noisy observations, then refines this estimate and constructs confidence intervals via the sieve bootstrap. This two-stage procedure effectively reduces estimation bias induced by pronounced short-memory dynamics while delivering reliable interval inference. Simulation experiments demonstrate that the proposed method substantially outperforms conventional local Whittle and detrended fluctuation analysis approaches, achieving superior accuracy in bias correction and markedly improved coverage properties for confidence intervals.

Abstract

We investigate a bias correction procedure based on sieve bootstrapping to estimate the long-memory parameter d in stationary or nonstationary fractionally integrated processes. The resampling method implements a sieve bootstrap method on data prefiltered by a preliminary estimate of the long-memory parameter. For the initial estimate, we recommend the local polynomial Whittle with noise (LPWN) estimator in Frederiksen et al. (2012) to reduce bias, especially in the presence of a strong short-range autoregressive dependence. Through a series of simulation studies, we first highlight the issue of bias, using the local Whittle or detrended fluctuation analysis estimator. Then, we consider the LPWN estimator and show the potential improvement in bias achieved by its sieve bootstrap enhancement. As a byproduct, the sieve bootstrap can also provide confidence intervals of the memory parameter.

Problem

• bias correction
• long-memory parameter
• functional time series
• fractionally integrated processes
• sieve bootstrap

Innovation

• sieve bootstrap
• bias correction
• long-memory parameter
• prefiltering
• LPWN estimator