Locally stationary long memory estimation

TL;DR

This paper introduces a novel method for estimating a time-varying long-memory parameter in locally stationary processes using wavelet-based log-regression, supported by theoretical proofs and practical examples.

Contribution

It extends existing long-memory estimation techniques to accommodate time-varying parameters within a locally stationary framework.

Findings

Proves weak consistency of the estimator.

Establishes a central limit theorem for the estimator.

Demonstrates effectiveness through simulations and real data.

Abstract

There exists a wide literature on modelling strongly dependent time series using a longmemory parameter d, including more recent work on semiparametric wavelet estimation. As a generalization of these latter approaches, in this work we allow the long-memory parameter d to be varying over time. We embed our approach into the framework of locally stationary processes. We show weak consistency and a central limit theorem for our log-regression wavelet estimator of the time-dependent d in a Gaussian context. Both simulations and a real data example complete our work on providing a fairly general approach.