An efficient estimator for locally stationary Gaussian long-memory processes

TL;DR

This paper introduces a new estimation method for locally stationary Gaussian long-memory processes, combining a time-varying model with Whittle likelihood, and demonstrates its strong theoretical properties and good finite-sample performance.

Contribution

It proposes a novel estimation approach for nonstationary long-memory processes using a time-varying parametric model and Whittle likelihood, with proven large sample properties.

Findings

Estimates are consistent, normal, and efficient asymptotically.

Finite sample simulations show good estimator performance.

Method effectively handles nonstationarity and long-range dependence.

Abstract

This paper addresses the estimation of locally stationary long-range dependent processes, a methodology that allows the statistical analysis of time series data exhibiting both nonstationarity and strong dependency. A time-varying parametric formulation of these models is introduced and a Whittle likelihood technique is proposed for estimating the parameters involved. Large sample properties of these Whittle estimates such as consistency, normality and efficiency are established in this work. Furthermore, the finite sample behavior of the estimators is investigated through Monte Carlo experiments. As a result from these simulations, we show that the estimates behave well even for relatively small sample sizes.