A Generalization of a Gaussian Semiparametric Estimator on Multivariate Long-Range Dependent Processes

TL;DR

This paper introduces a broad class of Gaussian Semiparametric Estimators for multivariate long-range dependent processes, establishing their large sample properties and demonstrating their effectiveness through simulations.

Contribution

It generalizes existing GSE methods to a wider class of processes, including VARFIMA, without requiring Gaussianity, and analyzes their asymptotic behavior.

Findings

Estimator performs well in large samples

Supports VARFIMA process modeling

Simulation confirms estimator's competitiveness

Abstract

In this paper we propose and study a general class of Gaussian Semiparametric Estimators (GSE) of the fractional differencing parameter in the context of long-range dependent multivariate time series. We establish large sample properties of the estimator without assuming Gaussianity. The class of models considered here satisfies simple conditions on the spectral density function, restricted to a small neighborhood of the zero frequency and includes important class of VARFIMA processes. We also present a simulation study to assess the finite sample properties of the proposed estimator based on a smoothed version of the GSE which supports its competitiveness.