A Semiparametric Estimator for Long-Range Dependent Multivariate Processes

TL;DR

This paper introduces a generalized semiparametric estimator for long-range dependent multivariate processes, extending existing methods by modifying the spectral density estimation and analyzing its properties without Gaussian assumptions.

Contribution

It proposes a new variant of Gaussian Semiparametric Estimators for multivariate long-range dependence, applicable to VARFIMA models, with theoretical analysis and empirical validation.

Findings

Estimator performs well in finite samples

Supports hypothesis testing for long-range dependence

Empirical application to exchange rate data demonstrates usefulness

Abstract

In this paper we propose a generalization of a class of Gaussian Semiparametric Estimators (GSE) of the fractional differencing parameter for long-range dependent multivariate time series. We generalize a known GSE-type estimator by introducing some modifications at the objective function level regarding the process' spectral density matrix estimator. We study large sample properties of the estimator without assuming Gaussianity as well as hypothesis testing. The class of models considered here satisfies simple conditions on the spectral density function, restricted to a small neighborhood of the zero frequency. This includes, but is not limited to, the class of VARFIMA models. A simulation study to assess the finite sample properties of the proposed estimator is presented and supports its competitiveness. We also present an empirical application to an exchange rate data.