  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.
