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In this paper we propose a generalization of a class of GaussianSemiparametric Estimators (GSE) of the fractional differencing parameter forlong-range dependent multivariate time series. We generalize a known GSE-typeestimator by introducing some modifications at the objective function levelregarding the process' spectral density matrix estimator. We study large sampleproperties of the estimator without assuming Gaussianity as well as hypothesistesting. The class of models considered here satisfies simple conditions on thespectral density function, restricted to a small neighborhood of the zerofrequency. This includes, but is not limited to, the class of VARFIMA models. Asimulation study to assess the finite sample properties of the proposedestimator is presented and supports its competitiveness. We also present anempirical application to an exchange rate data.

A Semiparametric Estimator for Long-Range Dependent Multivariate Processes