Mallows Distance in VARFIMA(0, d, 0) Processes

In this work we present an extensive simulation study on Mallows distance in the context of Gaussian and non-Gaussian VARFIMA processes. Our main goal is to analyze the dependence among the components of VARFIMA processes through the Mallows distance point of view. A possible relationship between the Mallows distance and the fractional differencing parameter d, the type and level of dependence in the innovation process as well as its marginal behavior is investigated. We study the behavior of the Kendall’s τ dependence coefficient under the same framework for comparison purposes. For the Mallows distance, we consider an estimator based on the empirical marginal distribution function. Based on our simulation results, we propose both a semiparametric estimator for the fractional differencing parameter and a testing procedure to assess the presence of strong long range dependence in the components of VARFIMA processes of any (finite) dimension.