  This article considers multivariate linear processes whose components are
either short- or long-range dependent. The functional central limit theorems
for the sample mean and the sample autocovariances for these processes are
investigated, paying special attention to the mixed cases of short- and
long-range dependent series. The resulting limit processes can involve
multivariate Brownian motion marginals, operator fractional Brownian motions
and matrix-valued versions of the so-called Rosenblatt process.
