Weak convergence of multivariate fractional processes

Weak convergence to a form of fractional Brownian motion is established for a wide class of nonstationary fractionally integrated multivariate processes. Instrumental for the main argument is a result of some independent interest on approximations for partial sums of stationary linear vector sequences. A functional central limit theorem for smoothed processes is established under more general assumptions. (C) 2000 Elsevier Science B.V. All rights reserved.