  Let W be an integrable positive Hermitian q x q -matrix valued function on
the dual group of a discrete abelian group G such that W^{-1} is integrable.
Generalizing results of T. Nakazi and of A. G. Miamee and M. Pourahmadi for q=1
we establish a correspondence between trigonometric approximation problems in
L^2(W) and certain approximation problems in L^2(W^{-1}). The result is applied
to prediction problems for q-variate stationary processes over G, in
particular, to the case where G is the group of integers Z.
