A duality method in prediction theory of multivariate stationary sequences

Details A duality method in prediction theory of multivariate stationary sequences A duality method in prediction theory of multivariate stationary sequences

2001-06-08

arxiv.org/abs/math/0106056v1

Math. Nachr. 244(2002), 64-77

Mathematics

Probability

Scientific paper

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.

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