A duality method in prediction theory of multivariate stationary sequences
Probability
2025-05-08 v1 Functional Analysis
Abstract
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.
Cite
@article{arxiv.math/0106056,
title = {A duality method in prediction theory of multivariate stationary sequences},
author = {Michael Frank and Lutz P. Klotz},
journal= {arXiv preprint arXiv:math/0106056},
year = {2025}
}