On Vector ARMA Models Consistent with a Finite Matrix Covariance Sequence

TL;DR

This paper addresses the problem of matching covariance sequences with Vector ARMA models, establishing the existence of solutions through topological degree theory, which advances understanding of model fitting in multivariate time series.

Contribution

It introduces a novel formulation of the VARMA covariance matching problem and proves the existence of solutions using differential topology methods.

Findings

Existence of VARMA models matching given covariance sequences

Application of degree theory to establish solution existence

Theoretical foundation for covariance matching in multivariate models

Abstract

We formulate the so called "VARMA covariance matching problem" and demonstrate the existence of a solution using the degree theory from differential topology.