Relationship between Granger non-causality and graph structure of state-space representations

TL;DR

This paper explores the connection between Granger non-causality and the structure of state-space models, providing conditions for minimal representations that reveal causal relationships in multivariate time series.

Contribution

It introduces an equivalent form of Granger non-causality in state-space models and offers necessary and sufficient conditions for minimal coordinated representations.

Findings

Established an equivalent form of Granger non-causality in state-space models

Provided conditions for minimal coordinated state-space representations

Enhanced understanding of causal structure in multivariate processes

Abstract

In this paper we present an equivalent form of Granger noncausality in state space representation. As a generalization of this result, necessary and sufficient conditions are provided for an output process to admit a particular minimal coordinated state space representation.