Directed Redundancy in Time Series

TL;DR

This paper introduces a method to quantify and bound the redundant information transferred from relevant source processes to a target in time series, accounting for hidden redundancy mechanisms.

Contribution

It proposes a novel framework to identify and bound redundancy in time series by considering hidden processes that govern shared information among sources.

Findings

Redundancy can exist without direct information exchange between sources.

A hidden redundancy process can explain shared information among relevant sources.

Bounds on redundancy are established using minimal directed redundancy measures.

Abstract

We quantify the average amount of redundant information that is transferred from a subset of relevant random source processes to a target process. To identify the relevant source processes, we consider those that are connected to the target process and in addition share a certain proportion of the total information causally provided to the target. Even if the relevant processes have no directed information exchange between them, they can still causally provide redundant information to the target. This makes it difficult to identify the relevant processes. To solve this issue, we propose the existence of a hidden redundancy process that governs the shared information among the relevant processes. We bound the redundancy by the minimal average directed redundancy from the relevant processes to the target, from the hidden redundancy process to the target, and from the hidden redundancy process to the relevant processes.