Causality between time series

TL;DR

This paper introduces a rigorous, quantitative method based on information flow to determine causality between time series, validated on synthetic data and applied to climate phenomena like El Niño and Indian Ocean Dipole.

Contribution

It provides a concise, formulaic approach to measure causality in time series using statistical covariances, advancing the analysis of cause-effect relationships in various fields.

Findings

Validated with synthetic series showing one-way causality

Applied to climate data revealing causal links between El Niño and Indian Ocean Dipole

The measure is asymmetric and vanishes when no causality exists

Abstract

Given two time series, can one tell, in a rigorous and quantitative way, the cause and effect between them? Based on a recently rigorized physical notion namely information flow, we arrive at a concise formula and give this challenging question, which is of wide concern in different disciplines, a positive answer. Here causality is measured by the time rate of change of information flowing from one series, say, X2, to another, X1. The measure is asymmetric between the two parties and, particularly, if the process underlying X1 does not depend on X2, then the resulting causality from X2 to X1 vanishes. The formula is tight in form, involving only the commonly used statistics, sample covariances. It has been validated with touchstone series purportedly generated with one-way causality. It has also been applied to the investigation of real world problems; an example presented here is the cause-effect relation between two climate modes, El Ni\~no and Indian Ocean Dipole, which have been linked to the hazards in far flung regions of the globe, with important results that would otherwise be difficult, if not impossible, to obtain.