Path Signature Area-Based Causal Discovery in Coupled Time Series

TL;DR

This paper introduces a novel data-driven method using path signatures and signed areas, combined with confidence sequences, to identify causal relationships in coupled time series without relying on domain-specific models.

Contribution

It proposes a new approach for causal discovery in dynamical systems using path signatures and confidence sequences, enabling model-free analysis of causality from observational data.

Findings

Path signatures effectively capture causal influence in time series.

Confidence sequences help determine the significance of causal links.

Method can identify lag/lead causal relationships in coupled systems.

Abstract

Coupled dynamical systems are frequently observed in nature, but often not well understood in terms of their causal structure without additional domain knowledge about the system. Especially when analyzing observational time series data of dynamical systems where it is not possible to conduct controlled experiments, for example time series of climate variables, it can be challenging to determine how features causally influence each other. There are many techniques available to recover causal relationships from data, such as Granger causality, convergent cross mapping, and causal graph structure learning approaches such as PCMCI. Path signatures and their associated signed areas provide a new way to approach the analysis of causally linked dynamical systems, particularly in informing a model-free, data-driven approach to algorithmic causal discovery. With this paper, we explore the use of path signatures in causal discovery and propose the application of confidence sequences to analyze the significance of the magnitude of the signed area between two variables. These confidence sequence regions converge with greater sampling length, and in conjunction with analyzing pairwise signed areas across time-shifted versions of the time series, can help identify the presence of lag/lead causal relationships. This approach provides a new way to define the confidence of a causal link existing between two time series, and ultimately may provide a framework for hypothesis testing to define whether one time series causes another