Causal inference for temporal patterns

TL;DR

This paper introduces a systematic method to analyze causal relationships in complex dynamical systems by combining time-series representations with causal inference, especially focusing on frequency domain analysis and temporal impulse-response patterns.

Contribution

It proposes a novel framework that integrates time-series transforms with causal inference, including causal effects in the frequency domain and the development of Causal Orthogonal Functions (COF).

Findings

Framework effectively studies causal effects in the frequency domain.

COF provides a new way to represent how one process influences another over time.

Comparison with Granger Causality highlights advantages of the proposed approach.

Abstract

Complex dynamical systems are prevalent in many scientific disciplines. In the analysis of such systems two aspects are of particular interest: 1) the temporal patterns along which they evolve and 2) the underlying causal mechanisms. Time-series representations like discrete Fourier and wavelet transforms have been widely applied in order to obtain insights on the temporal structure of complex dynamical systems. Questions of cause and effect can be formalized in the causal inference framework. We propose an elementary and systematic approach to combine time-series representations with causal inference. Our method is based on a notion of causal effects from a cause on an effect process with respect to a pair of temporal patterns. In particular, our framework can be used to study causal effects in the frequency domain. We will see how our approach compares to the well known Granger Causality in the frequency domain. Furthermore, using a singular value decomposition we establish a representation of how one process drives another over a time-window of specified length in terms of temporal impulse-response patterns. To these we will refer to as Causal Orthogonal Functions (COF), a causal analogue of the temporal patterns derived with covariance-based multivariate Singular Spectrum Analysis (mSSA).