Reconstructing regime-dependent causal relationships from observational time series

Abstract

Inferring causal relations from observational time series data is a key problem across science and engineering whenever experimental interventions are infeasible or unethical. Increasing data availability over the past decades has spurred the development of a plethora of causal discovery methods, each addressing particular challenges of this difficult task. In this paper we focus on an important challenge that is at the core of time series causal discovery: regime-dependent causal relations. Many dynamical systems feature transitions in time, depending on some, often persistent, unobserved background regime, and different regimes may exhibit different causal relations. Here, we assume a persistent and discrete regime variable leading to a finite number of regimes within which we may assume stationary causal relations. To allow for flexible linear and nonlinear, high-dimensional analysis settings, we utilize the constraint-based PCMCI causal discovery method, and combine it with a regime assigning linear optimisation, inspired by the regime learning in non-stationary Markov regression or clustering, to detect regime-dependent causal relations. Our method, Regime- PCMCI, is evaluated on a number of numerical experiments demonstrating that it can distinguish regimes with different causal directions, time lags, effects and sign of causal links, as well as changes in the variables autocorrelation. Further, Regime-PCMCI is employed to observations of El Niño Southern Oscillation and Indian rainfall, demonstrating skill also in real-world data sets.