Causal inference in a nonlinear system of multivariate time series is instrumental in disentangling the intricate web of relationships among variables, enabling us to make more accurate predictions and gain deeper insights into real-world complex systems. Causality methods typically identify the causal structure of a multivariate system by considering the cause-effect relationship of each pair of variables while ignoring the collective effect of a group of variables or interactions involving more than two-time series variables. In this work, we test model invariance by group-level interventions on the trained deep networks to infer causal direction in groups of variables, such as climate and ecosystem, brain networks, etc. Extensive testing with synthetic and real-world time series data shows a significant improvement of our method over other applied group causality methods and provides us insights into real-world time series. The code for our method can be found at: https://github.com/wasimahmadpk/gCause.

Time series data from real-world systems often display non-stationary behavior, indicating varying statistical characteristics over time. This inherent variability poses significant challenges in deciphering the underlying structural relationships within the data, particularly in correlation and causality analyses, model stability, etc. Recognizing distinct segments or regimes within multivariate time series data, characterized by relatively stable behavior and consistent statistical properties over extended periods, becomes crucial. In this study, we apply the regime identification (RegID) technique to multivariate time series, fundamentally designed to unveil locally stationary segments within data. The distinguishing features between regimes are identified using covariance matrices in a Riemannian space. We aim to highlight how regime identification contributes to improving the discovery of causal structures from multivariate non-stationary time series data. Our experiments, encompassing both synthetic and real-world datasets, highlight the effectiveness of regime-wise time series causal analysis. We validate our approach by first demonstrating improved causal structure discovery using synthetic data where the ground truth causal relationships are known. Subsequently, we apply this methodology to climate-ecosystem dataset, showcasing its applicability in real-world scenarios.

Highly sensitive laser strainmeters at Moxa Geodynamic Observatory (MGO) measure motions of the upper Earth's crust. Since the mountain overburden of the laser strainmeters installed in the gallery of the observatory is relatively low, the recorded time series are strongly influenced by local meteorological phenomena. To estimate the nonlinear effect of the meteorological variables on strain measurements in a non-stationary environment, advanced methods capable of learning the nonlinearity and discovering causal relationships in the non-stationary multivariate tectonic-climate time series are needed. Methods for causal inference generally perform well in identifying linear causal relationships but often struggle to retrieve complex nonlinear causal structures prevalent in real-world systems. This work presents a novel model invariance-based causal discovery (CDMI) method that utilizes deep networks to model nonlinearity in a multivariate time series system. We propose to use the theoretically well-established Knockoffs framework to generate in-distribution, uncorrelated copies of the original data as interventional variables and test the model invariance for causal discovery. To deal with the non-stationary behavior of the tectonic-climate time series recorded at the MGO, we propose a regime identification approach that we apply before causal analysis to generate segments of time series that possess locally consistent statistical properties. First, we evaluate our method on synthetically generated time series by comparing it to other causal analysis methods. We then investigate the hypothesized effect of meteorological variables on strain measurements. Our approach outperforms other causality methods and provides meaningful insights into tectonic-climate causal interactions.

Cause-effect analysis is crucial to understand the underlying mechanism of a system. We propose to exploit model invariance through interventions on the predictors to infer causality in nonlinear multivariate systems of time series. We model nonlinear interactions in time series using DeepAR and then expose the model to different environments using Knockoffs-based interventions to test model invariance. Knockoff samples are pairwise exchangeable, in-distribution and statistically null variables generated without knowing the response. We test model invariance where we show that the distribution of the response residual does not change significantly upon interventions on non-causal predictors. We evaluate our method on real and synthetically generated time series. Overall our method outperforms other widely used causality methods, i.e, VAR Granger causality, VARLiNGAM and PCMCI+.

Estimating causal relations is vital in understanding the complex interactions in multivariate time series. Non-linear coupling of variables is one of the major challenges in accurate estimation of cause-effect relations. In this paper, we propose to use deep autoregressive networks (DeepAR) in tandem with counterfactual analysis to infer nonlinear causal relations in multivariate time series. We extend the concept of Granger causality using probabilistic forecasting with DeepAR. Since deep networks can neither handle missing input nor out-of-distribution intervention, we propose to use the Knockoffs framework (Barber and Candes, 2015) for generating intervention variables and consequently counterfactual probabilistic forecasting. Knockoff samples are independent of their output given the observed variables and exchangeable with their counterpart variables without changing the underlying distribution of the data. We test our method on synthetic as well as real-world time series datasets. Overall our method outperforms the widely used vector autoregressive Granger causality and PCMCI in detecting nonlinear causal dependency in multivariate time series.