Discovering Causal Structures from Time Series Data via Enhanced Granger Causality.

Granger causality has been applied to explore predictive causal relations among multiple time series in various fields. However, the existence of non-stationary distributional changes among the time series variables poses significant challenges. By analyzing a real dataset, we observe that factors such as noise, distribution changes and shifts increase the complexity of the modelling, and large errors often occur when the underlying distribution shifts with time. Motivated by this challenge, we propose a new regression model for causal structure discovery - a Linear Model with Weighted Distribution Shift (linear WDS), which improves the prediction accuracy of the Granger causality model by taking into account the weights of the distribution-shift samples and by optimizing a quadratic-mean based objective function. The linear WDS is integrated in the Granger causality model to improve the inference of the predictive causal structure. The performance of the enhanced Granger causality model is evaluated on synthetic datasets and real traffic datasets, and the proposed model is compared with three different regression-based Granger causality models (standard linear regression, robust regression and quadratic-mean-based regression). The results show that the enhanced Granger causality model outperforms the other models especially when there are distribution shifts in the data.