Causal Discovery in Semi-Stationary Time Series

Discovering causal relations from observational time series without making the stationary assumption is a significant challenge. In practice, this challenge is common in many areas, such as retail sales, transportation systems, and medical science. Here, we consider this problem for a class of non-stationary time series. The structural causal model (SCM) of this type of time series, called the semi-stationary time series, exhibits that a finite number of different causal mechanisms occur sequentially and periodically across time. This model holds considerable practical utility because it can represent periodicity, including common occurrences such as seasonality and diurnal variation. We propose a constraint-based, non-parametric algorithm for discovering causal relations in this setting. The resulting algorithm, PCMCI$_{\Omega}$, can capture the alternating and recurring changes in the causal mechanisms and then identify the underlying causal graph with conditional independence (CI) tests. We show that this algorithm is sound in identifying causal relations on discrete time series. We validate the algorithm with extensive experiments on continuous and discrete simulated data. We also apply our algorithm to a real-world climate dataset.

Causal Discovery-Driven Change Point Detection in Time Series

Change point detection in time series seeks to identify times when the probability distribution of time series changes. It is widely applied in many areas, such as human-activity sensing and medical science. In the context of multivariate time series, this typically involves examining the joint distribution of high-dimensional data: If any one variable changes, the whole time series is assumed to have changed. However, in practical applications, we may be interested only in certain components of the time series, exploring abrupt changes in their distributions in the presence of other time series. Here, assuming an underlying structural causal model that governs the time-series data generation, we address this problem by proposing a two-stage non-parametric algorithm that first learns parts of the causal structure through constraint-based discovery methods. The algorithm then uses conditional relative Pearson divergence estimation to identify the change points. The conditional relative Pearson divergence quantifies the distribution disparity between consecutive segments in the time series, while the causal discovery method enables a focus on the causal mechanism, facilitating access to independent and identically distributed (IID) samples. Theoretically, the typical assumption of samples being IID in conventional change point detection methods can be relaxed based on the Causal Markov Condition. Through experiments on both synthetic and real-world datasets, we validate the correctness and utility of our approach.