Multiscale Non-stationary Causal Structure Learning from Time Series Data

This paper introduces a new type of causal structure, namely multiscale non-stationary directed acyclic graph (MN-DAG), that generalizes DAGs to the time-frequency domain. Our contribution is twofold. First, by leveraging results from spectral and causality theories, we expose a novel probabilistic generative model, which allows to sample an MN-DAG according to user-specified priors concerning the time-dependence and multiscale properties of the causal graph. Second, we devise a Bayesian method for the estimation of MN-DAGs, by means of stochastic variational inference (SVI), called Multiscale Non-Stationary Causal Structure Learner (MN-CASTLE). In addition to direct observations, MN-CASTLE exploits information from the decomposition of the total power spectrum of time series over different time resolutions. In our experiments, we first use the proposed model to generate synthetic data according to a latent MN-DAG, showing that the data generated reproduces well-known features of time series in different domains. Then we compare our learning method MN-CASTLE against baseline models on synthetic data generated with different multiscale and non-stationary settings, confirming the good performance of MN-CASTLE. Finally, we show some insights derived from the application of MN-CASTLE to study the causal structure of 7 global equity markets during the Covid-19 pandemic.