A Learning Causal Relations in Multivariate Time Series Data

Many applications naturally involve time series data and the vector autoregression (VAR), and the structural VAR (SVAR) are dominant tools to investigate relations between variables in time series. In the first part of this work, we show that the SVAR method is incapable of identifying contemporaneous causal relations for Gaussian process. In addition, least squares estimators become unreliable when the scales of the problems are large and observations are limited. In the remaining part, we propose an approach to apply Bayesian network learning algorithms to identify SVARs from time series data in order to capture both temporal and contemporaneous causal relations, and avoid high-order statistical tests. The difficulty of applying Bayesian network learning algorithms to time series is that the sizes of the networks corresponding to time series tend to be large, and high-order statistical tests are required by Bayesian network learning algorithms in this case. To overcome the difficulty, we show that the search space of conditioning sets d-separating two vertices should be a subset of the Markov blankets. Based on this fact, we propose an algorithm enabling us to learn Bayesian networks locally, and make the largest order of statistical tests independent of the scales of the problems. Empirical results show that our algorithm outperforms existing methods in terms of both efficiency and accuracy.