B0829
Title: The arrow of time in multivariate time series
Authors: - ()
Bernhard Scholkopf - Max Planck Institute for Intelligent Systems (Germany)
Stefan Bauer - ETH Zurich (Switzerland)
Abstract: A time series satisfying a linear multivariate autoregressive moving average (VARMA) model is proved to satisfy the same model assumption in the reversed time direction, too, if all innovations are normally distributed. This reversibility breaks down if the innovations are non-Gaussian. Therefore, under the assumption of a VARMA process with non-Gaussian noise, the arrow of time becomes detectable. This result extends earlier work for one-dimensional time series. We present a practical algorithm that estimates the time direction for a finite sample and prove its consistency. An application to real world data from economics shows that considering multivariate processes instead of univariate processes can be beneficial. Our work relates to the concept of causal inference, where recent methods exploit non-Gaussianity of the error terms for causal structure learning.
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