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Statistical Tests for the Detection of the Arrow of Time in Vector Autoregressive Models

Pablo Morales-Mombiela, Daniel Hernández-Lobato, Alberto Suárez

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Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence. Pages 1544-1549.

Abstract

The problem of detecting the direction of time in vector Autoregressive (VAR) processes using statistical techniques is considered. By analogy to causal AR(1) processes with non-Gaussian noise, we conjecture that the distribution of the time reversed residuals of a linear VAR model is closer to a Gaussian than the distribution of actual residuals in the forward direction. Experiments with simulated data illustrate the validity of the conjecture. Based on these results, we design a decision rule for detecting the direction of VAR processes. The correct direction in time (forward) is the one in which the residuals of the time series are less Gaussian. A series of experiments illustrate the superior results of the proposed rule when compared with other methods based on independence tests.

Pablo Morales-Mombiela, Daniel Hernández-Lobato, and Alberto Suárez. 2013. Statistical Tests for the Detection of the Arrow of Time in Vector Autoregressive Models. In Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence, IJCAI-13. IJCAI, 1544–1549. https://ijcai.org/proceedings/2013/230
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