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Gaussianity Measures for Detecting the Direction of Causal Time Series

José Miguel Hernández-Lobato, Pablo Morales-Mombiela and Alberto Suárez

We conjecture that the distribution of the time-reversed residuals of a causal linear process is closer to a Gaussian than the distribution of the noise used to generate the process in the forward direction. This property is demonstrated for causal AR(1) processes assuming that all the cumulants of the distribution of the noise are defined. Based on this observation, it is possible to design a decision rule for detecting the direction of time series that can be modeled as linear processes: The true direction of the time series is identified as the one in which the residuals of a linear fit are less Gaussian. Experiments with simulated and real-world data illustrate the superior performance of the proposed method with respect to current state-of-the-art approaches based on independence tests.