Abstract We conjecture that the distribution of the timereversed 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 de?ned. Based on this observation, it is possible to design a decision rule for detecting the direction of time series that can be described as linear processes: The correct direction (forward in time) is the one in which the residuals from a linear ?t to the time series are less Gaussian. A series of experiments with simulated and real-world data illustrate the superior results of the proposed rule when compared with other stateof-the-art methods based on independence tests.