On the Entropy Production of Time Series with Unidirectional Linearity

There are non-Gaussian time series that admit a causal linear autoregressive moving average (ARMA) model when regressing the future on the past, but not when regressing the past on the future. The reason is that, in the latter case, the regression residuals are not statistically independent of the regressor. In previous work, we have experimentally verified that many empirical time series indeed show such a time inversion asymmetry.