Multiple testing strategy for the detection of temporal irreversibility in stationary time series

We propose a strategy for the detection of temporal irreversibility in stationary time series based on multiple bidimensional tests. The test is helpful to evaluate the displacement of irreversibility toward high dimensions. The test can be used independently of the theoretical functionals actually utilized to check irreversibility. The method was applied to simulated nonlinear signals generated by the delayed Henon map and a two-loop negative feedback model to show how the presence of a delay could produce the displacement of irreversibility toward higher dimensions. The method was applied also to series of a biological variable (i.e., heart period) that is known to be regulated by multiple feedback loops. Simulations and real data support the need of exploring progressively increasing embedding dimensions when assessing temporal irreversibility.