Detecting Time's Arrow: A method for identifying nonlinearity and deterministic chaos in time-series data

A method is described for detecting the presence of nonlinearity in ecological and epidemiological time series. We make use of a nonlinear-prediction technique to probe data-sets for evidence of temporal directionality, and take advantage of the fact that the predictive properties of a signal generated from a stochastic linear Gaussian process as it evolves forwards in time, are exactly the same as when the signal is temporally reversed. In contrast nonlinear, and in particular chaotic processes, often fail to display such time reversibility. Hence one need only check for time directionality in order to test the null hypothesis that the erratic fluctuations in a time series are generated by a linear gaussian process. Strong evidence of time reversibility forces us to reject the null hypothesis and suggests that nonlinear dynamics play an important role. The method is tested on various model and real ecological time series.