DETECTING TIMES ARROW - A METHOD FOR IDENTIFYING NONLINEARITY AND DETERMINISTIC CHAOS IN TIME-SERIES DATA

A method is described for detecting the presence of nonlinearity in ec ological and epidemiological time series. We make use of a nonlinear-p rediction technique to probe data-sets for evidence of temporal direct ionality, and take advantage of the fact that the predictive propertie s of a signal generated from a stochastic linear Gaussian process as i t 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 n eed only check for time directionality in order to test the null hypot hesis that the erratic fluctuations in a time series are generated by a linear gaussian process. Strong evidence of time reversibility force s us to reject the null hypothesis and suggests that nonlinear dynamic s play an important role. The method is tested on various model and re al ecological time series.