Distinguishing chaos from random fractal sequences by the comparison of forward and backward predictions: utilization of the difference in time reversal symmetry of time series

Abstract

The authors propose a method for distinguishing chaos from random fractal sequences which have been difficult to discriminate from chaos. In the proposed method, the time series is predicted both in the forward direction and in the backward direction, and the accuracy of the two types of predictions is compared. They show, considering the time reversal symmetry of time series, that if the time series is chaotic and originates from a dissipative dynamical system, the accuracy is in general better for the forward prediction than for the backward prediction, whereas the accuracy is the same if the time series is a random fractal sequence. The method is also applicable to distinguishing between chaos and stationary noise. It is possible to give a quantitative evaluation of the distinction without a large amount of data or calculation.