Testing Chaotic Dynamics Via Lyapunov Exponents

In this paper, we propose a new test, based on the stability of the largest Lyapunov exponent from different sample sizes, to detect chaotic dynamics in time series. We apply this new test to the simulated data used in the single-blind controlled competition among tests for nonlinearity and chaos generated by Barnett et al. (1997), as well as to several chaotic series, both for small and large samples. The results suggest that the new test has a high power against different stochastic alternatives (both linear and nonlinear), and also performs well in small samples