A1489
Title: Empirical probability density function of Lyapunov exponents
Authors: Clement Goulet - Paris Sorbonne (France) [presenting]
Abstract: We introduce a simple method to approximate the empirical distribution of Lyapunov exponent for one-dimensional discrete dynamical systems. We recall that its positivity provides a necessary condition for being chaotic. Hence, if a dynamical system has a positive Lyapunov exponent and if it has an attractor with fractal dimension, then forecasts can be done inside this attractor. Nevertheless, the estimation of Lyapunov exponent on observed dynamical systems often produce results close to zero and so it is hard to assess whether the dynamical system is chaotic or not. The approximation of the Lyapunov exponent distribution and the computation of confidence intervals overcome this limitation. The distribution approximation is done through Maximum Entropy bootstrapping technique. This technique does not require neither stationarity of the system nor any law assumption and preserve path dependency. To our knowledge this is the first time that such technique is used to approximate the empirical distribution of the Lyapunov exponent. We propose an application of our method on a denoised phase space generated by financial data.
