期刊名称：Documents de Travail du Centre d'Economie de la Sorbonne
印刷版ISSN：1955-611X
出版年度：2015
出版社：Centre d'Economie de la Sorbonne
摘要：In this paper we introduce a simple method to compute the empirical distribution of the Lyapunov exponent, that allows to test whether a dynamical system is chaotic or not. The main stake is to know whether we should use a stochastic approach to forecast a time series or a chaotic evolution function inside a phase spaces. Our method is based on a Maximum Entropy bootstrap. This algorithm allows for heterogeneity in the time series including non-stationarity or jumps. The estimators obtained satisfy both ergodic and central limit theorems. To our knowledge this is the first time that such technique is used to estimate the empirical distribution of the Lyapunov exponent. We apply our algorithm on Lorenz and Rössler systems. At last, applications are presented on financial data.
关键词：Chaos; Lyapunov exponent; Maximum Entropy; Bootstapping; empirical distribution
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