基于Lyapunov指数渐近分布的混沌特征存在性检验——以人民币汇率波动序列为例

Research on the Test of Chaotic Characteristics Based on the Asymptotic Distribution of Lyapunov Exponent: An Example of RMB Exchange Rate Series

当前对于动态系统是否具有混沌特征的判断主要根据最大Lyapunov指数是否大于零进行,但是要得到混沌现象存在的充分证据,还需通过相应的假设检验过程,判断最大Lyapunov指数是否在统计意义上显著大于零。在探讨Lyapunov指数渐近分布的基础上给出了最大Lyapunov指数是否大于零的假设检验过程,并以人民币汇率波动序列为例进行相应的实证测算。

To diagnose the chaotic characteristics of a dynamic system,one often examines whether the maximum exponent is greater than zero,while in order to obtain the sufficient evidence of the chaos,we need to process hypothesis test to determine whether the maximum exponent is significantly greater than zero.This paper gives a hypothesis test to determine whether the maximum exponent is greater than zero based on the asymptotic distribution of exponent,then the authors implement the empirical estimates by the RMB exchange rate series.