改进的临近返回检测法:时间序列的混沌性诊断

Chaotic analysis of time series based on improved close returns test

利用受随机扰动时系统时间序列的拓扑学特点,建立了带随机项的差分方程模型以模拟经济时间序列,指出了临近返回检测(CR检测)方法在反映混沌的敏感依赖性等方面的不足,改进了原CR方法的判断步骤,并从数理统计及动力学角度给出了理论依据,提出了改进的临近返回检测方法(ICR检测).最后对上海股票市场非线性与混沌进行了实证,指出了上海股票市场存在非线性,噪声较大,但不存在混沌.

A model of difference equations with perturbations to simulate economic systems and analyze the topological characteristics of the dynamic systems with perturbation is established. The drawbacks of the close returns test （ CR test） such as sensitive dependence of chaotic systems are pointed out. Thus an improved close returns test （ICR test） is given and probabilistic and dynamic support are provided. Finally the ICR test is applied to the examination of nonlinearity and chaos in the Shanghai Stock Market. The results indicate that the data are not chaotic but contain lots of nonlinearities with noises.