Chaotic Characteristics of the SSE Composite Index Time Series

This paper studies the Shanghai Stock Exchange (SSE) Composite Index, sample period of which spreads from December 16th 1996 to December 31st 2009. The index close prices, its logarithm, its logarithmic first differences, and its log linear detrended series are used. To judge the existence of chaotic dynamical features in time series, the technique of phase space reconstruction is applied. The C-C method, Grassberger and Procaccia (1983) algorithm and the algorithm of small data sets are used to estimate respectively delay times, best embedding dimensions, correlation dimensions and the largest Lyapunov exponents. The result shows that although the largest Lyapunov exponents are different for the index close prices, its logarithm, and its log linear detrended series, they are all positive, which suggests the existence of chaos. However, for the logarithmic first differences, the conclusion of chaos existence can not be drawn, because although the largest Lyapunov exponent is positive, the correlation dimension does not convergence.