The chaotic dynamics analysis of stock market

Abstract

This paper proves the China stock market to be a chaotic system and establishes a nonlinear dynamical model for it based on the study on the nonlinear dynamical properties of Shanghai stock composite index sequence by using chaos and fractal theory. The phase space of the stock sequence is reconstructed and the correlation dimension is analyzed, which indicate that the dynamical system has finite degree of freedom. The nonlinear evolution mechanism is observed and the initial value sensitive characteristic of the system is demonstrated through Lyapunov exponent analysis. Finally, the stock sequence is reconstructed by using finite degree of freedom based fractal interpolation algorithm and gaining reasonably accurate replications. The experimental results indicate that the nonlinear dynamical model is more effective to describe the China stock market than the conventional “random walk” theory based stochastic models.