| Financial market is a complex evolved dynamic system with high volatilities and noises, and the modeling and analyzing of financial time series are regarded as the rather challenging tasks in financial research. In this work, by applying the Potts dynamic sys-tem, a classical statistical physical model, combined with the theory of financial stock pricing and statistical physics, a financial agent-based time series model is developed. Potts model, a generalization of the Ising model to more than two components, is a model of interacting spins on a crystalline lattice which we used to describe the inter-action strength among the different type of investors or the spreading of the investment information, so as to reproduce stock price process. Furthermore, through computer simulation, we obtain the imitate stock price and return series.We study the volatility of stock price by selecting the price returns as the statistic. While presenting numerical research in conjunction with statistical analysis, the cor-responding statistical behaviors of the daily returns of Shanghai Composite Index and Shenzhen Component Index are also comparatively investigated. In the first, by com-paring with the actual data, we studied the effect of parameters in the financial model by multiscale entropy analysis. Moreover, through introducing of empirical mode decom-position, the correlation behavior of returns of the proposed model and actual data are explored by time-dependent intrinsic correlation and power law classification scheme analysis. We also investigated the multifractal property of time series by applying mul-tifractal detrending moving average analysis.After investigating some important statistical behaviors like, complexity, correla-tion and multifractal property, the empirical results exhibit the similar statistical behav-iors between the simulated data and the real market indexes, indicating certain rational-ity of the construction of this proposed price model with proper parameters. |
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