Nonlinear Complexity and Chaotic Behaviors on Finite-Range Stochastic Epidemic Financial Dynamics

In this paper, a novel stochastic financial price model, based on the theory of finite-range stochastic interacting epidemic system, is proposed to reproduce the nonlinear dynamic mechanism of price fluctuations in financial markets. To better understand the complexity behavior of the proposed model, we develop a new entropy-based approach called index fluctuation fuzzy entropy (IFFE) and construct four measure criteria. The effectiveness of this approach is experimentally validated by logistic map time series, white noise time series, 1/f noise time series and six financial time series. Moreover, the largest Lyapunov exponents and Kolmogorov-Sinai entropy method are applied to analyze the chaotic property of the proposed model. To verify the rationality of the proposed model, the same analyses for the real market data are comparatively investigated with the simulation ones. The empirical results reveal that the novel financial price model is able to reproduce some important features of the financial markets.