This paper investigates the complex behaviors and entropy properties for a novel random complex interacting stock price dynamics, which is established by the combination of stochastic contact process and compound Poisson process, concerning with stock return fluctuations caused by the spread of investors' attitudes and random jump fluctuations caused by the macroeconomic environment, respectively. To better understand the fluctuation complex behaviors of the proposed price dynamics, the entropy analyses of random logarithmic price returns and corresponding absolute returns of simulation dataset with different parameter set are preformed, including permutation entropy, fractional permutation entropy, sample entropy and fractional sample entropy. We found that a larger λ or γ leads to more complex dynamics, and the absolute return series exhibit lower complex dynamics than the return series. To verify the rationality of the proposed compound price model, the corresponding analyses of actual market datasets are also comparatively preformed. The empirical results verify that the proposed price model can reproduce some important complex dynamics of actual stock markets to some extent.
The finite-range voter system, one of stochastic particle systems, is applied to model a financial price process for further description and investigation of fluctuations of Shanghai Composite Index. For different parameter values of the intensity and the range R , we investigate the statistical behaviors of the simulation data for this financial model. Then we develop the random jump time effective neural network model to forecast the fluctuations of Shanghai Composite Index. Moreover, we compare the two models by analyzing the returns and the absolute returns of Shanghai Composite Index, the simulation data and the predictive data through Detrended Fluctuation Analysis and classic Rescaled Range Analysis.
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