Statistical Analysis And Forecasting System Research:Stochastic Interacting Financial Dynamic System

Stochastic interacting percolation system is one of the statistical physics systems. A financial time series model is developed and investigated by the oriented percolation, which is percolation with a special direction along which the activity can only propagate one way but not the other. The water flow spreading of the percolation model is con-sidered as the spreading of the investors investment attitudes towards the stock market, and suppose that the stock price fluctuation results from the investors investment atti-tudes. Further, we complete modeling stock price, return and return intervals from the financial model by computer simulation. A new model, Legendre neural network with random time strength function (LeNNRT) is built to predict the κ-day moving average of Shanghai Composite Index and the simulated price series of the proposed model.Nonlinear and statistical analysis of fluctuation behaviors of stock markets have long been a focus of economic research. The behaviors are mainly uncovered by high frequency financial time series. Return-interval series is one of them, reflecting the time gaps between fixed returns, which is found to be significant in doing researches on the period of stock fluctuations.From this financial model, we study the statistical behaviors of return and return intervals time series, while the corresponding behaviors for Shanghai and Shenzhen stock composite prices index are also comparatively studied. We not only investigate the scaling behaviors of return intervals based on previous research, but also introduce a new scaling function of exponential parameter to analyze fluctuation behaviors of return intervals. Furthermore, the nonlinear statistical behaviors of return interval time series are studied by applying multifractal detrended fluctuation and visibility graph method. It is a new try that we forecast and investigate the k-day moving average of the stock prices by an improved Legendre neural network-Legendre neural network with random time strength function, and the whole empirical researches exhibit that for proper parameters, the proposed financial model can fit the real markets to a certain extent.