Statistical analysis and forecasting of return interval for SSE and model by lattice percolation system and neural network

We investigate and compare the scaling behaviors of the return intervals for Shanghai composite index and a financial model, where the financial price model is developed by the stochastic lattice percolation theory (a random network). For the different values of threshold, the probability density functions of the return intervals for both Shanghai composite index and the simulation data are analyzed and described by the computer computations and simulations, and the trends of the corresponding distributions are also studied by the empirical research. Further, according to the randomness and the nonlinear nature of return interval, the artificial neural network which has the strong non‐linear approximation capability is introduced to train and forecast the fluctuations of the return intervals for the real and the simulative data.