Fluctuation prediction of stock market index by Legendre neural network with random time strength function

Stock market forecasting has long been a focus of financial time series prediction. In this paper, we investigate and forecast the price fluctuation by an improved Legendre neural network. In the predictive modeling, we assume that the investors decide their investing positions by analyzing the historical data on the stock market, so that the historical data can affect the volatility of the current stock market, and a random time strength function is introduced in the forecasting model to give a weight for each historical data. The impact strength of the historical data on the market is developed by a random process, where a tendency function and a random Brownian volatility function are applied to describe the behavior of the time strength, here Brownian motion makes the model have the effect of random movement while maintaining the original fluctuation. Further, the empirical research is made in testing the predictive effect of SAI, SBI, DJI and IXIC in the established model, and the corresponding statistical comparisons of the above market indexes are also exhibited.