Research On The Prediction Of Financial Time Series Based On The Stochastic Differential Equations

Financial market is increasingly active with the rapid development of economy.Financialindustry involves many aspects of life and plays an important role in the economic field. Moreand more investors in stocks and futures want to get great benefit. In the promotion ofinvestment behavior,the investors began to realise the importance of financial forecast. Timeseries analysis describes the change rule of historical data about time. Financial time seriescan be used to predict economic data and it can provide reference to the government andinvestment institutions. There is an important significance to the risk management forenterprises and individuals. Domestic and overseas scholars pay much attention to financialtime series analysis and prediction research.In recent years, there are many prediction models about financial time series. Forexample， ARIMA model, neural network model,the support vector machine (SVM) modeland so on. These models all forecast the short-term development trend in a certainrange.They all have high precision of prediction.The financial system is a dynamic systemwhich is complex, nonlinear and chaotic.It is caused by the running mechanism of itself. So theapplication of the previous prediction models can’t expound all interference factors and thechaotic character about the financial markets.Along with the development of modern mathematics,It has achieved good results ofdifferential equation system which is applied in economic field. This paper puts forward thestochastic differential equation model to get the characteristics of stochastic dynamics. Thismodel adds random item based on the differential equation.It can explain the natural operationrule of financial system.In this paper,we use difference equations instead of stochasticdifferential equation,avoiding the random integral problems which is unsolved in modernmathematics.We study the evolutionary algorithm deeply, then optimizes the structure of theequation with Multi Expression Programming and evolves the parameters of the equation withGenetic Algorithms and Particle Swarm Optimization. In the paper,we use the prediction ofstocks and exchange rate to illustrate the extensive applicability and good prediction effect ofthe model. Finally, we perceive the results through the graphic which is made by Matlab.This paper mainly introduces the content in the four aspects as follows: (1)At firse,it Summarizes the definition and properties of time series.Then it introduces itsapplication in daily life. It focuses on the features of the financial prediction models which isexisting.(2) It expounds the basic knowledge which is involved in the model of stochasticdifferential equations. It introduces a series of mathematics knowledge,such as thecharacteristics of chaos, the concept of differential equations, Brownian Motion, etc.It alsoexplains the reasons and methods which is used to make difference equations instead ofstochastic differential equation.(3) This paper briefly introduces the theory about evolution algorithm and geneticprogramming.It discusses Multi Expression Programming detailedly. At last, It describes theprinciple and the process of realization about genetic algorithm and particle swarmoptimization algorithm.(4) Finally, it applies this model to predict the stock and the exchange rate.The main stepsare as follows: data collection, optimizing equation with evolutionary algorithm, error analysisand so on. The conclusion shows that the model is efficient and feasible.