Non-stationary Time Series Modeling And Forecasting

According to the characteristic of statistics, time series is divided into two classes. One is stationary time series, the other is non-stationary time series. In daily time we usually observe time series which is almost non-stationary especially in the phenomena of society and economic. Forecasting these series correctly can control and direct the advancement of society and economic greatly. So the research of the modeling and the forecasting of non-stationary time series is very important in practice. The study narrates mainly about the method of the modeling and the forecasting of non-stationary time series.Based on the study of four methods of non-stationary time series modeling and forecasting, two algorithmic means are committed to be improved, one is using ARIMA modeling to reconstruction signals of approximation coefficients from a wavelet decomposition , it will more fit practice condition; two is using ARMA process to tendency vectors filtered from Kalman filter, it will improve forecasting precision. Furthermore, the study of using gray compounding model and BP neural network model is carried on.Four methods are all actualized to software programs with Matlab . Based on experiment data of SSE(Shanghai Stock Exchange) Composite, four algorithmic means are compared each other, and summed up merits and disadvantages. It can be proved that the forecasting method based on wavelet decomposition and the method of Kalman-ARMA are better than gray compounding model and BP neural network model in forecasting precision and the fitting curve.