The Study Of Shanghai Stock Price Index Based On Grey Theory And Autoregressive Integrated Moving Average Models

Autoregressive integrated moving average models (ARIMA) has been widely used as a famous liner time series model; A character of financial time series is unstable, what ARIMA model to do with it is to differ it until it become stable, and then use an ARMA model to close it.But, if a series with trends will become a whit noise after differing it, we can't use an ARMA model to close it. So, the initial series can't be closed by an ARIMA model. Besides that, as ARIMA model is a linear model, and financial series mostly are nonlinears, and the random part of its is not usually GAUSS distribution, so use an ARIMA model to close them is not very good. So, this article used a metabolism Grey System with five dimension to close the trend of unstable series (the index of shanghai A stock form 8-9-2004 to18-3-2005), and use an ARIMA model to close the residual, at last use the mixed model to predict, it prove that the result of this model is well.