Case Research On Conditional Heteroskedasticity Model

The time series in the early time has been dominated by linear hypothesis. In the late 70 's, it is more and more clear that the linear model has many limitations. In order to solve these problems, the nonlinear time series model was put forward. This thesis mainly studies the modeling method of nonlinear time series, and combines them with practical applications, using Matlab software to model for stock data and exchange rate data.In time series modeling, the conditional variance of the regression error is no longer a constant value. The traditional linear models can not describe this phenomenon objectively, in 1982, Engle proposed that using the autoregressive conditional heteroscedasticity model to simulate the phenomenon. This thesis introduces the modeling process of the ARCH and generalized autoregressive conditional heteroskedasticity model in detail, including the test of ARCH effect, modeling method and procedure, the model testing and the estimated parameters testing method and forecast and so on. This thesis realizes the whole process on the Shanghai index, the 95% 1-step ahead forecast intervals results show that the ARCH model reacts the fluctuations better.In 1978, Tong proposed threshold autoregressive model, which can explain some of the nonlinear nature of the financial data, such as the periodic and asymmetric, the volatility of the aggregation, the volatility of the jump phenomenon and the time of the non reversibility, etc. The thesis introduces the Tong's modeling method and Tsay's theory for model test and modeling in detail. At the same time, the thesis summarizes the threshold autoregressive conditional heteroscedasticity model procedure and the model testing method. At last, the thesis realizes the model procedure using the U.S.dollar versus Australia dollar time series, and receives an ideal result.