Agarch Model And Multi-dimensional Constant Garch Model Of Statistical Analysis

In recent several decades, the development of time series analysis is rapid. Especially ,the investigation of linear time series, the systematic and abundant achievements have been obtained. However, the statisticians and econometricians have gradually paid attention to investigation of nonlinear time series for the last two decades.In the last decade, there exist two active lines on the investigation of nonlinear time series. One is the autoregressive conditional heteroscedasticity(ARCH) model, the another is the nonstationary(unit root) time series model.The concept of ARCH, which stands for autoregressive heteroscedasticity, was first introduced by Engle(1982) to handle time series with a changing conditional variance. Thereafter, mathematician and econometricians brought forward various subsidiaries of ARCH models according to the request in the practical research and formed a ARCH model system .In this paper, the limit theory is discussed and the main problems are solved as followed:1 .We will obtain asymptotic normality and consistency of MLE for AGARCH model introduced by Wu shuosi and Fang zhaoben (2000).2. We will give the asymptotic normality and consistency of MLE for multivariate model with constant correlation introduced by Bollerslev(1990).3. Moreover we will introduce the AGARCH model with non-normal distribution and have empirical study shows that the model suggested is feasible.