AGARCH模型及多维常数相关GARCH模型的统计分析

【作者】 张蕾；

【导师】 赵选民；

【作者基本信息】 西北工业大学 ， 应用数学， 2004， 硕士

【摘要】 近几十年来，关于时间序列分析的研究得到了迅速发展，特别是对于线性时间序列，取得了系统而丰富的成果。但是，对非线性时间序列的研究，仅在近二十年来才逐渐被重视起来。 对非线性时间序列的研究，近几十年来，有两条研究路线非常活跃，其一是自回归条件异方差(ARCH)模型，其二是非平稳(单位根)时间序列模型。具有自回归条件异方差(ARCH)的时间序列模型，首先是由Engle(1982)提出，这类模型在金融和经济领域有着广泛的应用。此后，经济学家和数学家又根据在实际研究中的需要，提出了许多GARCH模型的变异，形成了一个ARCH模型体系。 本文进行了极限理论的研究，主要解决了以下问题： 1．对于吴硕思和方兆本(2000)提出的非对称广义自回归条件异方差新模型，证明了它的极大似然估计(MLE)的渐近正态性和相合性。 2．在多维的情形下，着重研究Bollerslev(1990)提出的常数相关的多维GARCH模型的极大似然估计(MLE)的渐近正态性和相合性。 3．本文提出了非正态的AGARCH模型，并进行了实证研究，实证结果表明这样的方法是可行的和较优的。更多还原

【Abstract】 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.更多还原