一类GARCH-M模型的拟极大指数似然估计  

Quasi-maximum Exponential Likelihood Estimation for a GARCH-M Type Model

作　　者：张兴发[1] 李元[1] 

机构地区：[1]广州大学经济与统计学院,广州510006

出　　处：《应用数学学报》2016年第3期321-333,共13页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11401123;11271095);高等学校博士学科点专项科研基金(20124410110002)资助项目

摘　　要：由于可以用来刻画金融市场波动与收益之间的关系,GARCH-M模型自提出之后,就受到了广泛的研究.关于GARCH-M模型,传统的估计方法大多是基于拟极大似然估计.然而这类方法通常对矩条件的要求比较高,而实际数据未必能够满足这些条件.因此研究如何在较弱的矩条件下来估计GARCH-M模型就有一定的实际意义.本文研究了一类特殊的GARCHM模型.与传统GARCH-M模型不同的地方在于该类模型的条件方差决定于可观测的序列.通过拟极大指数似然估计的方法给出了模型参数的局部估计.在较弱的矩条件下给出了估计的渐近正态性证明.文章给出的模拟和实证研究表明该估计方法表现很好,有一定的应用价值.Due to the availability to describe the relationship between financial market volatility and return, GARCH-M model has been widely studied since it was proposed. The majority of traditional methods used to estimate GARCH-M type models are based on quasi maximum likelihood estimation. However, these approaches normally require strong moment conditions of the innovations, which may not be satisfied by the practical data. Hence, it makes sense to investigate how to estimate GARCH-M models under weaker mo- ment conditions. In this article, a special parametric GARCH-M type model is considered. Different from the traditional GARCH-M model, the considered one is of conditional vari- ance driven by past observable time series. Local estimation for model parameters is given with the basis of the quasi-maximum exponential likelihood estimation approach. Under weak moment conditions, asymptotic normality of the estimation is proved. Simulation studies demonstrate that the estimation performs well. Empirical study implies that the estimation is of certain practical value.

关 键 词：GARCH-M模型 拟极大指数似然估计 渐近正态性 

分 类 号：O212.1[理学—概率论与数理统计]