广义泊松整值GARCH模型.docVIP

广义泊松整值 GARCH 模型 朱复康 吉林大学数学学院，长春　130012 摘要：本文介绍了一个广义泊松整值 GARCH 模型，它既能处理偏大离差，也能处理偏小离 差。与已有的 double Poisson 整值 GARCH 模型相比，新模型的存在性和遍历性容易给出。 导出了自相关结构以及 1 阶和 2 阶矩的表达式，给出了参数的最大似然估计量及其渐近性质。 关键词：渐近性；广义泊松；整值 GARCH 模型 中图分类号： o212.1 Generalized Poisson integer-valued GARCH models ZHU Fukang School of Mathematics, Jilin University, Changchun 130012 Abstract: In this paper we introduce a generalized Poisson INGARCH model, which can account for both overdispersion and underdispersion. Compared with the double Poisson INGARCH model, conditions for the existence and ergodicity of such a process are easily given. We analyze the autocorrelation structure and also derive expressions for moments of order 1 and 2. We consider the maximum likelihood estimators for the parameters and establish their consistency and asymptotic normality. Key words: Asymptotics; Generalized Poisson; Integer-valued GARCH models 0 Introduction Time series of counts are commonly observed in real-world applications, so a number of time series models for counts have been proposed, which are able to describe di?erent types of marginal distribution and autocorrelation structure. The Poisson distribution provides a standard framework for the analysis of count data, but the requirement that the variance should equal the mean is often too restrictive in practice. Frequently data are overdispersed, with the variance greater than the mean, and there are many alternative distributions that can be used to model the data. The opposite phenomenon of underdispersion, where the variance is less than the mean, occurs less frequently and the choice 基金项目： National Natural Science Foundation of China , Specialized Research Fund for the Doctoral Program of Higher Education (20090061120037) 作者简介： ZHU Fukang（1980-），male，associate professor，major research direction：time series. -1- of distributions is much narrower. However, there are situations in which underdispersion is well documented, see Ridout and Besbeas (2004) an