An Asymptotic Expansion Associated with the Maximum Likelihood Estimators in ARMA Models
An Asymptotic Expansion Associated with the Maximum Likelihood Estimators in ARMA Models
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ARMA模型中与最大似然估计相关的渐近展开式
DOI：
10.1111/j.2517-6161.1984.tb01276.x
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发表时间：
1984
期刊：
影响因子：
--
通讯作者：
Katsuto Tanaka
中科院分区：
文献类型：
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作者：
Katsuto Tanaka
摘要 给出了自回归移动平均 (ARMA) 模型中最大似然估计量的联合分布以及边际分布和条件分布的 Edgeworth 型渐近展开技术。说明了我们的方法，并介绍了一些简单 ARMA 模型的扩展结果。本文提出了一种用于获得与 ARMA 模型中的最大似然估计量 (MLE) 相关的 Edgeworth 型渐近展开式的技术。展开涉及联合分布以及边际分布和条件分布。这里开发的方法很简单，分为两个步骤。第一个是从确定 MLE 的隐式函数中获得 MLE 本身的泰勒展开式。在 MLE 显式表达式的基础上，第二步导出 MLE 分布的渐近展开式。这些过程在第 2 节中进行了描述。在第 3 节中，我们使用一个简单的模型说明了我们的方法，并显示了一些简单 ARMA 模型的扩展结果。本文最后在第 4 节中进行了一些讨论。
SUMMARY A technique is given for the Edgeworth type asymptotic expansion for the joint as well as marginal and conditional distributions of the maximum likelihood estimators in autoregressive moving-average (ARMA) models. Our methodology is illustrated and results on the expansions for some simple ARMA models are presented. The present paper suggests a technique for obtaining the Edgeworth type asymptotic expansion associated with the maximum likelihood estimator (MLE) in ARMA models. The expansion relates to joint as well as marginal and conditional distributions. The approach developed here is simple and divided into two steps. The first is to obtain the Taylor expansion for the MLE itself from the implicit function determining the MLE. On the basis of the explicit expression for the MLE an asymptotic expansion for the distribution of the MLE is derived at the second step. These procedures are described in Section 2. In Section 3 our methodology is illustrated using a simple model and results on the expansions for some simple ARMA models are shown. This paper ends with some discussion in Section 4.