Generalized autoregressive moving average models with GARCH errors
Generalized autoregressive moving average models with GARCH errors
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DOI：
10.1111/jtsa.12602
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发表时间：
2021-05
影响因子：
0.9
通讯作者：
Tingguo Zheng;Han Xiao;Rong Chen
中科院分区：
文献类型：
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作者：
Tingguo Zheng;Han Xiao;Rong Chen
广义自回归模型平均模型（G阿尔马）是非高斯时间序列的重要且广泛使用的一类模型，它为基础时间序列的条件均值过程指定了一个阿尔马结构。然而，在许多应用中，人们经常遇到条件异方差。在这篇文章中，我们提出了一类新的模型，称为GARMA-GARCH模型，它联合指定了一般非高斯时间序列的条件均值和条件方差过程。在一般的建模框架下，我们提出了三个具体的模型，作为例子，比例时间序列，非负时间序列，倾斜和重尾金融时间序列。最大似然估计（MLE）和拟高斯MLE的参数估计。仿真研究和三个应用程序被用来证明模型和估计程序的属性。
One of the important and widely used classes of models for non‐Gaussian time series is the generalized autoregressive model average models (GARMA), which specifies an ARMA structure for the conditional mean process of the underlying time series. However, in many applications one often encounters conditional heteroskedasticity. In this article, we propose a new class of models, referred to as GARMA‐GARCH models, that jointly specify both the conditional mean and conditional variance processes of a general non‐Gaussian time series. Under the general modeling framework, we propose three specific models, as examples, for proportional time series, non‐negative time series, and skewed and heavy‐tailed financial time series. Maximum likelihood estimator (MLE) and quasi Gaussian MLE are used to estimate the parameters. Simulation studies and three applications are used to demonstrate the properties of the models and the estimation procedures.