Generalized autoregressive moving average models with GARCH errors
提出GARMA-GARCH模型，同时刻画非高斯时间序列的条件均值和条件方差，适用于比例、非负及偏斜厚尾金融数据，并用极大似然估计参数。
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.