  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 paper 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, nonnegative time series, and skewed and heavy-tailed
financial time series. Maximum likelihood estimator (MLE) and quasi Gaussian
MLE (GMLE) are used to estimate the parameters. Simulation studies and three
applications are used to demonstrate the properties of the models and the
estimation procedures.
