Generalized autoregressive moving average models with GARCH errors

One of the important and widely used classes models for non-Gaussian time series is generalized autoregressive model average (GARMA), which specifies an ARMA structure conditional mean process underlying series. However, in many applications one often encounters heteroskedasticity. In this paper we propose a new class models, referred to as GARMA-GARCH that jointly specify both variance processes general Under modeling framework, three specific examples, proportional series, nonnegative skewed heavy-tailed financial Maximum likelihood estimator (MLE) quasi Gaussian MLE (GMLE) are estimate parameters. Simulation studies demonstrate properties estimation procedures.