Generalized Autoregressive Moving Average Models with GARCH Errors

TL;DR

This paper introduces GARMA-GARCH models that jointly model the mean and variance of non-Gaussian time series, improving analysis of heteroskedastic data like financial series.

Contribution

It proposes a new class of models combining GARMA with GARCH errors, with specific variants for different types of non-Gaussian time series.

Findings

Models effectively capture heteroskedasticity in non-Gaussian data

Maximum likelihood estimation performs well in simulations

Applications demonstrate practical utility of the models

Abstract

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.