Linear Models and Time-Series Analysis

10Univariate GARCH Modeling

The goal of this chapter is to develop the primary topics associated with the class of univariate GARCH models, as well as some less common but highly useful methods for estimation. One of their primary applications is for risk prediction of financial portfolios of assets, and this will be detailed in Chapter 11. This basic univariate GARCH framework is not as limited as it might seem: It can be used to form multivariate models of financial asset returns and as an important application in the context of portfolio optimization. We save that discussion also for Chapter 11, concentrating herein on several core aspects of the univariate case.

The outline of this chapter is as follows. After some introductory remarks in Section 10.1 , Section 10.2 presents the fundamental properties of the baseline Gaussian GARCH model and details its estimation. Section 10.3 builds on this by discussing some simple but important extensions. Section 10.4 is concerned with estimation of GARCH models when the underlying i.i.d. process is specifically noncentral Student's , denoted NCT‐GARCH. Section 10.5 is dedicated to the GARCH model with a stable Paretian distributional assumption, denoted ‐GARCH, and discusses testing the stability and i.i.d. assumptions of the filtered ...