Univariate GARCH Modeling
Marc S Paolella · Wiley series in probability and statistics · 2018
This chapter develops the primary topics associated with the class of univariate GARCH models, as well as some less common but highly useful methods for estimation. The basic univariate GARCH framework can be used to form multivariate models of financial asset returns and as an important application in the context of portfolio optimization. The chapter presents the fundamental properties of the baseline Gaussian GARCH model and details its estimation. It is concerned with estimation of GARCH models when the underlying i.i.d. process is specifically noncentral Student's t, denoted NCT-GARCH. The chapter is dedicated to the GARCH model with a stable Paretian distributional assumption, denoted S 𝛼,𝛽-GARCH, and discusses testing the stability and i.i.d. assumptions of the filtered innovations process. It details a GARCH-type model that does not fit into the class of extensions, but embodies a richer dynamic structure based on a discrete normal mixture distribution that leads to improved out-of-sample forecasts.