Chapter 5 - Single-Factor Conditionally Heteroskedastic Models, ARCH and GARCH

Abstract

This chapter describes the class of Autoregressive Conditional Heteroskedasticity (ARCH) models and their generalizations (GARCH), applied to capture conditional heteroskedasticity in financial data, that is, when the data display time-varying variances and covariances. Section 5.1 introduces the concept of conditional heteroskedasticity and explains the role of ARCH models in this framework. Section 5.2 describes simple univariate, parametric models, starting from the rolling window model and the exponential smoothing one, and developing the class of ARCH and generalized ARCH models. Section 5.3 illustrates more advanced models to deal with non-normal error distributions and asymmetric effects in conditional variance. Section 5.4 illustrates how to assess the appropriateness of ARCH models. Section 5.5 emphasizes how GARCH models can be used to forecast conditional variances. Finally, Section 5.6 explains how to estimate the parameters of a GARCH model and the statistical properties of the resulting estimates.