The Basics of Financial Econometrics: Tools, Concepts, and Asset Management Applications

CHAPTER 11

Autoregressive Heteroscedasticity Model and Its Variants

After reading this chapter you will understand:

• The concepts of homoscedasticity and heteroscedasticity.
• The concept of conditional heteroscedasticity.
• The empirical basis for conditional heteroscedasticity.
• Autoregressive modeling of conditional heteroscedasticity.
• Autoregressive conditional heteroscedasticity (ARCH) models.
• Extensions of ARCH models: generalized autoregressive conditional heteroscedasticity (GARCH) models and multivariate ARCH models.
• How to apply estimation software for ARCH models.

In Chapter 9, we described a time series tool, the autoregressive moving average (ARMA) model, that focuses on estimating and forecasting the mean. Now we turn to financial econometric tools that are used to estimate and forecast an important measure in finance: the variance of a financial time series. The variance is an important measure used in the quantification of risk for a portfolio or a trading position, strategies for controlling the risk of a portfolio or a trading position (i.e., determination of the hedge ratio), and as an input in an option pricing model.

Among the financial econometric tools used for forecasting the conditional variance, the most widely used are the autoregressive conditional heteroscedasticity (ARCH) model and the generalized autoregressive conditional heteroscedasticity (GARCH) model.¹ These tools are described in this chapter along with a brief description of variants of these models. ...