User’s Guide : Advanced Single Equation Analysis : ARCH and GARCH Estimation
ARCH and GARCH Estimation
Most of the statistical tools in EViews are designed to model the conditional mean of a random variable. The tools described in this chapter differ by modeling the conditional variance, or volatility, of a variable.
There are several reasons that you may wish to model and forecast volatility. First, you may need to analyze the risk of holding an asset or the value of an option. Second, forecast confidence intervals may be time-varying, so that more accurate intervals can be obtained by modeling the variance of the errors. Third, more efficient estimators can be obtained if heteroskedasticity in the errors is handled properly.
Autoregressive Conditional Heteroskedasticity (ARCH) models are specifically designed to model and forecast conditional variances. The variance of the dependent variable is modeled as a function of past values of the dependent variable and independent, or exogenous variables.
ARCH models were introduced by Engle (1982) and generalized as GARCH (Generalized ARCH) by Bollerslev (1986) and Taylor (1986). These models are widely used in various branches of econometrics, especially in financial time series analysis. See Bollerslev, Chou, and Kroner (1992) and Bollerslev, Engle, and Nelson (1994) for surveys.
In the next section, the basic ARCH model will be described in detail. In subsequent sections, we consider the wide range of specifications available in EViews for modeling volatility. For brevity of discussion, we will use ARCH to refer to both ARCH and GARCH models, except where there is the possibility of confusion.