In this recipe, we present how to work with an extension of the ARCH model, namely the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model. GARCH can be considered an ARMA model applied to the variance of a time series—the AR component was already expressed in the ARCH model, while GARCH additionally adds the moving average part. In other words, the ARCH model specifies the conditional variance as a linear function of past sample variances, while the GARCH model adds lagged conditional variances to the specification.
The equation of the GARCH model can be presented as:
While the interpretation is very similar to the ARCH model presented in the previous recipe, the difference lies in the last equation, where there is an additional component. Parameters are constrained to meet the following...
