The generalized autoregressive conditional heteroscedastic (GARCH) model is an extension of Engle's ARCH model for variance heteroscedasticity . If a series exhibits volatility clustering, this suggests that past variances might be predictive of the current variance.
The GARCH(P,Q) model is an autoregressive moving average model for conditional variances, with P GARCH coefficients associated with lagged variances, and Q ARCH coefficients associated with lagged squared innovations. The form of the GARCH(P,Q) model in Econometrics Toolbox™ is
For stationarity and positivity, the GARCH model has the following constraints:
To specify Engle's original ARCH(Q) model, use the equivalent GARCH(0,Q) specification.
 Engle, Robert F. "Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation." Econometrica. Vol. 50, 1982, pp. 987–1007.