The ARCH model is relatively simple but often requires many parameters to capture the volatility patterns of an asset-return series. The generalized ARCH (GARCH) model applies to a log-return series, r_t, with disturbances, ε_t = r_t - μ, that follow a GARCH(p, q) model if:

The GARCH(p, q) model assumes an ARMA(p, q) model for the variance of the error term, ε_t.

Similar to ARCH models, the tail distribution of a GARCH(1,1) process is heavier than that of a normal distribution. The model encounters the same weaknesses as the ARCH model. For instance, it responds equally to positive and negative shocks.