In econometrics, autoregressive conditional heteroskedasticity (ARCH) (Engle, 1982) is a model used for forecasting volatility which captures the conditional heteroscedasticity (serial correlation of volatility) of financial returns. Today's conditional variance is a weighted average of past squared unexpected returns. ARCH is an AR process for the variance.
A generalized autoregressive conditional heteroskedasticity (GARCH) (Bollerslev, 1986) model generalizes the ARCH model. Today's conditional variance is a function of past squared unexpected returns and its own past values. The model is an infinite weighted average of all past squared forecast errors, with weights that are constrained to be geometrically declining. GARCH is an ARMA(p,q) process in the variance.