A time series model in which the random error is conditionally heteroscedastic with respect to its past realizations. This model is used to describe volatility clustering, i.e. a pattern observed in many financial data where large and small deviations appear to occur in clusters. The simplest form is ARCH (1),

where ${\varepsilon }_t=u_t\sqrt{{\alpha }_0+{\alpha }_1{\varepsilon }_{t-1}}$ and u_t has a standard normal distribution.