Robert Engle and the ARCH model

In the January 2007 issue of Bloomberg Markets, Peter Carr profiles Robert Engle, co-recipient of the Nobel Prize in Economics in 2003 for his autoregressive conditional heteroskedasticity (ARCH) model [Link]. 

To understand the ARCH model, we first need to know the definition of the terms: heteroskedasticity and volatility clustering. A univariate stochastic process is said to be heteroskedastic if its standard deviation is not constant. Further, such a process is said to be conditionally heteroskedastic, if its conditional standard deviations are not constant. Returns of stocks or bonds are found to be conditionally heteroskedastic. Heteroskedastic stochastic processes may exhibit volatility clustering - interspersed periods of high or low volatility. The ARCH model by Engle (1982) expresses the conditional volatility (standard deviation) as being dependent on past values of the stochastic process. This model was further extended by one of his students, Bollerslev, in which the expression for conditional volatility included an additional dependence on past values of itself. This latter model is referred to as the Generalized ARCH model or the GARCH model (1987). A simple description of the ARCH and the GARCH models can be found here.