The autoregressive conditional heteroskedasticity (ARCH) model concerns time series with time-varying heteroskedasticity, where variance is conditional on the information existing at a given point in time.
The ARCH Models
An ARCH (autoregressive conditionally heteroscedastic) model is a model for the variance of a time series. ARCH models are used to describe a changing, possibly volatile variance. Although an ARCH model could possibly be used to describe a gradually increasing variance over time, most often it is used in situations in which there may be short periods of increased variation. (Gradually increasing variance connected to a gradually increasing mean level might be better handled by transforming the variable.)