In finance, volatility clustering refers to the observation, first noted by Mandelbrot (1963), that "large changes tend to be followed by large changes, of either sign, and small changes tend to be followed by small changes.
or their squares display a positive, significant and slowly decaying autocorrelation function: corr(|rt|, |rt+τ |) > 0 for τ ranging from a few minutes to several weeks.
[4] Some studies point further to long-range dependence in volatility time series, see Ding, Granger and Engle (1993)[5] and Barndorff-Nielsen and Shephard.
The ARCH (Engle, 1982) and GARCH (Bollerslev, 1986) models aim to more accurately describe the phenomenon of volatility clustering and related effects such as kurtosis.
This is a more precise formulation of the intuition that asset volatility tends to revert to some mean rather than remaining constant or moving in monotonic fashion over time.