# Volatility clustering

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."[1] A quantitative manifestation of this fact is that, while returns themselves are uncorrelated, absolute returns ${\displaystyle |r_{t}|}$ 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. This empirical property has been documented in the 90's by Granger and Ding (1993)[2] and Ding and Granger (1996)[3] among others; see also.[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.[6]