In [[finance]], '''volatility clustering''' refers to the observation, first noted as [[Benoît Mandelbrot|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."<ref>Mandelbrot, B. B., [[https://www.jstor.org/stable/2351623| The Variation of Certain Speculative Prices]], The Journal of Business 36, No. 4, (1963), 394-419</ref> A quantitative manifestation of this fact is that, while returns themselves are uncorrelated, absolute returns <math>|r_{t}|</math> or their squares display a positive, significant and slowly decaying autocorrelation function: corr(|r{{sub|t}}|, |r{{sub|t+τ}} |) > 0 for τ ranging from a few minutes to several weeks.<ref>{{cite conference |url=https://doi.org/10.1007/978-3-540-34625-8_10 |title= Volatility Clustering in Financial Markets: Empirical Facts and Agent-Based Models|last1=Cont |first1=Rama |date=2007 |publisher= Springer|book-title=Long Memory in Economics|editor2-last=Teyssiere|editor2-first=Gilles|editor1-last=Kirman|editor1-first=Alan|pages= 289-309 |doi=10.1007/978-3-540-34625-8_10 }}</ref>
Some studies point further to long-range dependence in volatility time series.
<ref>Cont, Rama (2005). "[https://doi.org/10.1007/1-84628-048-6_11 Long range dependence in financial markets]". In Lévy-Véhel J., Lutton E. (eds) Fractals in Engineering. Springer, London. pp. 159–179.</ref><ref>
