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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. This empirical property has been documented since by [[Clive Granger|Granger]] and Ding (1993) and Ding and [[Clive Granger|Granger]] (1996) .<ref>{{cite conference|last1=Cont|first1=Rama|date=2007|editor1-last=Teyssière|editor1-first=Gilles|editor2-last=Kirman|editor2-first=Alan|title=Volatility Clustering in Financial Markets: Empirical Facts and Agent-Based Models|url=https://doi.org/10.1007/978-3-540-34625-8_10|conference=|publisher=Springer|volume=|pages=289-309|doi=10.1007/978-3-540-34625-8_10|via=|book-title=Long Memory in Economics}}</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>
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