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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 in the 90's by [[Clive Granger|Granger]] and Ding (1993)
<ref>Granger, C.W. J., Ding, Z. [http://www.jstor.org/stable/20076016 Some Properties of Absolute Return: An Alternative Measure of Risk ], Annales d'Économie et de Statistique, No. 40 (Oct. - Dec., 1995), pp. 67-91 </ref> and Ding and [[Clive Granger|Granger]] (1996) <ref>Ding, Z., Granger, C.W.J. [https://doi.org/10.1016/0304-4076(95)01737-2 Modeling volatility persistence of speculative returns: A new approach], Journal of Econometrics), 1996, vol. 73, issue 1, 185-215 </ref> among others; see also <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> {{cite encyclopedia |author= Ole E. Barndorff-Nielsen, Neil Shephard|title= Volatility|encyclopedia= Encyclopedia of Quantitative Finance|date= October 2010 |year= 2010 |publisher= Wiley|editor-last= Cont|editor-first=Rama |doi=10.1002/9780470061602.eqf19019 }}
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