In [[finance]], '''volatility clustering''' refers to the observation, asfirst noted asby [[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> ContGranger, RamaC.W. J., Ding, Z. [https://www.jstor.org/stable/20076016 Some Properties of Absolute Return: An Alternative Measure of Risk ], Annales d'Économie et de Statistique, No. 40 ( 2005Oct. - Dec., 1995) , pp. "67-91</ref> and Ding and [[Clive Granger|Granger]] (1996)<ref>Ding, Z., Granger, C.W.J. [https://doi.org/10. 10071016/ 0304-4076(95)01737-2 Modeling volatility persistence of speculative returns: A new approach], Journal of Econometrics), 1996, vol. 73, issue 1 , 185- 84628215</ref> among others; see also.<ref>{{cite conference|last1=Cont|first1=Rama|date=2007|editor1- 048last=Teyssière|editor1- 6_11first=Gilles|editor2-last=Kirman|editor2-first=Alan|title=Volatility Clustering in Financial Markets: Empirical Facts and Agent-Based Models|publisher=Springer|pages=289–309|doi=10.1007/978-3-540-34625-8_10|book-title=Long Memory in Economics}}</ref> Some studies point further to long-range dependence in financialvolatility markets]".time Inseries, Lévy-Véhelsee J.Ding, LuttonGranger Eand [[Robert F. Engle|Engle]] ( eds1993) <ref>Zhuanxin FractalsDing, inClive EngineeringW.J. SpringerGranger, London.Robert ppF. 159–179.</ref>Engle (1993)▼{{Refimprove|date=August 2017}}
[https://doi.org/10.1016/0927-5398(93)90006-D A long memory property of stock market returns and a new model], Journal of Empirical Finance,
▲In [[finance]], '''volatility clustering''' refers to the observation, as 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>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>
Volume 1, Issue 1, 1993, Pages 83-106</ref> and Barndorff-Nielsen and Shephard.<ref>{{cite encyclopedia |author= Ole E. Barndorff-Nielsen, Neil Shephard| titlechapter= Volatility|encyclopedia= Encyclopedia of Quantitative Finance|date= October 2010 |year= 2010 |publisher= Wiley|editor-last= Cont|editor-first=Rama |doi=10.1002/9780470061602.eqf19019 |isbn= 9780470057568}} ▼
Observations of this type in financial time series have led to the use of [[GARCH]] models in financial forecasting and [[Derivative (finance)|derivatives]] pricing. The [[ARCH]] ([[Robert F. Engle|Engle]], 1982) and [[GARCH]] ([[Tim Bollerslev|Bollerslev]], 1986) models aim to more accurately describe the phenomenon of volatility clustering and related effects such as [[kurtosis]]. The main idea behind these two widely used models is that volatility is dependent upon past realizations of the asset process and related volatility process. This is a more precise formulation of the intuition that asset [[Volatility (finance)|volatility]] tends to revert to some mean rather than remaining constant or moving in [[monotonic]] fashion over time. ▼</ref>
▲Observations of this type in financial time series go against simple random walk models and have led to the use of [[GARCH ]] models and mean-reverting [[stochastic volatility]] models in financial forecasting and [[Derivative (finance)|derivatives]] pricing. The [[ARCH]] ([[Robert F. Engle|Engle]], 1982) and [[GARCH ]] ([[Tim Bollerslev|Bollerslev]], 1986) models aim to more accurately describe the phenomenon of volatility clustering and related effects such as [[kurtosis]]. The main idea behind these two widely used models is that volatility is dependent upon past realizations of the asset process and related volatility process. This is a more precise formulation of the intuition that asset [[Volatility (finance)|volatility]] tends to revert to some mean rather than remaining constant or moving in [[monotonic]] fashion over time.
==See also==
==References==
{{Reflist}}
==Additional References==
{{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 }}
▲{{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 }}
{{Volatility}}
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