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. {{cite conferenceThis empirical property has been documented in the 90's by [[Clive Granger| url=Granger]] and Ding (1993)<ref>Granger, C.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 (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. 10071016/ 9780304- 34076(95)01737- 540-34625-8_102 |title=Modeling Volatilityvolatility Clusteringpersistence inof Financialspeculative Marketsreturns: EmpiricalA Factsnew andapproach], AgentJournal of Econometrics), 1996, vol. 73, issue 1, 185- Based215</ref> Modelsamong others; see also.<ref>{{cite conference|last1=Cont |first1=Rama |date=2007 | publishereditor1-last= SpringerTeyssière| bookeditor1- first=Gilles|editor2-last=Kirman|editor2-first=Alan|title= Volatility TeyssièreClustering G.,in KirmanFinancial A.P.Markets: (eds)Empirical LongFacts Memoryand inAgent-Based EconomicsModels|publisher=Springer|pages= 289-309 289–309|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 volatility time series, see Ding, Granger and [[Robert F. Engle|Engle]] (1993)<ref>Zhuanxin Ding, Clive W.J. Granger, Robert F. 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., 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.{{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= Teyssière G., Kirman A.P. (eds) Long Memory in Economics|pages= 289-309 |doi=10.1007/978-3-540-34625-8_10 }}
Volume 1, Issue 1, 1993, Pages 83-106</ref> and Barndorff-Nielsen and Shephard.<ref>{{cite encyclopedia |author= Ole E. Barndorff-Nielsen, Neil Shephard|chapter= Volatility|encyclopedia= Encyclopedia of Quantitative Finance|date= October 2010 |publisher= Wiley|editor-last= Cont|editor-first=Rama |doi=10.1002/9780470061602.eqf19019 |isbn= 9780470057568}}
</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.{{cite encyclopedia |author= Ole E. Barndorff-Nielsen, Neil Shephard|title= Volatility|encyclopedia= Encyclopedia of Quantitative Finance|date= October |year= 2010 |publisher= Wiley|editor= [[Rama Cont]] |doi=10.1002/9780470061602.eqf19019 }}
==See also==
*[[GARCH]]
*[[Stochastic volatility]]
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