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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 }}
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.{{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==
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