- Volatility clustering
In

finance ,**volatility clustering**refers to the observation, as noted by Mandelbrot, that "large changes tend to be followed by large changes, of either sign, and small changes tend to be followed by small changes." A quantitative manifestation of this fact is that, while returns themselves are uncorrelated, absolute returns |rt| or their squares display a positive, significant and slowly decaying autocorrelation function: corr(|rt|, |rt+τ |) > 0 for τ ranging from a few minutes to a several weeks.Observations of this type in financial time series have led to the use of

GARCH models in financial forecasting andderivatives pricing. TheARCH (Engle, 1982) andGARCH (Bollerslev, 1986) models aim to more accurately describe the phenomenon of volatility clustering and related effects such askurtosis . 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 assetvolatility tends to revert to some mean rather than remaining constant or moving inmonotonic fashion over time.**ee also***

Stochastic volatility

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