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'''Volatility Clustering''': as noted by Mandelbrot, “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 and [[derivatives]] pricing. The [[ARCH]] (Engle, 1982) and [[GARCH]] (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]] tends to revert to some mean rather than remaining constant or moving in [[monotonic]] fashion over time.
{{econ-stub}}
[[Category:Time Series]]
[[Category:Derivatives]]
[[Category:Stock market]]
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