- Volatility clustering
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
GARCHmodels in financial forecasting and derivativespricing. 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 volatilitytends to revert to some mean rather than remaining constant or moving in monotonicfashion over time.
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