Volatility clustering

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. 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.