Volatility clustering

In finance, volatility clustering refers to the observation, as noted as 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." A quantitative manifestation of this fact is that, while returns themselves are uncorrelated, absolute returns or their squares display a positive, significant and slowly decaying autocorrelation function: corr(|r_t|, |r_t+τ |) > 0 for τ ranging from a few minutes to several weeks.