Volatility clustering

<p>In <a href="/facts/Finance/fLh1GgN8">finance</a>, volatility clustering refers to the observation, first noted by <a href="/facts/Beno%C3%AEt_Mandelbrot/fa8tKP93">Mandelbrot</a> (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 
  
    
      
        
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 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 several weeks. This empirical property has been documented in the 90's by <a href="/facts/Clive_Granger/GtKQHHE9">Granger</a> and Ding (1993)  and Ding and <a href="/facts/Clive_Granger/GtKQHHE9">Granger</a> (1996) among others; see also. Some studies point further to long-range dependence in volatility time series, see Ding, Granger and <a href="/facts/Robert_F._Engle/EcBW9M2w">Engle</a> (1993) and Barndorff-Nielsen and Shephard.
</p><p>Observations of this type in financial time series go against simple random walk models and have led to the use of <a href="/facts/GARCH/CyPM79ao">GARCH</a> models and mean-reverting <a href="/facts/Stochastic_volatility/d5zBCcUP">stochastic volatility</a> models in financial forecasting and <a href="/facts/Derivative_(finance)/jx4CbakW">derivatives</a> pricing. The <a href="/facts/ARCH/CyPM79ao">ARCH</a> (<a href="/facts/Robert_F._Engle/EcBW9M2w">Engle</a>, 1982) and GARCH (<a href="/facts/Tim_Bollerslev/2BDkYBQ8">Bollerslev</a>, 1986) models aim to more accurately describe the phenomenon of volatility clustering and related effects such as <a href="/facts/Kurtosis/yqGgry89">kurtosis</a>. The main idea behind these two 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 <a href="/facts/Volatility_(finance)/mCdus1MW">volatility</a> tends to revert to some mean rather than remaining constant or moving in <a href="/facts/Monotonic/MjQK0YL2">monotonic</a> fashion over time.
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Volatility clustering open-in-new

Volatility clustering