Volatility clustering
In
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."[1]
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(|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 Granger and Ding (1993)[2] and Ding and Granger (1996)[3] among others; see also.[4] Some studies point further to long-range dependence in volatility time series, see Ding, Granger and Engle (1993)[5] and Barndorff-Nielsen and Shephard.[6]
Observations of this type in financial time series go against simple random walk models and have led to the use of
monotonic
fashion over time.
See also
- GARCH
- Stochastic volatility
References
- ^ Mandelbrot, B. B., The Variation of Certain Speculative Prices, The Journal of Business 36, No. 4, (1963), 394-419
- ^ Granger, C.W. J., Ding, Z. Some Properties of Absolute Return: An Alternative Measure of Risk , Annales d'Économie et de Statistique, No. 40 (Oct. - Dec., 1995), pp. 67-91
- ^ Ding, Z., Granger, C.W.J. Modeling volatility persistence of speculative returns: A new approach, Journal of Econometrics), 1996, vol. 73, issue 1, 185-215
- .
- ^ Zhuanxin Ding, Clive W.J. Granger, Robert F. Engle (1993) A long memory property of stock market returns and a new model, Journal of Empirical Finance, Volume 1, Issue 1, 1993, Pages 83-106
- ISBN 9780470057568.
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