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This reminds me of a paper by Rama Cont: "Empirical properties of asset returns: stylized facts and statistical issues.". You can download here: http://www.cmap.polytechnique.fr/~rama/papers/empirical.pdf He also has a paper on volatility clustering: "Volatility clustering in financial markets: empirical facts and agent-based models.", which may be of your ...
Stationarity. The distribution of returns is non-stationary. Moreover, standard deviation of returns is not constant over time. Symmetry. The distribution of returns is approximately symmetric with increasing leptokurtosis as sampling frequency increases. However, large drawdowns are not matched with equally large upward movements. Gaussian behavior. ...
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