I have financial data (prices) which are believed to be q-Gaussian. I want to measure the dispersion for fixed periods in the dataset. Which tool is better, the mean absolute deviation, the coefficient of variation, the deviation from the center of gravity, or something like the fano factor?

The idea is to subtract price from the average of n periods, and then divide by the dispersion factor. I already tried the mean absolute deviation, but I don't like the outcome.

  • $\begingroup$ Why didn't you like the outcome? What happened & what would constitute a 'better' outcome? $\endgroup$ – gung - Reinstate Monica Aug 8 '16 at 17:03
  • $\begingroup$ the results didn't seem to add any value for analysis of change in behavior $\endgroup$ – steve huim Aug 10 '16 at 17:37

The q-Gaussian distribution has undefined/infinite mean and variance for certain values of the parameters. So, dispersion measures that use the mean and variance are very sensitive to the presence of outliers, and perhaps inappropriate to describe data modeled with heavy tailed distributions. An alternative measure is the Median absolute deviation, which is less sensitive to the presence of outliers and does not assume the existence of any moments.


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