Quote from MasterAtWork:
Hi hlpsg,
For broad purpose skewness of datas can be mesured by the third moment about the mean.
So if you got your serie (whatever you want, daily return, daily volatility...),
1-you compute the mean :sum of datas divided by number of datas.
2-you compute the standard deviation : you compute each difference between each data and mean, you compute then the square of each difference, you sum all the squared differences together , you compute the square root of the outcome, you divide the final amount by the number of datas
3-you compute the third moment: you compute each difference between each data and mean (you have already done above), you raise each difference to the third power, you sum all together, you divide the outcome by the number of datas.
Now to get the skewness, you divide the amount above by the standard deviation raised to the third power.
If the distribution is symmetric, the skewness will be zero.
4-you compute the fourth moment: you compute each difference between each data and mean (you have already done above), you raise each difference to the fourth power, you sum all together, you divide the outcome by the number of datas.
Now to get the kurtosis, you divide the amount above by the standard deviation raised to the fourth power.
The kurtosis describes the peakness of the distribution.
This kurtosis is called Pearson kurtosis.
Sometimes, we compute Fisher kurtosis that is Pearson's less 3 (3 is the kurtosis of the normal distribution).
Regards,
