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Re: st: How to calculate kurtosis on left tail and right tail separately?


From   David Hoaglin <dchoaglin@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: How to calculate kurtosis on left tail and right tail separately?
Date   Sun, 14 Apr 2013 08:39:18 -0400

Dear Mengjia,

Moment-based measures such as kurtosis are sensitive to outliers, so
approaches based on quantiles may be a better choice, especially if
you are interested in "great gain and great loss."

You did not mention the numbers of funds and years, but I suggest that
you start with a "normal probability plot" of the data for one year of
one fund.  Unless you have a good reason not to do so, you could
include multiple years for a given fund in a single plot.  I would
expect the plot to show heavier tails, but it will allow you to look
at the behavior of the two tails separately.

Since you have the same number of observations for each combination of
fund and year, it would be easy also to make empirical
quantile-quantile plots for pairs of years in the same fund or pairs
of funds in the same year (and aggregate versions of these).  For a
pair of years, for example, this amounts to sorting the weekly returns
for each year separately and plotting the pairs of ordered values:
(min1, min2), ..., (max1, max2).

Various more-quantitative analyses based on quantiles are possible.

David Hoaglin

On Sun, Apr 14, 2013 at 1:22 AM, 李 梦佳 <limengjia626@163.com> wrote:
> Dear statalist,
>
> I wish to test the kurtosis difference between female- and male-managed funds return to examine the possibility of great gain and great loss separately. The current code leads me to an overall kurtosis value on both tails. Is there any way to calculate the kurtosis value on each tail?
>
> My current code:
> bys Fund Year, egen kurt = kurt (Return)
>
> For each fund at each year, 52 weekly returns are provided.
>
> Thanks and regards,
> Mengjia

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