Kurtosis function

[Will]

I am trying to use the Kurtosis functions to examine the distribution
of a set of errors (forecast - actual). I am comparing the K values to
a histogram of the data.

To test I have deliberately peaked and flattened the distribution by
reducing the error values by 10%, 50% and 90% and increasing the error
values by 200%. The resulting histograms show the changes in
distribution for each adjusted set as you would expect but I am seeing
no change in the corresponding kurtosis values.

Anyone any ideas why this might be?

 

[David Biddulph]

What do you mean by "the error values"? What formula are you using? If you
are merely changing the standard deviation of the distribution, this won't
necessarily change the Kurtosis.

 

[Will]

What do you mean by "the error values"? What formula are you using? If you
are merely changing the standard deviation of the distribution, this won't
necessarily change the Kurtosis.
--
David Biddulph








- Show quoted text -

Thanks for your response.

I'm using forecast minus actual for each case to give a set of net
error readings. There are approx 24,000 readings. I am then applying
the KURT function to the set of net errors and also producing a
histogram of the data.

To vary the distribution I am reducing or increasing those values by a
proportional amount. For example to reduce the net error by 10% I am
taking the original value and multiplying by 0.9. I am applying this
same formula across the entire set of readings and the histogram
changes shape accordingly - when I double the error values I get a
flatter profile with thicker tails, as I reduce the error values I get
a more peaked distribution. Would you not expect the kurtosis value to
change accordingly?

By the way, there is a negative skew to the data i.e. the majority of
the readings are to the positive side of the histogram. Also I ran
KURT and SKEW functions over subsets of the data and that yields
different kurtosis and skewness values for each subset.

I'm a bit new to this - I basically stumbled across kurtosis and
skewness as a possible way of describing the accuracy of a set of
forecasts. We have run into issues with MAPE and other statistical
measures and these functions (in conjunction with histograms to
provide visual indication) would seem to be a useful way of describing
not only the magnitude of error but also the direction in terms of
tendency to over- or under-forecast.

 

[David Biddulph]

I get the impression that you're only changing the scaling factors, but not
actually changing the form of the distribution. If you have one
distribution which is N(0,1) and another which is N(0,10), the second will
be 10 times as wide (and therefore one tenth the height), but the kurtosis
will be unchanged. If you change it from a Normal distribution to another
distribution (uniform for example), then the Kurtosis will change.