Re: [Gretl-users] Normality Tests (once again)
On Fri, 9 Nov 2007, I wrote:
On Fri, 9 Nov 2007, Talha Yalta wrote:
> Gujarati's text along with other popular texts such as Hill,
> Griffiths,Lim mentions the Jarque-Bera normality test. Iknow that Lee
> Adkins' ebook offers a gretl script for this test, however, I was
> wondering if this test could be implemented.
I suppose so, though the literature suggests that Doornik-Hansen,
which is what we have, is better.
Let me expand on this a little, since it's an issue that comes up
from time to time.
Both the Jarque-Bera test and the Doornik-Hansen test (which is
derived from an earlier variant by Bowman-Shenton, and is
implemented by gretl) are based on the skewness and kurtosis of
the sample data.
The fact that the third and fourth sample central moments are
involved is what accounts for the 2 degrees of freedom in the
chi-square distribution to which these tests are referred (and not
the placement of the sample data into 2 bins).
As I understand it, the Doornik-Hansen test is better sized in
relation to the chi-square(2) distribution than Jarque-Bera.
That is, if you compute the Jarque-Bera statistic and refer it to
chi-square(2) -- which is the usual approximation -- the resulting
p-values may be quite misleading, even for fairly substantial
samples (e.g. n = 70). See for example
http://www.alglib.net/statistics/hypothesistesting/jarqueberatest.php
To get accurate p-values for Jarque-Bera you need specific
quantiles obtained via Monte Carlo methods. My understanding is
that you can refer the Doornik-Hansen statistic to chi-square(2)
with relative impunity, even for relatively modest sample sizes.
If anyone has information otherwise, please let us know.
Allin.