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.
