Re: [Gretl-users] Box-Pierce Q statistic
El 01/03/11 08:32, Sam Sam escribió:
Dear all:
The Q statistic to test if the series is white noise in gretl is
Box-Pierce Q statistic, is it ?
If you are talking about what appears in the ouput text window of the
correlogram. I think although in the help it is said to be the
Box-Pierce Q statistic, really it is the Ljung-Box statistic
If you apply an ols regression to a time series, you may test for
autocorrelation via the "test" menu. In such a case the output text
window shows a Q' estatistic, correctly described as Ljung-Box
But I can not find its formulation in gretl.
Is the formulation of Q statistic the same as the reference of Box &
Pierce (1970) ?
I think gretl is using in both places the Ljung-Box statistic:
(in latex format)
Q'= T(T+2)\sum_{j=1}^M (r_j)^2/(T-j)
being M the number of coeficients you want to test, T the number of
observations and r_j the sample autocorrelation coeficient of order j.
Q' has a chi-square asymptotic distribution with M-p-q degrees of freedom.
It is asymptotically equivalent to the Box-Pierce statistic but has an
smaller bias in small samples. So I think we should always prefer to use
Ljung-Box Q' instead of Box-Pierce Q.
--
Ignacio Diaz-Emparanza
DEPARTAMENTO DE ECONOMÍA APLICADA III (ECONOMETRÍA Y ESTADÍSTICA)
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