Dear all,
Portmanteau testing for
randomness........
I'm thinking that you might read
p 310 Brockwell & Davis
p 111-112 Kendall and Ord
p 153 Cryer.
Q testing is fairly primitive. Considered by
many to be unreliable.
But its your choice
----- Original Message -----
Sent: Tuesday, March 01, 2011 7:40
PM
Subject: 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)
UPV/EHU Avda. Lehendakari Aguirre, 83 | 48015
BILBAO
T.: +34 946013732 | F.: +34 946013754
www.ea3.ehu.es
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