Box-Pierce Q statistic
by Sam Sam

I am much more confused.
I estimate ARIMA by conditional maximum likelihood and choose the option /residual correlogram/
The Q statistic is Ljung-Box statistic, not Box-Pierce Q statistic. Is it ?
I do not understand. Because I choose the option /help/ and it shows it is Box-Pierce Q stastisitc.
13 years, 7 months

ABOUT SBIC
by Sam Sam

Dear all:
The formulation of the Schwarz Bayesian Information Criterion is -2 × L(θ)+ k log n in gretl user`s guide.
But the gretl output of ARIMA seems cauculated by the formulation of -2 × L(θ)+ k ln n .
Is it log or ln ?
Thanks a lot
13 years, 7 months

Re: [Gretl-users] ARCH and GARCH
by Allin Cottrell

On Tue, 1 Mar 2011 ajzhmkaven(a)hotmail.com wrote:
> So should I just use garch (0 2) for arch (2) ? And assume the
> garch (0 2) is the right one?
You are better using the garch command to estimate an ARCH(2)
model, but you are better still using the right model for the
data, which is surely not ARCH(2) for your NASDAQ returns. Neither
estimator will give "right" results for a wrong specification.
Allin Cottrell
brief back-story:
> On Tue, 1 Mar 2011, zhuhongming wrote:
>
> > I used the data in the attachment to run ARCH (2) and GARCH
> > (0,2), i assumed they would give me the same result but they did
> > not.
>
> They don't give the same results because (a) the estimators are
> completely different and (b) the model is misspecified [...]
13 years, 7 months

Re: [Gretl-users] ARCH and GARCH
by Allin Cottrell

On Tue, 1 Mar 2011, zhuhongming wrote:
> I used the data in the attachment to run ARCH (2) and GARCH
> (0,2), i assumed they would give me the same result but they did
> not.
They don't give the same results because (a) the estimators are
completely different and (b) the model is misspecified. gretl's
"arch" command is not much recommended other than for pedagogical
purposes; it's a rather basic feasible generalized least squares
thing (as explained in the help text), while the "garch" command
does the job properly via Maximum Likelihood.
In some cases the estimates may be fairly close, but I suspect
that misspecification here has something to do with the big gap
between the sets of alpha estimates.
I say the model is misspecified because if you run a GARCH(1,1)
you'll see that it dominates GARCH(0,2): the likelihood is much
higher.
open nasdaq.dat
setobs 1 1 --special
garch 0 2 ; re const
ll02 = $lnl
garch 1 1 ; re const
lldiff = $lnl - ll02
Allin Cottrell
13 years, 7 months

ARCH and GARCH
by zhuhongming

Hi, everyone,
I used the data in the attachment to run ARCH (2) and GARCH (0,2), i assumed they would give me the same result but they did not.
I have the result showing in below:
ARCH (2)
arch 2 re const
Model 1: WLS (ARCH), using observations 3-7837 (n = 7835)
Dependent variable: re
Variable used as weight: 1/sigma
coefficient std. error t-ratio p-value
----------------------------------------------------------
const 0.000515703 0.000109897 4.693 2.74e-06 ***
alpha(0) 8.11556e-05 6.06157e-06 13.39 1.96e-40 ***
alpha(1) 0.225945 0.0109590 20.62 5.15e-92 ***
alpha(2) 0.243682 0.0109590 22.24 2.85e-106 ***
Statistics based on the weighted data:
Sum squared resid 6676.296 S.E. of regression 0.923158
R-squared 0.000000 Adjusted R-squared 0.000000
Log-likelihood −10490.44 Akaike criterion 20982.87
Schwarz criterion 20989.84 Hannan-Quinn 20985.26
Statistics based on the original data:
Mean dependent var 0.000487 S.D. dependent var 0.012371
Sum squared resid 1.198934 S.E. of regression 0.012371
GARCH ( 0,2)
Model 2: GARCH, using observations 1-7837
Dependent variable: re
Standard errors based on Hessian
coefficient std. error t-ratio p-value
----------------------------------------------------------
const 0.00104076 9.69109e-05 10.74 6.65e-27 ***
alpha(0) 4.16523e-05 1.26856e-06 32.83 1.91e-236 ***
alpha(1) 0.400826 0.0222482 18.02 1.46e-72 ***
alpha(2) 0.437669 0.0224141 19.53 6.53e-85 ***
Mean dependent var 0.000486 S.D. dependent var 0.012370
Log-likelihood 25033.25 Akaike criterion −50056.50
Schwarz criterion −50021.67 Hannan-Quinn −50044.57
Unconditional error variance = 0.000257901
Likelihood ratio test for (G)ARCH terms:
Chi-square(2) = 3457.91 [0]
the Code i used is
open nasdaq.dat
arch 2 re const
garch 0 2; re
Can anyone help me explain why they are not the same?
13 years, 7 months