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CC-VARMA model
Posted: Sat Sep 06, 2014 7:09 am
by econo
Dear Friends;
I am trying to run mGARCH models for log-return oil prices & H index. (bi-variate) :
So I run this code in RATS 8.0 :
Code: Select all
open data Y1_O_A.xls
data(format=xls,org=columns) / O A
compute gstart=2,gend=2000
garch(p=1,q=1,mv=CC,variance=varma,pmethod=simplex,piters=5,hmatrices=hh, rvectors=rv) gstart gend O A
and I got this results:
Code: Select all
MV-GARCH, CC with VARMA Variances - Estimation by BFGS
Log Likelihood 12223.0018
Variable Coeff Std Error T-Stat Signif
************************************************************************************
1. Mean(1) 3.3466e-004 4.0690e-004 0.82246 0.41081547
2. Mean(2) 6.4086e-004 2.7855e-004 2.30071 0.02140775
3. C(1) 3.6206e-006 1.6079e-006 2.25172 0.02434008
4. C(2) -1.9890e-008 4.4641e-007 -0.04455 0.96446242
5. A(1,1) 0.0522 8.9554e-003 5.83329 0.00000001
6. A(1,2) -6.3090e-003 0.0113 -0.55932 0.57594292
7. A(2,1) -9.6068e-003 6.7144e-003 -1.43077 0.15249594
8. A(2,2) 0.0520 9.7580e-003 5.32894 0.00000010
9. B(1,1) 0.9312 0.0141 66.11622 0.00000000
10. B(1,2) 0.0969 0.0710 1.36506 0.17223538
11. B(2,1) 0.0952 0.0439 2.16951 0.03004371
12. B(2,2) 0.9355 0.0119 78.88939 0.00000000
13. R(2,1) 0.1271 0.0204 6.22132 0.00000000
Now, I have these questions and appreciate if somebody can help.
1. the parameters are a little bit different from the original paper:
Here I have A , B matrices which I assume are alpha & betas in table 4 of paper. (then how can calculate alpha+beta ? is it A(1,1)+B(1,1) and A(2,2)+B(2,2) ??
2.Then what is R(2,1) ?
3.is Mean (1) the same as AR ?
4.is mean (2) the same as MA?
thanks in advance.
Re: VARMA GARCH Model
Posted: Sat Sep 06, 2014 11:03 am
by TomDoan
omid_ie wrote:Dear Friends;
I am trying to run VARMA-GARCH models for log-return oil prices & HS300 index. (bi-variate) according to table 4 of Prof. McAleer and Prof. Chang paper:
http://ideas.repec.org/p/kyo/wpaper/743.html
They're doing ARMA mean models combined with McAleer CC-VARMA-GARCH. You're not doing the ARMA mean model. The other questions are answered in the other post.
They note that they did this with RATS 6.2. Have you asked them for the code?
Re: CC-VARMA model
Posted: Sat Sep 06, 2014 11:10 am
by econo
This is prof. McAleer answer :
"As an alternative, if you want to estimate VARMA-GARCH and VARMA-AGARCH using RATS, set MV = CC, VARIANCES = VARMA for VARMA-GARCH, and add ASYMMETRIC for VARMA-AGARCH."
I think, they are using ARMA (1,1) mean , VARMA GARCH. Then How can I adjust rats code with this?
Re: VARMA GARCH Model
Posted: Sat Sep 06, 2014 1:00 pm
by TomDoan
I would recommend not trying to do the ARMA(1,1) for the mean. The constant alone seems to be sufficient. Run the simpler model and do the diagnostics before doing a more complicated mean model that (at least for their data) seems to be unnecessary.
CC-VARMA model
Posted: Sat Sep 06, 2014 2:17 pm
by econo
TomDoan wrote: The constant alone seems to be sufficient. Run the simpler model and do the diagnostics before doing a more complicated mean model that (at least for their data) seems to be unnecessary.
Thanks a lot.
the interpretation is next problem:
you said the constant alone seems to be sufficient:
but the Mean(1) is not sufficient,the same for C(2).
Code: Select all
1.Mean(1) 3.3466e-004 4.0690e-004 0.82246 0.41081547
2. Mean(2) 6.4086e-004 2.7855e-004 2.30071 0.02140775
3. C(1) 3.6206e-006 1.6079e-006 2.25172 0.02434008
4. C(2) -1.9890e-008 4.4641e-007 -0.04455 0.96446242
13. R(2,1) 0.1271 0.0204 6.22132 0.00000000
so can you explain it more?
Re: VARMA GARCH Model
Posted: Sat Sep 06, 2014 2:21 pm
by TomDoan
There's no a priori reason to expect that the mean will be significant.
The c can be insignificant if the model (or at least that equation) is borderline IGARCH---see if b(2) and a(2) add up to very close to 1.
BTW, multiply those series by 100 to get the scale up on the mean and C coefficients.
CC-VARMA model
Posted: Sat Sep 06, 2014 3:12 pm
by econo
Ok , this is results where the variables are multiplied by 100
Code: Select all
Variable Coeff Std Error T-Stat Signif
************************************************************************************
1. Mean(1) 0.033465914 0.040926943 0.81770 0.41352917
2. Mean(2) 0.064086122 0.028401883 2.25640 0.02404534
3. C(1) 0.036206243 0.014510638 2.49515 0.01259033
4. C(2) -0.000199065 0.004717736 -0.04220 0.96634316
5. A(1,1) 0.052239319 0.009027327 5.78680 0.00000001
6. A(1,2) -0.006309001 0.011013540 -0.57284 0.56675276
7. A(2,1) -0.009606734 0.006542144 -1.46844 0.14198522
8. A(2,2) 0.051999486 0.009843136 5.28282 0.00000013
9. B(1,1) 0.931221690 0.013783808 67.55910 0.00000000
10. B(1,2) 0.096910622 0.072215028 1.34197 0.17960473
11. B(2,1) 0.095163376 0.046349974 2.05315 0.04005818
12. B(2,2) 0.935480030 0.012003656 77.93292 0.00000000
13. R(2,1) 0.127138818 0.021361871 5.95167 0.00000000
by " if b(2) and a(2) add up to very close to 1"
do you mean :
A(1,1)+B(1,1) = 0.983461009
A(2,2) + B(2,2) =0.987479516
??
Re: CC-VARMA model
Posted: Sat Sep 06, 2014 3:37 pm
by TomDoan
Note that I created a new thread because the thread you added on to was for a VARMA mean model, not a CC-VARMA model. The two are completely different.
With the VARMA model for the individual variances, it's possible to have one of the constants effectively zero, because the dynamics allow for a non-zero mean coming from the other variable. (You can solve out for the unconditional variance to verify that). That's not true for a regular CC model where a zero C only makes sense for an IGARCH.
Re: CC-VARMA model
Posted: Sun Jan 04, 2015 2:15 pm
by econo
Dear Tom;
based on our discussion, I want to implement VARMA GARCH (Mc aleer) model. so I used this code:
Code: Select all
open data LogReturn.xls
data(format=xls,org=columns) / O S
compute gstart=2,gend=2354
garch(p=1,q=1,mv=CC,variance=varma,pmethod=simplex,piters=5,hmatrices=Varmah, MVHSERIES=VarmaHmatrix, rvectors=Varmarv,STDRESIDS=Varmaeta ) gstart gend O S
set ccorr2 %regstart() %regend() = %cvtocorr(Varmah)(1,2)
open copy Varma-condcor.xls
copy(data,format=xls,org=columns) /ccorr2
open copy VarmaHmatrix.xls
copy(data,format=xls,org=columns) /VarmaHmatrix
open copy VarmaETA.xls
copy(data,format=xls,org=columns) /Varmaeta
the code works properly and ccorr2, gives constant result.
also this is the result of model:
Code: Select all
Variable Coeff Std Error T-Stat Signif
************************************************************************************
1. Mean(O) 4.4539e-004 2.2439e-004 1.98484 0.04716255
2. Mean(S) 2.7720e-004 3.7445e-004 0.74030 0.45911921
3. C(1) 1.0030e-006 4.4469e-007 2.25547 0.02410384
4. C(2) 2.0619e-006 8.4266e-007 2.44685 0.01441117
5. A(1,1) 0.0545 8.9269e-003 6.10448 0.00000000
6. A(1,2) -0.0182 6.2230e-003 -2.92654 0.00342751
7. A(2,1) 6.1094e-003 8.9175e-003 0.68510 0.49327841
8. A(2,2) 0.0450 7.6579e-003 5.87076 0.00000000
9. B(1,1) 0.9399 0.0101 92.90224 0.00000000
10. B(1,2) 0.0389 0.0371 1.04799 0.29464551
11. B(2,1) 0.0444 0.0457 0.97121 0.33144291
12. B(2,2) 0.9436 0.0103 91.47552 0.00000000
13. R(2,1) 0.1398 0.0201 6.96538 0.00000000
Now, as I will use the VarmaETA for other models. Just want to make sure that this is correct?
also, if I am not mistaken the varmaETA will be is a sequence of i.i.d. random vectors, with zero mean and
covariance (gamma). Not Normally distributed??
Re: CC-VARMA model
Posted: Sun Jan 04, 2015 4:11 pm
by TomDoan
omid_ie wrote:Now, as I will use the VarmaETA for other models. Just want to make sure that this is correct?
also, if I am not mistaken the varmaETA will be is a sequence of i.i.d. random vectors, with zero mean and
covariance (gamma). Not Normally distributed??
i.i.d. is overstating it. They are (if the underlying model is correct), uncorrelated across time and having an identity covariance matrix. If the residuals are conditionally Normal, then the standardized residuals will be as well.
Re: CC-VARMA model
Posted: Mon Jan 19, 2015 4:03 am
by econo
Now, in this model ( Mcaleer CC-varma=variance) if I want to change mean equation to VAR(1) or VARMA mean model, how can I do it?
Thanks in advance
Re: CC-VARMA model
Posted: Mon Jan 19, 2015 10:09 am
by TomDoan
The mean model is specified the same way regardless of the form of the GARCH model. See Section 9.4.5 of the (v9) User's Guide. However, I would recommend testing the residuals from the simpler model first. If they pass a test for lack of serial correlation, then there is nothing really to be gained by going to a VAR, and a VARMA model would be almost impossible to fit due to cancellation.
You might want to look into getting the
ARCH/GARCH course.
Re: CC-VARMA model
Posted: Mon Jan 19, 2015 3:01 pm
by econo
Can I define VAR(1), something like this?
Code: Select all
system(model=var)
variables O S
lags 1
det constant u(1){1} u(2){1}
end(system)
*
do i=1,2
set u(i) = 0.0
end do i
garch(p=1,q=1,model=var,mv=CC,variance=varma,pmethod=simplex,piters=5,hmatrices=Varmah, MVHSERIES=VarmaHmatrix, rvectors=Varmarv,STDRESIDS=Varmaeta ) gstart gend O S
Re: CC-VARMA model
Posted: Mon Jan 19, 2015 3:12 pm
by TomDoan
For a VAR(1), you just want:
det constant
You're about halfway towards the setup for a VARMA, which again, I wouldn't recommend. If you find serial correlation in the standardized residuals, start with the simpler VAR. VARMA (mean models) have all kinds of numerical issues; VAR's don't.
Re: CC-VARMA model
Posted: Mon Jan 19, 2015 3:18 pm
by econo
Dear Tom;
I just really want to run VAR(1) with variance following : CCC- VARMA (Mcaleer 2003).
The thing is I dont have just 2 indices it is 31 pairs!!
I will do the test for residuals but as there 31 pairs of data, so still I need to check VAR(1)
so please help me to finish this. thanx a lot.