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Residuals of VARMA-GARCH Model
Posted: Tue Jun 13, 2017 9:12 am
by lirona
Hello,
I estimate a VARMA-GARCH(1,1,1,1) Model according to Ling & McAleer (2003). I use the following code:
garch(p=1,q=1,mv=cc,variances=varma,pmethod=simplex,piters=10,rvectors=rd) / oil gas
Can anyone tell me how to get the residuals as a time series of this model for diagnostic checking?
Thank you!
Re: Residuals of VARMA-GARCH Model
Posted: Tue Jun 13, 2017 9:55 am
by TomDoan
The diagnostics are the same for any multivariate GARCH model. See
https://estima.com/docs/RATS%209%20User ... f#page=331. The GARCHMV.RPF example also includes some example code for this.
Re: Residuals of VARMA-GARCH Model
Posted: Thu Jun 15, 2017 1:59 am
by lirona
Thank you for your answer!
I have one more question: using this code I receive only the estimates for the GARCH part of the model but not for the VARMA part. How can I get this?
btw: I tried it this way but it didn't work and includes VAR only but not VARMA which must be:
Code: Select all
equation(constant) wti
equation(constant) brent
group ar1 wti brent
garch(p=1,q=1,model=ar1,mv=cc,pmethod=simplex,piter=10) / wti brent
Re: Residuals of VARMA-GARCH Model
Posted: Thu Jun 15, 2017 8:05 am
by TomDoan
You left the VARIANCES=VARMA option off that last try.
Re: Residuals of VARMA-GARCH Model
Posted: Thu Jun 15, 2017 8:21 am
by lirona
Thanks, I didn't see this. I corrected it but the error message is still the same. I definitely have no typing errors in my variable names. Do you have an idea?
Thank you in advance!
My code:
Code: Select all
equation(constant) sp500
equation(constant) brent
group ar1 sp500 brent
garch(p=1,q=1,model=ar1,variances=varma,mv=cc,pmethod=simplex,piter=10) / sp500 brent
The error message:
Code: Select all
## SX11. Identifier AR1 is Not Recognizable. Incorrect Option Field or Parameter Order?
>>>>(p=1,q=1,model=ar1,<<<<
If the name isn't mistyped, it's possible that you have a poorly formatted instruction
Common errors are
* a space before the ( in an option field
* a missing space before = in a SET or FRML
* a missing $ at the end of a long line which continues to the next
Re: Residuals of VARMA-GARCH Model
Posted: Thu Jun 15, 2017 8:49 am
by TomDoan
You have to make sure you execute all four of those instructions. (Select the four, then hit the running icon).
Re: Residuals of VARMA-GARCH Model
Posted: Thu Jun 15, 2017 9:07 am
by lirona
This leads me to a new error message:
Can you tell me what this is about? I tried to figure it out but failed.
Code: Select all
## SX22. Expected Type EQUATION, Got SERIES[REAL] Instead
>>>>on(constant) sp500<<<<
How to modify this code to get VARMA-GARCH (Ling & McAleer) instead of VAR-GARCH?
Thank you so much!
Re: Residuals of VARMA-GARCH Model
Posted: Thu Jun 15, 2017 9:20 am
by TomDoan
What exactly is your intended model for the mean? If you just want intercepts, you can just do
garch(p=1,q=1,variances=varma,mv=cc,pmethod=simplex,piter=10) / sp500 brent
without the first three instruction. If (based upon your name), you want to do separate AR1 models for each series, then you want
equation sp500eq sp500
# constant sp500{1}
equation brenteq brent
# constant brent{1}
group ar1 sp500eq brenteq
garch(p=1,q=1,model=ar1,variances=varma,mv=cc,pmethod=simplex,piter=10)
The first parameter in an EQUATION instruction is the name of the equation you're defining; it's the second that has the dependent variable.
I would note, however, that a VARMA-CC is unlikely to be a good choice for that pair of variables. CC and DCC really aren't designed for a pair of series with relatively little in common.
Re: Residuals of VARMA-GARCH Model
Posted: Thu Jun 15, 2017 9:31 am
by lirona
Thank you for your answer!
My mean model must be VARMA(1,1). Using your code, I receive VAR(1) model for the mean plus the GARCH-part in the output. So, the MA(1) part is still missing. It is important that the estimated model is the VARMA-GARCH according to Ling & McAleer in the end. How can I add the MA(1) part to this?
Thank you for your hint concerning the choice of model, too. These variables are only part of my model choice, so I guess that including other variables (instead or in addition) will improve my model.
Re: Residuals of VARMA-GARCH Model
Posted: Thu Jun 15, 2017 9:42 am
by TomDoan
I think you're confusing VARMA for the mean with VARMA for the variance process---the latter is what Ling and McAleer do. If those are SP500 and BRENT returns, you most certainly do not want a VARMA mean model---that's going to be overparameterized.
Re: Residuals of VARMA-GARCH Model
Posted: Thu Jun 15, 2017 9:55 am
by lirona
I want the VARMA-GARCH model (the volatility model) of Ling and McAleer with the option of asymmetric shocks etc. I have never heard of the other VARMA-GARCH model, so I made the mistake.
Now, I am confused. The last code was for the wrong VARMA-GARCH model, do I understand you right?
So the code for the Ling & McAleer (2003,2009) model with matrices of VMA; VAR; ARCH; GARCH is my first code? This one:
Code: Select all
garch(p=1,q=1,mv=cc,variances=varma,pmethod=simplex,piters=10,rvectors=rd) / oil gas
But where are the VAR; VMA matrices there?
Re: Residuals of VARMA-GARCH Model
Posted: Thu Jun 15, 2017 10:38 am
by TomDoan
VARIANCES=VARMA is described in the User's Guide, and the output is described in the help:
https://estima.com/ratshelp/garchmvrpf. ... tput_VARMA
VARMA is the name they apply to their variance calculation based upon similarities to a regular VARMA model from the time series literature. The "VAR" are the lagged variances and the "MA" are the lags of the squared residuals.
The two examples above are both of CC-VARMA models---the first has a mean-only mean model, the second has univariate AR(1)'s. But the only difference between those is how they handle the mean---the variance model is the same.
Re: Residuals of VARMA-GARCH Model
Posted: Thu Jun 15, 2017 10:53 am
by lirona
Thank you. I have already read the manual before but it didn't help me get the model with the output I am searching for.
Ling & McAleer state a VARMA-GARCH model with VARMA conditional mean equation and GARCH conditional variance equation. Lateron, they advanced this model by an asymmetric component. These are the models I am searching for. That is why, there is not enough information in the output using the code
Code: Select all
garch(p=1,q=1,mv=cc,variances=varma,pmethod=simplex,piters=10,rvectors=rd) / oil gas
since the conditional mean (VARMA) part is not included. The VARMA part includes matrices for VMA and VAR and a constant. I need these outputs as well as I am searching for the "full" VARMA-GARCH model. Salisu & Oloko (2015) used this for their research for example.
Now, I hope that we now about what kind of model we are talking.
So, can you help me finding the right code for this, please?
Re: Residuals of VARMA-GARCH Model
Posted: Thu Jun 15, 2017 1:25 pm
by TomDoan
While McAleer and his co-authors have several papers describing the theory of GARCH models with VARMA means, in practice they typically stick to the simpler VAR(1) or AR(1) (which I assume means univariate AR's rather than full VAR's). Actual VARMA mean models (meaning having lagged residuals) either don't work or are unnecessarily complicated. (A VAR does just as well). You'll also note that any information about the estimates of the mean parameters are most likely suppressed in favor of behavior of the variance parameters only. We've just posted an example of a VARMA(mean)-GARCH model and it shows exactly the behavior that you would expect in the VARMA estimates.
Re: Residuals of VARMA-GARCH Model
Posted: Thu Jun 15, 2017 2:21 pm
by lirona
Thank you for your answer. I understand your thoughts about the full VARMA-GARCH. Is the code in the example for the full VARMA-GARCH model including the matrices in the VARMA part? (Due to technical problems I can not test it at the moment). I will try with a full VAR(1)-GARCH(1,1) model as well. I think it is the one also included in your example.
Thank you for your help, I hope it will work tomorrow!