[R-SIG-Finance] Problem with estimation results of ARMAX-GARCHX

[Alexios Ghalanos]

I think I've already answered that question and also provided a reference which you can consult (apart from the myriad resources on the internet with regards to this).

Regards,

Alexios

> On 18 Sep 2014, at 14:32, "Philipp Lammers" <Philipp_Lammers at gmx.de> wrote:
> 
> Dear Alexios,
> 
> thank you for taking your time to help me.
> Now I receive the exact results as you do.
> 
> But there is still a difference in the estimation of the external
> parameters, if the ARMAX-GARCH is regarded. Is this due to the limited
> asymptotic efficiency you mentioned?
> 
> Thank you.
> 
> Regards,
> 
> Philipp 
> 
> 
> -----Ursprüngliche Nachricht-----
> Von: alexios ghalalanos [mailto:alexios at 4dscape.com] 
> Gesendet: Donnerstag, 18. September 2014 11:15
> An: Philipp Lammers; r-sig-finance at r-project.org
> Cc: alexios at 4dscape.com
> Betreff: Re: AW: [R-SIG-Finance] Problem with estimation results of
> ARMAX-GARCHX
> 
> Philipp,
> 
> I've checked your data and here are my comments:
> 
>> 
> spec <- arfimaspec(mean.model = list(armaOrder = c(1,
> 1),include.mean=FALSE,arfima=FALSE,
> external.regressors=X),distribution.model ="norm")
> setbounds(spec)<-list(mxreg1=c(-2,2), mxreg2=c(-2,2), mxreg3=c(-2,2))
> fit1 <- arfimafit(spec,data=P)
> fit2 = arima(P, order=c(1,0,1), method="ML",xreg=X, include.mean=FALSE)
> 
> cbind(c(coef(fit1),"LLH"=likelihood(fit1)), c(coef(fit2),
> "sigma"=sqrt(fit2$sigma2), "LLH"=fit2$loglik))
> 
> ar1       0.22517917    0.22668311
> ma1      -0.99999998   -0.99999860
> mxreg1    1.39220340    1.35950370
> mxreg2   -0.04714268   -0.04866735
> mxreg3    0.03632310    0.03341936
> sigma     0.34747055    0.34745002
> LLH    -247.51441921 -250.50795353
> 
> As far as the pure arma estimation goes, I don't see any problems here.
> rugarch and arima are identical (small difference which gives a higher
> likelihood to the rugarch estimation is probably down to start-up recursion
> method).
> 
> As regards the ARMA-GARCH model:
> 
> spec <- ugarchspec(mean.model = list(armaOrder = c(1,
> 1),include.mean=FALSE,arfima=FALSE,
> external.regressors=X),distribution.model ="norm")
> fit3 <- ugarchfit(spec,data=P)
> 
> 
> data.frame("ARMA-GARCH"=c(coef(fit3), "LLH"=likelihood(fit3)))
> 
>          ARMA.GARCH
> ar1      0.709683664
> ma1     -0.997124020
> mxreg1   0.448243364
> mxreg2  -0.031824864
> mxreg3  -0.016998532
> omega    0.001552758
> alpha1   0.315193600
> beta1    0.241478834
> LLH    942.895313178
> 
> The log-likelihood is significantly higher, but the GARCH persistence is not
> very high. If you look at your dataset (P), you have a HUGE spike/outlier.
> Try removing that and re-test for heteroscedasticity...but I am guessing
> that you already know all this since you must have learned it in class?
> 
> Alexios
> 
>> On 18/09/2014 11:42, Philipp Lammers wrote:
>> Dear Alexios,
>> 
>> thank you for your help. Now, I get decent results for AR and MA part 
>> from ugarchfit. These are approximately the same as for arima(). 
>> Nevertheless, the results for the exogenous variables added are still 
>> different between the two functions.
>> 
>> I attachted the data in a .csv file.
>> 
>> Regards,
>> 
>> Philipp
>> 
>> -----Ursprüngliche Nachricht-----
>> Von: alexios ghalalanos [mailto:alexios at 4dscape.com]
>> Gesendet: Donnerstag, 18. September 2014 10:01
>> An: Philipp Lammers; r-sig-finance at r-project.org
>> Cc: alexios at 4dscape.com
>> Betreff: Re: [R-SIG-Finance] Problem with estimation results of 
>> ARMAX-GARCHX
>> 
>> Philipp,
>> 
>> In the presence of heteroscedasticity, there is a loss in the 
>> asymptotic efficiency of the parameter estimates which are no longer 
>> BLUE (see the original ARCH paper by Engle 1982). This effectively 
>> means that for most datasets of length N (where N is some finite 
>> number), the parameters will be somewhat different.
>> In the rugarch package, ARMA-GARCH is jointly estimated.
>> 
>> If you want to compare non-GARCH ARMA with the typical arima function 
>> in R, use the arfimaspec/arfimafit functions (or set the ugarchspec 
>> garchOrder to
>> c(0,0) and the stationarity flag in the fit.control to 0).
>> You should also choose method="ML" for arima.
>> 
>> Regards,
>> 
>> Alexios
>> 
>> PS I could not download your dataset from dropbox (only the code).
>> 
>>> On 18/09/2014 10:35, Philipp Lammers wrote:
>>> Hello everybody,
>>> 
>>> 
>>> 
>>> I am currently facing an estimation problem in the ARMAX-GARCHX model. 
>>> The "rugarch"-package is used for estimation. The problem arises 
>>> because my professor is not satisfied with the estimation results, he 
>>> expects the ARMAX-GARCH results in the mean equation to be the same 
>>> as the normal ARMAX results. But this is not the case and the results 
>>> differ
>> significantly.
>>> 
>>> 
>>> 
>>> I already wrote to the programmer of the rugarch package, who 
>>> thankfully gave me a hint , that the results are different under the 
>>> presence of heteroskedasticity. He recommended me to post to this 
>>> mailing list. Can anybody confirm that the results are different?
>>> Where can I find this issue in the literature?
>>> 
>>> 
>>> 
>>> My R-code can be downloaded from my Dropbox:
>>> https://www.dropbox.com/s/k557ev4lmmnykqu/ARMAGARCH.R?dl=0 .Note that 
>>> the corresponding data will be downloaded from the Dropbox as well, 
>>> when the code is executed.
>>> 
>>> 
>>> 
>>> I hope that you can help me.
>>> 
>>> 
>>> 
>>> Thank you all in advance.
>>> 
>>> 
>>> 
>>> Philipp Lammers
>>> 
>>> 
>>> 
>>> 
>>>    [[alternative HTML version deleted]]
>>> 
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> 
>