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

[alexios ghalalanos]

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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