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:alex...@4dscape.com] > Gesendet: Donnerstag, 18. September 2014 10:01 > An: Philipp Lammers; r-sig-finance@r-project.org > Cc: alex...@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]] >> >> _______________________________________________ >> R-SIG-Finance@r-project.org mailing list >> https://stat.ethz.ch/mailman/listinfo/r-sig-finance >> -- Subscriber-posting only. If you want to post, subscribe first. >> -- Also note that this is not the r-help list where general R questions > should go. >> _______________________________________________ R-SIG-Finance@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.