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
Problem with estimation results of ARMAX-GARCHX
6 messages · Alexios Ghalanos, Philipp Lammers
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 at 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.
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 -----Urspr?ngliche 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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should go.
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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 -----Urspr?ngliche 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]]
_______________________________________________ R-SIG-Finance at 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.
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 -----Urspr?ngliche 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 -----Urspr?ngliche 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]]
_______________________________________________ R-SIG-Finance at 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.
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 -----Urspr?ngliche 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 -----Urspr?ngliche 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]]
_______________________________________________ R-SIG-Finance at 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.