Gareth,
First off, please show the likelihood of the 2 estimated models.
Following up from Marc's comments, there are at least 3 things you
should keep in mind when estimating ARMA models (and detailed in well
over 100 lecture notes/papers on the web):
1. Causality: roots of AR part of ARMA lie outside unit circle
2. Invertibility: roots of MA part of ARMA lie outside the unit circle.
3. Redundancy: Check that polynomial of ARMA process have no common factor.
A fast way to check all this is to use the very nice function with plot
from fArma:
>fArma::armaRoots(armacoef)
-Alexios
On 19/09/2014 14:39, Wildi Marc (wlmr) wrote:
> Here's an explanation:
>
> -ARMA-models are not uniquely identified: x_t-a1x_{t-1}=epsilon_t-a1
> epsilon_{t-1} is the same as x_t=epsilon_t i.e. white noise.
>
> -Your two ARMA-models are fakes: both sides of each equality could be
> simplified (AR- and MA lag polynomials are `almost' identical). Stated
> otherwise: in both cases you really just have white noise (efficient market
> hypothesis...)! The spurious differences are due to (generally inocuous)
> differences in numerical algorithms. Since the estimation problem is nearly
> singular, you can obtain substantially different estimates depending on the
> algorithm. Mind you: these estimates are `fakes'.
>
> To summarize: everything's OK. Just simplify your ARMA-model specification.
> ________________________________
> Von: [email protected]
> [[email protected]]" im Auftrag von "Gareth McEwan
> [[email protected]]
> Gesendet: Freitag, 19. September 2014 13:22
> An: [email protected]
> Betreff: [R-SIG-Finance] Different results using "rugarch" and "fGarch"
> packages
>
> Hi Alexios
>
> I am modelling the same data and getting vastly different estimates using
> "rugarch" package and "fGarch" package (all installs and packages have been
> recently downloaded and should be up to date). The data is 242 monthly log
> returns in raw log return format (i.e. not multiplied by 100 to get percent
> format). I have attached the file for reproducible results.
>
> In estimating an ARMA(2,2)-GARCH(1,1) with "normal" errors, I get the
> following output using:
>
> (1) "rugarch" package:
> spec <- ugarchspec(variance.model=list(model="sGARCH",garchOrder=c(1,1),
> submodel=NULL,external.regressors=NULL,variance.targeting=F),
>
> mean.model=list(armaOrder=c(2,2),include.mean=T,external.regressors=NULL),
> distribution.model="norm")
> tempgarch <- ugarchfit(spec=spec,data=ALSI.reg.log.ret,solver="hybrid")
> show(tempgarch)
>
> Output:
> Optimal Parameters
> ------------------------------------
> Estimate Std. Error t value Pr(>|t|)
> mu 0.015107 0.003310 4.56480 0.000005
> ar1 0.561145 0.577557 0.97158 0.331258
> ar2 -0.303709 0.526705 -0.57662 0.564195
> ma1 -0.629355 0.555266 -1.13343 0.257033
> ma2 0.430343 0.511488 0.84135 0.400149
> omega 0.000257 0.000343 0.75094 0.452687
> alpha1 0.197622 0.148026 1.33505 0.181862
> beta1 0.730256 0.228730 3.19265 0.001410
>
> (2) "fGarch" package
> garch.fit=garchFit(formula=~arma(2,2)+garch(1,1),data=ALSI.reg.log.ret,cond.dist="norm",trace=F,include.mean=T)
> summary(garch.fit)
>
> Output:
> Error Analysis:
> Estimate Std. Error t value Pr(>|t|)
> mu 0.0368275 0.0070622 5.215 0.000000184 ***
> ar1 -0.4909910 0.0955405 -5.139 0.000000276 ***
> ar2 -0.8424945 0.0538062 -15.658 < 2e-16 ***
> ma1 0.4733331 0.0904955 5.230 0.000000169 ***
> ma2 0.8844500 0.0550194 16.075 < 2e-16 ***
> omega 0.0003106 0.0001838 1.690 0.0910 .
> alpha1 0.3696620 0.1496237 2.471 0.0135 *
> beta1 0.5808720 0.1434332 4.050 0.000051267 ***
>
> I am confused as to why the output differs to such a great extent. Any idea
> why this is happening?
>
> Thank you very much
> Gareth
>
>
> [[alternative HTML version deleted]]
>
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