[R-SIG-Finance] Different results using "rugarch" and "fGarch" packages

[alexios ghalalanos]

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: r-sig-finance-bounces at r-project.org [r-sig-finance-bounces at r-project.org]" im Auftrag von "Gareth McEwan [mcewan.gareth at gmail.com]
> Gesendet: Freitag, 19. September 2014 13:22
> An: r-sig-finance at r-project.org
> 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
> 
> 
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