
Thanks, Peterson. I try to describe the problem more clearly. 

I use rugarch package.  My question is, I fit a AR(1), t-GARCH(1,1) model to the Yen-USD exchange rate from 1995 to 2004
and test whether the parameters change following the introduction of euro.
 
I do it in two steps:
Step 1, fit a AR(1),t-GARCH(1,1) model to Yen-USD exchange rate return from 1995.1 to 2004.12.

The model is as follows, [.] are the coefficients.
y_t=[mu1] + [ar1]*y_{t-1} +epsilon_t
sigma_t^2=[omega1] + [alpha1]*epsilon_{t-1}^2 + [beta1]*sigma_{t-1}^2
epsilon_t/sigma_t~t([shape])
 
My code is as follows, 
spec=ugarchspec(variance.model=list(model="sGARCH",garchOrder=c(1,1)),
mean.model = list(armaOrder = c(1,0), include.mean = TRUE), distribution.model = "std",
start.pars = list(), fixed.pars = list())
fit=ugarchfit(spec,data=returns)
 
I got the following outputs,
------------------------------------
               Estimate       Std. Error  t value     Pr(>|t|)
mu1       -0.032963    0.019254  -1.7120  0.086890
ar1         -0.046786    0.030325  -1.5428  0.122876
omega1   0.004678    0.004578   1.0219   0.306845
alpha1     0.026866    0.011168   2.4056   0.016146
beta1      0.965258    0.016990   56.8131  0.000000
shape      5.527051    0.925862   5.9696    0.000000
 
Step 2: test whether the parameters(mu1, ar1, omega1, alpha1, beta1, shape) change following the introduction of euro. 
 
My idea is to include a dummy vector i, i=1 after the introduction of euro, i=0 before the introduction of euro. 
I calculate i*mu1, i*y_{t-1}, i*omega1, i*epsilon_{t-1}^2 and i*sigma_{t-1}^2 and put them as exogenous variables to see 
whether their parameters ([mu2],[ar2],[omega2], [alpha2],[beta2]) are significant. 
If they are, the parameters change following the introduction of euro. If they are not, the parameters do not change.
 
 
The model becomes,
y_t=[mu] + [ar1]*y_{t-1} + [mu2]*i*mu1 + [ar2]*i*y_{t-1}+varepsilon_t
eta_t^2=[omega] + [alpha1]*varepsilon_{t-1}^2 + [beta1]*eta_{t-1}^2 + [omega2]*i*omega1 + [alpha2]*i*epsilon_{t-1}^2 + [beta2]*i*sigma_{t-1}^2
varepsilon_t/eta_t~t[shape1]
 
 
My code is as follows,
spec=ugarchspec(variance.model=list(model="sGARCH",garchOrder=c(1,1),submodel=NULL, 
external.regressors=as.matrix(i*omega1, i*epsilon_{t-1}^2, i*sigma_{t-1}^2), variance.targeting = FALSE),
mean.model = list(armaOrder = c(1,0), include.mean = TRUE, garchInMean = FALSE,
inMeanType = 1, arfima = FALSE, external.regressors =as.matrix(i*mu1, i*y_{t-1})), distribution.model = "std",
start.pars = list(), fixed.pars = list())
fit=ugarchfit(spec,data=returns)
 
My question is,
(1)How can I get sigma_t^2 from the first step?
(2)Am I right at the step two?
(3)How can I tell whether [shape] changes following the introduction of euro?

Thanks,
Juan Lin

 

> Subject: Re: [R-SIG-Finance] test for the change in the parameters in t-GARCH model
> From: brian@braverock.com
> To: ecsniffer@hotmail.com
> CC: r-sig-finance@r-project.org
> Date: Mon, 27 Feb 2012 05:49:41 -0600
> 
> On Mon, 2012-02-27 at 03:10 +0000, LINJUAN wrote:
> > I fit a AR(1), t-GARCH(1,1) model to the Yen-USD exchange rate from
> > 1995 to 2004. 
> > 
> > I add a dummy variable to the model, which takes the value zero in
> > the pre-euro sample and one in the post-euro sample.
> > 
> > My question is how can I test whether the degree of freedom parameter
> > changes following the introduction of euro?
> > 
> > Thanks,
> > Juan Lin 
> 
> Since there is clearly no 'secret sauce' in this question, it would make
> things easier for everyone else to help you if you posted a
> *reproducible example*.
> 
> 
> -- 
> Brian
> 
 		 	   		  
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