
'Q-Statistics on Standardized Residuals' will be reported as the output of the ugarchfit function.
Here is my sample code (I use ARMA(2,1), t-GARCH(1,1) to estimate the volatility series, rate is the exogenous variable.):
spec=ugarchspec(variance.model=list(model="eGARCH",garchOrder=c(1,1),submodel=NULL, 
external.regressors=as.matrix(rate), variance.targeting = FALSE),
mean.model = list(armaOrder = c(2,1), include.mean = TRUE, garchInMean = FALSE,
inMeanType = 1, arfima = FALSE, external.regressors =as.matrix(rate)), distribution.model = "std",
start.pars = list(mxreg1=0.01,vxreg1=3), fixed.pars = list())
fit=ugarchfit(spec,data=volatility)
fit
 
Here is the output,
Q-Statistics on Standardized Residuals
------------------------------------
      statistic   p-value
Lag10     20.22 0.0051156
Lag15     26.46 0.0092400
Lag20     44.40 0.0002987
H0 : No serial correlation
Q-Statistics on Standardized Squared Residuals
------------------------------------
      statistic   p-value
Lag10     13.05 0.0709829
Lag15     37.01 0.0002226
Lag20     38.44 0.0021370
ARCH LM Tests
------------------------------------
             Statistic DoF P-Value
ARCH Lag[2]      1.790   2  0.4085
ARCH Lag[5]      6.719   5  0.2424
ARCH Lag[10]    14.399  10  0.1555

My question is 
(1) Are  the Standardized Residuals  in 'Q-Statistics on Standardized Residuals'  equal to residuals(fit)/sigma(fit)Јї
(2) If the p value for the 'Q-Statistics on Standardized Residuals' is very small, like the case in my post,
should I adjust the ARMA model or GARCH model or both?

Thanks,
Juan Lin

 

> Date: Sat, 11 Feb 2012 22:07:22 +0000
> From: alexios@4dscape.com
> To: baskins89@gmail.com
> CC: r-sig-finance@r-project.org
> Subject: Re: [R-SIG-Finance] ugarchfit() ARCH LM tests contradict ArchTest()?
> 
> Hi Brian,
> 
> Testing on the ARMA (or other filtration) residuals should be done prior 
> to the estimation to test for the presence of ARCH effects. Once a GARCH 
> model is fitted, then you need to incorporate this information by using 
> the residuals standardized by the conditional sigma of the GARCH model. 
> The details of all tests used in the rugarch package are detailed in the 
> vignette.
> 
> Regards,
> Alexios
> 
> On 11/02/2012 21:58, Brian Askins wrote:
> > Thank you for posting that, Alexios. I was working on code for an
> > example (because my current code is homework code so I cannot post it)
> > but you showed me what was different. I was doing the ArchTest on the
> > residuals, not the standardized residuals. This makes much more sense now.
> >
> > My apologies for not including code in the first post, I'll be sure to
> > include a working example in all future posts.
> >
> > Thanks again everyone, I'll let the other people in my class know what
> > was going on with this.
> >
> > --Brian
> >
> > On Sat, Feb 11, 2012 at 1:45 PM, alexios <alexios@4dscape.com
> > <mailto:alexios@4dscape.com>> wrote:
> >
> > I find that they agree completely:
> >
> > library(rugarch)
> > data(dji30ret)
> > fit = ugarchfit(ugarchspec(),__dji30ret[,1])
> >
> > # The ARCH LM Test on the squared standardized residuals shows:
> > ARCH LM Tests
> > ------------------------------__------
> > Statistic DoF P-Value
> > ARCH Lag[2] 0.6795 2 0.7119
> > ARCH Lag[5] 1.9091 5 0.8616
> > ARCH Lag[10] 4.2709 10 0.9343
> >
> > z = residuals(fit)/sigma(fit)
> >
> > library(FinTS)
> > ArchTest(z, 2)
> > Chi-squared = 0.6795, df = 2, p-value = 0.7119
> > ArchTest(z, 10)
> > Chi-squared = 4.2709, df = 10, p-value = 0.9343
> >
> > i.e. EXACTLY the same.
> >
> > Regards,
> > Alexios
> >
> >
> > On 11/02/2012 21:14, Brian G. Peterson wrote:
> >
> > On Sat, 2012-02-11 at 12:50 -0800, Brian Askins wrote:
> >
> > Hello all,
> >
> > My name is Brian Askins and I'm a student at the University
> > of Washington
> > currently working on an M.S. in computational finance. Our
> > current homework
> > is to fit a few GARCH models and do some diagnostic tests on
> > them, one of
> > which is an LM test on the residuals to make sure there is
> > no more
> > autocorrelation among them. If I use the ArchTest() function
> > from the FinTS
> > package the results make sense and match (to a degree of
> > error) a manual
> > test that I coded to check this. However, the results from
> > that are
> > completely different from the results shown in the output of
> > ugarchfit()
> > under the section "ARCH LM Tests." This also confused other
> > people in the
> > class, including the TA. So can anyone tell me a little more
> > information
> > about this discrepancy? I can't find any information on the
> > LM test
> > performed in ugarchfit() from any of the documentation in
> > the rugarch
> > package. Any help or pointers on where to find this
> > information would be
[[elided Hotmail spam]]
> >
> >
> > Brian,
> >
> > It would help everyone out if you followed the posting guide and
> > took
> > some time to create a reproducible example that demonstrates
> > what you're
> > talking about. From your question, you've obviously already
> > written the
> > code, and the data is probably readily available, so roll it up,
> > comment
> > it, and be specific about the differences that are confusing you.
> >
> > Regards,
> >
> > - Brian
> >
> >
> >
> 
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