[R-SIG-Finance] About Garch models

Patrick Burns patrick at burns-stat.com
Tue Sep 18 17:52:08 CEST 2012


I'm not a big fan of testing, especially
this form of testing.  My prior is that all
market data experience volatility clustering.

The question is more whether the heteroscedasticity
has an affect on what you are trying to do with
the results of your model.

But to answer your question:  You should never
believe a Ljung-Box test on squared residuals
no matter what the p-value.  The reason is because
the Ljung-Box test (which is really robust) is
not robust enough when used on the squares of a
long-tailed distribution.  The outliers can mess
with the p-value as they wish.

You can trust Ljung-Box tests on the ranks of
squared residuals.

I don't know enough about other tests of autocorrelation
to comment.  But if they don't agree with a rank Ljung-Box
test, then I'd be suspicious.


On 18/09/2012 12:52, jaimie villanueva wrote:
> OK Patrick, Thanks.
> I'm not sure if I've understood this sentence:
> ".If you are used to looking at p-values from goodness of fit tests, you
> might notice something strange.  The p-values are suspiciously close to
> 1.  The tests are saying that we have overfit 1547 observations with 4
> parameters.  That is 1547 really noisy observations.  I don’t think so.
> A better explanation is that the test is not robust to this extreme
> data, even though the test is very robust.  It is probably
> counter-productive to test the squared residuals.  An informative test
> is on the ranks of the squared standardized residuals."
> it is exactly what is happening to me. p-values close to 1.
> What does the sentence mean:
> - Whenever Ljung -Box  p-values close to 1 , never belive it.? or
> - Should I run other type of autocorrelation test?
> best
> Jaimie
> 2012/9/18 Patrick Burns <patrick at burns-stat.com
> <mailto:patrick at burns-stat.com>>
>     You should *not* believe the Ljung-Box
>     test.  For an explanation of why, see:
>     http://www.portfolioprobe.com/__2012/07/06/a-practical-__introduction-to-garch-__modeling/
>     <http://www.portfolioprobe.com/2012/07/06/a-practical-introduction-to-garch-modeling/>
>     Pat
>     On 18/09/2012 11:55, jaimie villanueva wrote:
>         Hi R users,
>         I'm trying to fit an ARMA or GARCH or ARMA/GARCH model over a
>         financial
>         time series of daily Log returns.
>         I've followed the same procedure as most texts are recommending
>         in order to
>         check whether an autocorrelation structure exist (either on
>         residuals or
>         squared residuals) or not. After run the Ljung-Box and LM ARCH
>         test over
>         squared residuals and I realise that NO autocorrelation
>         structure exist, I
>         supposed that, if i try to fit a GARCH model the fitting results
>         would be
>         quite useless.
>         Instead of that, I've found that the fitting was pretty good.
>         The question is: Should I go ahead with the GARCH model or
>         Should i belive
>         the Ljung-Box and LM ARCH test ?.
>         Thanks in advance.
>         Jaimie
>                  [[alternative HTML version deleted]]
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>     Patrick Burns
>     patrick at burns-stat.com <mailto:patrick at burns-stat.com>
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>     twitter: @portfolioprobe

Patrick Burns
patrick at burns-stat.com
twitter: @portfolioprobe

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