Measure quality of fit for MA(q), ARMA(p, q) and GARCH(p, q)

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Measure quality of fit for MA(q), ARMA(p, q) and GARCH(p, q)

Robert A'gata
Hi,

I would like to ask for a guideline on how to assess quality of fit
for MA, ARMA and GARCH process. For AR, it still looks like a
regression for me. So I still can rely on R-square as long as the time
series itself is stationary. However, for MA, ARMA or GARCH, I do not
know what measure I should use to assess fit quality. Any suggestions
would be appreciated. Thank you.

Robert

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Re: Measure quality of fit for MA(q), ARMA(p, q) and GARCH(p, q)

Patrick Burns-2
A common thing to do is the Ljung-Box
test on the residuals.  For garch it
would be the residuals squared.

Actually for garch it should be the
rank of the squared residuals -- see
http://www.burns-stat.com/pages/Working/ljungbox.pdf

However, this is an in-sample test.  Much
better is to do out-of-sample tests.

On 04/06/2011 04:46, Robert A'gata wrote:

> Hi,
>
> I would like to ask for a guideline on how to assess quality of fit
> for MA, ARMA and GARCH process. For AR, it still looks like a
> regression for me. So I still can rely on R-square as long as the time
> series itself is stationary. However, for MA, ARMA or GARCH, I do not
> know what measure I should use to assess fit quality. Any suggestions
> would be appreciated. Thank you.
>
> Robert
>
> _______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-finance
> -- Subscriber-posting only. If you want to post, subscribe first.
> -- Also note that this is not the r-help list where general R questions should go.
>

--
Patrick Burns
[hidden email]
http://www.burns-stat.com
http://www.portfolioprobe.com/blog
twitter: @portfolioprobe

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Re: Measure quality of fit for MA(q), ARMA(p, q) and GARCH(p, q)

alexios
For out of sample in particular you might like to look at the Predictive
Density Tests (e.g. Berkowitz), and maybe Directional Accuracy Tests
(e.g. Pesaran & Timmermann, Anatolyev & Gerko).

Best,
Alexios Ghalanos

On Sat, 2011-06-04 at 08:36 +0100, Patrick Burns wrote:

> A common thing to do is the Ljung-Box
> test on the residuals.  For garch it
> would be the residuals squared.
>
> Actually for garch it should be the
> rank of the squared residuals -- see
> http://www.burns-stat.com/pages/Working/ljungbox.pdf
>
> However, this is an in-sample test.  Much
> better is to do out-of-sample tests.
>
> On 04/06/2011 04:46, Robert A'gata wrote:
> > Hi,
> >
> > I would like to ask for a guideline on how to assess quality of fit
> > for MA, ARMA and GARCH process. For AR, it still looks like a
> > regression for me. So I still can rely on R-square as long as the time
> > series itself is stationary. However, for MA, ARMA or GARCH, I do not
> > know what measure I should use to assess fit quality. Any suggestions
> > would be appreciated. Thank you.
> >
> > Robert
> >
> > _______________________________________________
> > [hidden email] mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-sig-finance
> > -- Subscriber-posting only. If you want to post, subscribe first.
> > -- Also note that this is not the r-help list where general R questions should go.
> >
>

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Re: Measure quality of fit for MA(q), ARMA(p, q) and GARCH(p, q)

Jeffrey Ryan
In reply to this post by Robert A'gata
Intuitively the idea is to have no structure remaining in the residuals.

The practical has been answered by Pat and Alexios.

Jeff

Jeffrey Ryan    |    Founder    |    [hidden email]

www.lemnica.com

On Jun 3, 2011, at 10:46 PM, "Robert A'gata" <[hidden email]> wrote:

> Hi,
>
> I would like to ask for a guideline on how to assess quality of fit
> for MA, ARMA and GARCH process. For AR, it still looks like a
> regression for me. So I still can rely on R-square as long as the time
> series itself is stationary. However, for MA, ARMA or GARCH, I do not
> know what measure I should use to assess fit quality. Any suggestions
> would be appreciated. Thank you.
>
> Robert
>
> _______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-finance
> -- Subscriber-posting only. If you want to post, subscribe first.
> -- Also note that this is not the r-help list where general R questions should go.

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Re: Measure quality of fit for MA(q), ARMA(p, q) and GARCH(p, q)

Robert A'gata
In reply to this post by Patrick Burns-2
Thank you so much all for your invaluable inputs.

On Sat, Jun 4, 2011 at 3:36 AM, Patrick Burns <[hidden email]> wrote:

> A common thing to do is the Ljung-Box
> test on the residuals.  For garch it
> would be the residuals squared.
>
> Actually for garch it should be the
> rank of the squared residuals -- see
> http://www.burns-stat.com/pages/Working/ljungbox.pdf
>
> However, this is an in-sample test.  Much
> better is to do out-of-sample tests.
>
> On 04/06/2011 04:46, Robert A'gata wrote:
>>
>> Hi,
>>
>> I would like to ask for a guideline on how to assess quality of fit
>> for MA, ARMA and GARCH process. For AR, it still looks like a
>> regression for me. So I still can rely on R-square as long as the time
>> series itself is stationary. However, for MA, ARMA or GARCH, I do not
>> know what measure I should use to assess fit quality. Any suggestions
>> would be appreciated. Thank you.
>>
>> Robert
>>
>> _______________________________________________
>> [hidden email] mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-sig-finance
>> -- Subscriber-posting only. If you want to post, subscribe first.
>> -- Also note that this is not the r-help list where general R questions
>> should go.
>>
>
> --
> Patrick Burns
> [hidden email]
> http://www.burns-stat.com
> http://www.portfolioprobe.com/blog
> twitter: @portfolioprobe
>

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