Problems when estimating GARCH parameters with fGarch

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Problems when estimating GARCH parameters with fGarch

Curtis Miller
Hello all,

I have encountered bad behavior in fGarch's garchFit() function used for
estimating the parameters of a GARCH model. The estimates behave in
highly erratic ways on simulated data. For example, when beta = 0.2
according to the simulation, the function sometimes estimates beta to be
0.0000001 even for sample sizes as large as 1000, and there are other
irregularities. I believe this behavior is tied to how the numerical
optimizers are computing the parameters.

In my research I planned on using garchFit() from fGarch in a
changepoint detection context. I was hoping to use it to detect
structural change in GARCH parameters. (See, for example, Ling 2007
paper https://arxiv.org/abs/0708.2369 .) But with this behavior I don't
know if such a test using garchFit() is possible; the estimates are too
unreliable.

Has anyone else observed this behavior? Is there a way to get around it?
I'm hoping someone who knows more about this can offer guidance.

I have written a blog post documenting the behavior I observed, with
numerical experiments. Here is a link:
https://ntguardian.wordpress.com/2017/11/02/problems-estimating-garch-parameters-r/


Curtis

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Bob
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Re: Problems when estimating GARCH parameters with fGarch

Bob
Have you tried rugarch or just "garch" in the tseries package?  Reproducible examples are always helpful as well.

> On Nov 2, 2017, at 1:56 PM, Curtis Miller <[hidden email]> wrote:
>
> Hello all,
>
> I have encountered bad behavior in fGarch's garchFit() function used for
> estimating the parameters of a GARCH model. The estimates behave in
> highly erratic ways on simulated data. For example, when beta = 0.2
> according to the simulation, the function sometimes estimates beta to be
> 0.0000001 even for sample sizes as large as 1000, and there are other
> irregularities. I believe this behavior is tied to how the numerical
> optimizers are computing the parameters.
>
> In my research I planned on using garchFit() from fGarch in a
> changepoint detection context. I was hoping to use it to detect
> structural change in GARCH parameters. (See, for example, Ling 2007
> paper https://arxiv.org/abs/0708.2369 .) But with this behavior I don't
> know if such a test using garchFit() is possible; the estimates are too
> unreliable.
>
> Has anyone else observed this behavior? Is there a way to get around it?
> I'm hoping someone who knows more about this can offer guidance.
>
> I have written a blog post documenting the behavior I observed, with
> numerical experiments. Here is a link:
> https://ntguardian.wordpress.com/2017/11/02/problems-estimating-garch-parameters-r/
>
>
> Curtis
>
> _______________________________________________
> [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: Problems when estimating GARCH parameters with fGarch

Curtis Miller
In reply to this post by Curtis Miller
I only recently found out about rugarch. I�m going to try and look into that soon. I tried a quick test on a simulated time series and it seemed to have some similar behavior to what I observed with fGarch but I have not done as complete an investigation.



Curtis



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   1. Re: Problems when estimating GARCH parameters with        fGarch
      (Robert Harlow)


----------------------------------------------------------------------

Message: 1
Date: Fri, 3 Nov 2017 14:45:43 -0600
From: Robert Harlow <[hidden email]>
To: Curtis Miller <[hidden email]>
Cc: "[hidden email]" <[hidden email]>
Subject: Re: [R-SIG-Finance] Problems when estimating GARCH parameters
        with    fGarch
Message-ID: <[hidden email]>
Content-Type: text/plain;       charset=us-ascii

Have you tried rugarch or just "garch" in the tseries package?  Reproducible examples are always helpful as well.

> On Nov 2, 2017, at 1:56 PM, Curtis Miller <[hidden email]> wrote:
>
> Hello all,
>
> I have encountered bad behavior in fGarch's garchFit() function used for
> estimating the parameters of a GARCH model. The estimates behave in
> highly erratic ways on simulated data. For example, when beta = 0.2
> according to the simulation, the function sometimes estimates beta to be
> 0.0000001 even for sample sizes as large as 1000, and there are other
> irregularities. I believe this behavior is tied to how the numerical
> optimizers are computing the parameters.
>
> In my research I planned on using garchFit() from fGarch in a
> changepoint detection context. I was hoping to use it to detect
> structural change in GARCH parameters. (See, for example, Ling 2007
> paper https://arxiv.org/abs/0708.2369 .) But with this behavior I don't
> know if such a test using garchFit() is possible; the estimates are too
> unreliable.
>
> Has anyone else observed this behavior? Is there a way to get around it?
> I'm hoping someone who knows more about this can offer guidance.
>
> I have written a blog post documenting the behavior I observed, with
> numerical experiments. Here is a link:
> https://ntguardian.wordpress.com/2017/11/02/problems-estimating-garch-parameters-r/
>
>
> Curtis
>
> _______________________________________________
> [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: Problems when estimating GARCH parameters with fGarch

Rmetrics mailing list
If the likelihoods for the "erratic" parameter estimates are higher than for the
estimates you consider more plausible, then the program is doing what it should.
Have you checked this? If the parameter estimates do not maximize the likelihood,
can you call the fGARCH or RUGARCH estimation functions with different starting
points? This is a common approach to global optimization.

Vivek Rao
Boston, MA
________________________________
From: Curtis Miller <[hidden email]>
To: "[hidden email]" <[hidden email]>
Sent: Saturday, November 4, 2017 1:57 PM
Subject: Re: [R-SIG-Finance] Problems when estimating GARCH parameters with    fGarch


I only recently found out about rugarch. I�m going to try and look into that soon. I tried a quick test on a simulated time series and it seemed to have some similar behavior to what I observed with fGarch but I have not done as complete an investigation.



Curtis



Sent from Mail<https://go.microsoft.com/fwlink/?LinkId=550986> for Windows 10



________________________________
From: R-SIG-Finance <[hidden email]> on behalf of [hidden email] <[hidden email]>
Sent: Saturday, November 4, 2017 5:00:02 AM
To: [hidden email]
Subject: R-SIG-Finance Digest, Vol 162, Issue 3

Send R-SIG-Finance mailing list submissions to
        [hidden email]

To subscribe or unsubscribe via the World Wide Web, visit
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Today's Topics:

   1. Re: Problems when estimating GARCH parameters with        fGarch
      (Robert Harlow)


----------------------------------------------------------------------

Message: 1
Date: Fri, 3 Nov 2017 14:45:43 -0600
From: Robert Harlow <[hidden email]>
To: Curtis Miller <[hidden email]>
Cc: "[hidden email]" <[hidden email]>
Subject: Re: [R-SIG-Finance] Problems when estimating GARCH parameters
        with    fGarch
Message-ID: <[hidden email]>
Content-Type: text/plain;       charset=us-ascii

Have you tried rugarch or just "garch" in the tseries package?  Reproducible examples are always helpful as well.

> On Nov 2, 2017, at 1:56 PM, Curtis Miller <[hidden email]> wrote:
>
> Hello all,
>
> I have encountered bad behavior in fGarch's garchFit() function used for
> estimating the parameters of a GARCH model. The estimates behave in
> highly erratic ways on simulated data. For example, when beta = 0.2
> according to the simulation, the function sometimes estimates beta to be
> 0.0000001 even for sample sizes as large as 1000, and there are other
> irregularities. I believe this behavior is tied to how the numerical
> optimizers are computing the parameters.
>
> In my research I planned on using garchFit() from fGarch in a
> changepoint detection context. I was hoping to use it to detect
> structural change in GARCH parameters. (See, for example, Ling 2007
> paper https://arxiv.org/abs/0708.2369 .) But with this behavior I don't
> know if such a test using garchFit() is possible; the estimates are too
> unreliable.
>
> Has anyone else observed this behavior? Is there a way to get around it?
> I'm hoping someone who knows more about this can offer guidance.
>
> I have written a blog post documenting the behavior I observed, with
> numerical experiments. Here is a link:
> https://ntguardian.wordpress.com/2017/11/02/problems-estimating-garch-parameters-r/
>
>
> Curtis
>
> _______________________________________________
> [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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