Starting value of conditional mean and variance

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Starting value of conditional mean and variance

Samit Paul
Dear R users,

I am trying to estimate conditional mean and variance of a financial return
series using UGARCHSPEC and UGARCHFIt function of "rugarch" package. I am
trying to fit basic ARMA(1,1)-GARCH(1,1) with Student - t distribution.

Now, I am not sure how the starting values are considered in this case or
whether I need to set it manually. Since the starting value is very
important for the estimation purpose, there could be some robust method for
calculation of the same.

Any help in this regard will be highly appreciated.

Regards,

Samit Paul

        [[alternative HTML version deleted]]

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Re: Starting value of conditional mean and variance

Patrick Burns-2
I have two possible interpretations
of "starting values":

1) initial values of coefficients given
to the optimizer of the likelihood

2) the value of the conditional variance
at the time point before the first observation

If you are talking about the first, I
think you have little to worry about.
The default optimization in 'rugarch' is
reasonably good.  But there are options
to use different optimizers if you want to
check the quality of the optimum.

If you are talking about the second, then
that won't be an issue as long as you have
enough observations to make estimating a
garch model useful.  See:
http://www.portfolioprobe.com/2012/07/06/a-practical-introduction-to-garch-modeling/

Pat

On 04/10/2015 16:52, Samit Paul wrote:

> Dear R users,
>
> I am trying to estimate conditional mean and variance of a financial return
> series using UGARCHSPEC and UGARCHFIt function of "rugarch" package. I am
> trying to fit basic ARMA(1,1)-GARCH(1,1) with Student - t distribution.
>
> Now, I am not sure how the starting values are considered in this case or
> whether I need to set it manually. Since the starting value is very
> important for the estimation purpose, there could be some robust method for
> calculation of the same.
>
> Any help in this regard will be highly appreciated.
>
> Regards,
>
> Samit Paul
>
> [[alternative HTML version deleted]]
>
> _______________________________________________
> [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: @burnsstat @portfolioprobe

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Re: Starting value of conditional mean and variance

Samit Paul
Thanks a lot Pat,

I was more concerned about the second issue which you have pointed out
well. From the link given (thanks again for the same), I understand that if
the number of observations are more (around 2000), choice of starting value
won't matter much in conditional variance estimation by GARCH(1,1) model.

But is the same logic applicable for conditional mean estimation with the
help of ARIMA model, too? Or do I have to take any precaution for the same?

Best regards,

Samit Paul


On Sun, Oct 4, 2015 at 11:54 PM, Patrick Burns <[hidden email]>
wrote:

> I have two possible interpretations
> of "starting values":
>
> 1) initial values of coefficients given
> to the optimizer of the likelihood
>
> 2) the value of the conditional variance
> at the time point before the first observation
>
> If you are talking about the first, I
> think you have little to worry about.
> The default optimization in 'rugarch' is
> reasonably good.  But there are options
> to use different optimizers if you want to
> check the quality of the optimum.
>
> If you are talking about the second, then
> that won't be an issue as long as you have
> enough observations to make estimating a
> garch model useful.  See:
>
> http://www.portfolioprobe.com/2012/07/06/a-practical-introduction-to-garch-modeling/
>
> Pat
>
>
> On 04/10/2015 16:52, Samit Paul wrote:
>
>> Dear R users,
>>
>> I am trying to estimate conditional mean and variance of a financial
>> return
>> series using UGARCHSPEC and UGARCHFIt function of "rugarch" package. I am
>> trying to fit basic ARMA(1,1)-GARCH(1,1) with Student - t distribution.
>>
>> Now, I am not sure how the starting values are considered in this case or
>> whether I need to set it manually. Since the starting value is very
>> important for the estimation purpose, there could be some robust method
>> for
>> calculation of the same.
>>
>> Any help in this regard will be highly appreciated.
>>
>> Regards,
>>
>> Samit Paul
>>
>>         [[alternative HTML version deleted]]
>>
>> _______________________________________________
>> [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: @burnsstat @portfolioprobe
>

        [[alternative HTML version deleted]]

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Re: Starting value of conditional mean and variance

Patrick Burns-2
I haven't studied the issue with
ARIMA, but it is my belief that it
is even less of an issue there.

Maybe someone on the list has looked
into it and has a better sense of the
sensitivity -- rather than being like
the rest of us and not worrying about
it because no one else does.

Pat

On 05/10/2015 04:43, Samit Paul wrote:

> Thanks a lot Pat,
>
> I was more concerned about the second issue which you have pointed out
> well. From the link given (thanks again for the same), I understand that
> if the number of observations are more (around 2000), choice of starting
> value won't matter much in conditional variance estimation by GARCH(1,1)
> model.
>
> But is the same logic applicable for conditional mean estimation with
> the help of ARIMA model, too? Or do I have to take any precaution for
> the same?
>
> Best regards,
>
> Samit Paul
>
>
> On Sun, Oct 4, 2015 at 11:54 PM, Patrick Burns <[hidden email]
> <mailto:[hidden email]>> wrote:
>
>     I have two possible interpretations
>     of "starting values":
>
>     1) initial values of coefficients given
>     to the optimizer of the likelihood
>
>     2) the value of the conditional variance
>     at the time point before the first observation
>
>     If you are talking about the first, I
>     think you have little to worry about.
>     The default optimization in 'rugarch' is
>     reasonably good.  But there are options
>     to use different optimizers if you want to
>     check the quality of the optimum.
>
>     If you are talking about the second, then
>     that won't be an issue as long as you have
>     enough observations to make estimating a
>     garch model useful.  See:
>     http://www.portfolioprobe.com/2012/07/06/a-practical-introduction-to-garch-modeling/
>
>     Pat
>
>
>     On 04/10/2015 16:52, Samit Paul wrote:
>
>         Dear R users,
>
>         I am trying to estimate conditional mean and variance of a
>         financial return
>         series using UGARCHSPEC and UGARCHFIt function of "rugarch"
>         package. I am
>         trying to fit basic ARMA(1,1)-GARCH(1,1) with Student - t
>         distribution.
>
>         Now, I am not sure how the starting values are considered in
>         this case or
>         whether I need to set it manually. Since the starting value is very
>         important for the estimation purpose, there could be some robust
>         method for
>         calculation of the same.
>
>         Any help in this regard will be highly appreciated.
>
>         Regards,
>
>         Samit Paul
>
>                  [[alternative HTML version deleted]]
>
>         _______________________________________________
>         [hidden email] <mailto:[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] <mailto:[hidden email]>
>     http://www.burns-stat.com
>     http://www.portfolioprobe.com/blog
>     twitter: @burnsstat @portfolioprobe
>
>

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

_______________________________________________
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https://stat.ethz.ch/mailman/listinfo/r-sig-finance
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Re: Starting value of conditional mean and variance

alexios
A few years ago, on the suggestion of Pat, I implemented an option
which allows to choose whether to use all the data for the initialization
of the variance recursion or some other value e.g. for exponential smoothing
backast. This can be found in the fit.control option (of ugarchfit) under
'rec.init':

>From the documentation:

"The rec.init option determines the type of initialization for the
variance recursion.
Valid options are ‘all’ which uses all the values for the unconditional
variance
calculation, an integer greater than or equal to 1 denoting the number
of data
points to use for the calculation, or a positive numeric value less than
one
which determines the weighting for use in an exponential smoothing
backcast."

This is only for the variance recursion initialization, and not the
conditional mean.

Best,

Alexios

On 05/10/2015 01:49, Patrick Burns wrote:

> I haven't studied the issue with
> ARIMA, but it is my belief that it
> is even less of an issue there.
>
> Maybe someone on the list has looked
> into it and has a better sense of the
> sensitivity -- rather than being like
> the rest of us and not worrying about
> it because no one else does.
>
> Pat
>
> On 05/10/2015 04:43, Samit Paul wrote:
>> Thanks a lot Pat,
>>
>> I was more concerned about the second issue which you have pointed out
>> well. From the link given (thanks again for the same), I understand that
>> if the number of observations are more (around 2000), choice of starting
>> value won't matter much in conditional variance estimation by GARCH(1,1)
>> model.
>>
>> But is the same logic applicable for conditional mean estimation with
>> the help of ARIMA model, too? Or do I have to take any precaution for
>> the same?
>>
>> Best regards,
>>
>> Samit Paul
>>
>>
>> On Sun, Oct 4, 2015 at 11:54 PM, Patrick Burns <[hidden email]
>> <mailto:[hidden email]>> wrote:
>>
>>     I have two possible interpretations
>>     of "starting values":
>>
>>     1) initial values of coefficients given
>>     to the optimizer of the likelihood
>>
>>     2) the value of the conditional variance
>>     at the time point before the first observation
>>
>>     If you are talking about the first, I
>>     think you have little to worry about.
>>     The default optimization in 'rugarch' is
>>     reasonably good.  But there are options
>>     to use different optimizers if you want to
>>     check the quality of the optimum.
>>
>>     If you are talking about the second, then
>>     that won't be an issue as long as you have
>>     enough observations to make estimating a
>>     garch model useful.  See:
>>    
>> http://www.portfolioprobe.com/2012/07/06/a-practical-introduction-to-garch-modeling/
>>
>>     Pat
>>
>>
>>     On 04/10/2015 16:52, Samit Paul wrote:
>>
>>         Dear R users,
>>
>>         I am trying to estimate conditional mean and variance of a
>>         financial return
>>         series using UGARCHSPEC and UGARCHFIt function of "rugarch"
>>         package. I am
>>         trying to fit basic ARMA(1,1)-GARCH(1,1) with Student - t
>>         distribution.
>>
>>         Now, I am not sure how the starting values are considered in
>>         this case or
>>         whether I need to set it manually. Since the starting value
>> is very
>>         important for the estimation purpose, there could be some robust
>>         method for
>>         calculation of the same.
>>
>>         Any help in this regard will be highly appreciated.
>>
>>         Regards,
>>
>>         Samit Paul
>>
>>                  [[alternative HTML version deleted]]
>>
>>         _______________________________________________
>>         [hidden email] <mailto:[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] <mailto:[hidden email]>
>>     http://www.burns-stat.com
>>     http://www.portfolioprobe.com/blog
>>     twitter: @burnsstat @portfolioprobe
>>
>>
>

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Re: Starting value of conditional mean and variance

Samit Paul
Thanks a lot Pat and Alexios,

The explanations and insights shared by you are really helpful for me to
develop my understanding.

I sincerely appreciate your time and effort.

Best regards,

Samit Paul

On Mon, Oct 5, 2015 at 4:47 PM, alexios galanos <[hidden email]> wrote:

> A few years ago, on the suggestion of Pat, I implemented an option
> which allows to choose whether to use all the data for the initialization
> of the variance recursion or some other value e.g. for exponential
> smoothing
> backast. This can be found in the fit.control option (of ugarchfit) under
> 'rec.init':
>
> From the documentation:
>
> "The rec.init option determines the type of initialization for the
> variance recursion.
> Valid options are ‘all’ which uses all the values for the unconditional
> variance
> calculation, an integer greater than or equal to 1 denoting the number
> of data
> points to use for the calculation, or a positive numeric value less than
> one
> which determines the weighting for use in an exponential smoothing
> backcast."
>
> This is only for the variance recursion initialization, and not the
> conditional mean.
>
> Best,
>
> Alexios
>
> On 05/10/2015 01:49, Patrick Burns wrote:
> > I haven't studied the issue with
> > ARIMA, but it is my belief that it
> > is even less of an issue there.
> >
> > Maybe someone on the list has looked
> > into it and has a better sense of the
> > sensitivity -- rather than being like
> > the rest of us and not worrying about
> > it because no one else does.
> >
> > Pat
> >
> > On 05/10/2015 04:43, Samit Paul wrote:
> >> Thanks a lot Pat,
> >>
> >> I was more concerned about the second issue which you have pointed out
> >> well. From the link given (thanks again for the same), I understand that
> >> if the number of observations are more (around 2000), choice of starting
> >> value won't matter much in conditional variance estimation by GARCH(1,1)
> >> model.
> >>
> >> But is the same logic applicable for conditional mean estimation with
> >> the help of ARIMA model, too? Or do I have to take any precaution for
> >> the same?
> >>
> >> Best regards,
> >>
> >> Samit Paul
> >>
> >>
> >> On Sun, Oct 4, 2015 at 11:54 PM, Patrick Burns <[hidden email]
> >> <mailto:[hidden email]>> wrote:
> >>
> >>     I have two possible interpretations
> >>     of "starting values":
> >>
> >>     1) initial values of coefficients given
> >>     to the optimizer of the likelihood
> >>
> >>     2) the value of the conditional variance
> >>     at the time point before the first observation
> >>
> >>     If you are talking about the first, I
> >>     think you have little to worry about.
> >>     The default optimization in 'rugarch' is
> >>     reasonably good.  But there are options
> >>     to use different optimizers if you want to
> >>     check the quality of the optimum.
> >>
> >>     If you are talking about the second, then
> >>     that won't be an issue as long as you have
> >>     enough observations to make estimating a
> >>     garch model useful.  See:
> >>
> >>
> http://www.portfolioprobe.com/2012/07/06/a-practical-introduction-to-garch-modeling/
> >>
> >>     Pat
> >>
> >>
> >>     On 04/10/2015 16:52, Samit Paul wrote:
> >>
> >>         Dear R users,
> >>
> >>         I am trying to estimate conditional mean and variance of a
> >>         financial return
> >>         series using UGARCHSPEC and UGARCHFIt function of "rugarch"
> >>         package. I am
> >>         trying to fit basic ARMA(1,1)-GARCH(1,1) with Student - t
> >>         distribution.
> >>
> >>         Now, I am not sure how the starting values are considered in
> >>         this case or
> >>         whether I need to set it manually. Since the starting value
> >> is very
> >>         important for the estimation purpose, there could be some robust
> >>         method for
> >>         calculation of the same.
> >>
> >>         Any help in this regard will be highly appreciated.
> >>
> >>         Regards,
> >>
> >>         Samit Paul
> >>
> >>                  [[alternative HTML version deleted]]
> >>
> >>         _______________________________________________
> >>         [hidden email] <mailto:[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] <mailto:[hidden email]>
> >>     http://www.burns-stat.com
> >>     http://www.portfolioprobe.com/blog
> >>     twitter: @burnsstat @portfolioprobe
> >>
> >>
> >
>
>

        [[alternative HTML version deleted]]

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