# Starting value of conditional mean and variance

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## Starting value of conditional mean and variance

 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.
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## Re: Starting value of conditional mean and variance

 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.comhttp://www.portfolioprobe.com/blogtwitter: @burnsstat @portfolioprobe _______________________________________________ [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: Starting value of conditional mean and variance

 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]] _______________________________________________ [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: Starting value of conditional mean and variance

 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] > > 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 > > -- Patrick Burns [hidden email] http://www.burns-stat.comhttp://www.portfolioprobe.com/blogtwitter: @burnsstat @portfolioprobe _______________________________________________ [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: Starting value of conditional mean and variance

 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] >> > 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 >> >> > _______________________________________________ [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: Starting value of conditional mean and variance

 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] > >> > 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]] _______________________________________________ [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.