[R-SIG-Finance] rugarch: Initializing an AR1 model fit

[Mickey Petersen]

Alright, thanks! Much appreciated

2018-07-19 19:20 GMT+02:00 alexios ghalanos <alexios using 4dscape.com>:

> Best illustrated with an example:
>
> library(rugarch)
> data(sp500ret)
> spec=arfimaspec(mean.model=list(armaOrder=c(2,2)))
> fit = arfimafit(spec, sp500ret)
> head(fitted(fit))
>
> 1987-03-10  1.913217e-04
> 1987-03-11  1.913217e-04
> 1987-03-12 -4.294109e-04
>
> t(t(coef(fit)))
>
> mu     0.0001913217
> ar1   -0.0643659160
> ar2    0.2625192564
> ma1    0.0241934750
> ma2   -0.3439672864
> sigma  0.0118930801
>
> Therefore, until we have enough data (T>Lag), we use the estimated mean
> (mu) to initialize the recursion. There are certainly other ways to do this
> such as building up incrementally from Lag1 to LagN, but not currently
> implemented.
>
> I don't know how matlab estimates ARMA models, but the documentation
> provides the formulation used (https://cran.r-project.org/
> web/packages/rugarch/vignettes/Introduction_to_the_rugarch_package.pdf)
> in Section 2.1
>
> Regards,
>
> Alexios
>
> On Thu, 19 Jul 2018 18:32:20 +0200, Mickey Petersen <mickeyzkp using gmail.com>
> wrote:
>
> > Hi all,
> >
> > I'm using the rugarch package in R to fit (among others) an AR1 process,
> in
> > turn leading to some risk numbers. Doing the same fit in Matlab, I get
> > slightly different numbers.
> >
> > The reason is that the estimated AR1-parameters differ and I've narrowed
> it
> > down to differences in the starting conditions for each process.
> > In other words, in the Matlab script, I specify that the first
> observation
> > should be interpreted as a presample response (Y0) and that the AR1
> process
> > should then be fitted to the rest of the time series (1018 observations).
> > Apparently, leaving out this specification would lead to Matlab
> > 'back-forecasting' Y0 and I presume rugarch does something similar. But
> the
> > risk numbers still disagree slightly.
> >
> > My question is thus two-fold:
> > - How can I specify the single presample response (Y0) to use in fitting
> an
> > AR1 process using arfimafit from rugarch?
> > - Supplying the whole time series (all 1019 observations), what procedure
> > does arfimafit then apply as default to estimate the presample response?
> > Mean? First observation?
> >
> > Kind regards,
> > Mickey Petersen
>
>
>

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