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

[alexios ghalanos]

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