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I am trying to estimate a FIGARCH(1,1) model in R for Value-at-Risk purposes. As I understand it, the rugarch package does not support FIGARCH or FIEGARCH. To that end, I used the garchOxFit function (which runs the estimation in Ox, whilst interfacing with R).

It all works and I am left with the the fitted conditional volatility and the parameter estimates. My problem now is to use that to get the analytic VaR estimate for the next day.

For a simple GARCH(1,1) that is fine: take the last estimated conditional volatility of the sample as well as the last squared residual; plug those into the GARCH equation along with the parameter estimates to get the next day's predicted volatility. One would then use with a quantile function based on whatever distribution was assumed to calculate the analytic VaR.

Problem is I am too simple to see how to do get the vol estimate with a FIGARCH model. I have the following maximum likelihood estimates for the FIGARCH parameters:

Cst(V) x 10^4 : 0.076547 #ie. constant in GARCH equation (omega)
d-Figarch : 0.584467
ARCH(Phi1) : 0.122547
GARCH(Beta1) : 0.643318

I have looked at Bollerslev's initial paper on FIGARCH, and am still clueless as to how one gets the next recursive volatility estimate given the parameter estimates and previous day's volatility and squared residual. Any ideas? Any help would be very much appreciated.

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If you scroll down the results of the GarchOxModelling output you will see the default 15 forecasts. You can edit the .ox file if you like. There is a G@rch help page that explains more options. core.ucl.ac.be/~laurent/G@RCH/site/default.htm There is also a paper that says 1 day ahead figarch is no better than basic garch. editorialexpress.com/cgi-bin/conference/… –  brian Aug 10 '13 at 17:44
    
Thank you very Brian for your help on this question and my previous –  user5910 Aug 11 '13 at 15:07
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