forecasting conditional covariance matrix for bivar GARCH?

[m.hallam]

Ok so I have hit a bit of a wall and was wondering whether anyone may be able to offer some advice. My problem is that I am doing some work on hedging using futures contracts, specifically constructing out-of-sample estimates for the optimal hedge ratio. As a starting point I am jointly modelling the futures and spot returns using a simple VECM with a bivariate GARCH(1,1) error structure. The problem is that since the optimal hedge ratio in each period is generally calculated as the current covariance of spot and futures returns divided by the variance of futures returns, in order to construct out-of-sample estimates of the ratio, I need forecasts of the conditional covariance matrix and can’t seem to work out how to do this.

I can attach a simplified version of my program file (with all the irrelevant stuff omitted) if that helps, but my basic method so far has been:
1) use the var command to create the VECM
2) use the makesystem command to create a system from the VECM
3) estimate the system over the in-sample period with GARCH(1,1) errors using {system name}.arch @diagbekk c(diag) arch(1) garch(1)

Now obviously because I am dealing with a system of equations, to produce any type of forecasts I have to create a model and then use solve, rather than use the fit or forecast command as in the univariate case. So I created a model from the VECM system object using the makemodel command and up to this point everything seems to work fine.

However, using the solve command on the model only appears to be able to produce forecasts of the two proper endogenous variables (the spot and futures returns) and not the associated conditional covariance matrix, which is what I actually need in this case. Is what I am attempting to do actually possible using my current method, or is there an alternative?

It seems like I may be able to do it the long way by estimating the VECM manually using a log-likelihood object, converting this to a model and then using solve on that, because then the conditional variances/covariance may be treated as separate endogenous variables. Any ideas would be much appreciated.

Mark

[trubador]

Here is an example

[m.hallam]

Wow thanks for the quick reply. Don't know how I managed to miss that previous thread - I thought I searched both this forum and the programming forum for both ARCH and GARCH. Just been one of those days I guess.

Mark

[m.hallam]

Ok so I finally got around to modifying the code in that post you linked to and then realised it (obviously) produces a dynamic forecast of the conditional variances/covariance, but what I require is a static forecast (though I forgot to make this clear in my original post). Is there any way of modifying this code to produce a static forecast of the conditional covariance matrix, or will this require a different approach? Thanks again,

Mark

[trubador]

You can easily modify the code so as to perform static forecast.