Closed SebRollen closed 3 years ago
Thanks for this!
The fix for the mean forecast looks correct to me. However the error message for the VaR forecast was there on purpose: the distribution of the multi-period return is not the same as the error distribution, even if the errors are normal. Computing the true distribution is only possible via its characteristic function, which has a very complicated form even for a simple GARCH(1, 1). Thus, one would probably have to rely on simulation to get the quantiles. As long as that isn't implemented, I'd rather give an error than a wrong result.
Come to think of it, we should also disallow forecasting the variance of an EGARCH more than 1-period ahead. What it's doing now is forecasting log variance and then taking the exponential. Due to Jensen's inequality, that's not a correct forecast in the conditional expectation sense.
Hi, thanks for the explanation! That makes a lot of sense, I've updated the PR to only incorporate the updates for the mean forecast as that was really the issue I set out to fix in the first place
Great, thanks! If CI clears this should be good to go, except that the docstring needs some tweaking.
Feel like tackling the multivariate case as well? Getting greedy, I know :)
Updated the docstring, open to suggestions on language! I might have some time to tackle the multivariate case in the next couple of weeks, but can't make any promises haha.
Merged. Thanks for your contribution!
I'll tag a new release.
This PR adds in multi-step forecasts for
what=:return
andwhat=:VaR
by using the one-period prediction for timet
ofreturn
as the data for thet+1
prediction