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Waggoner and Zha (1999), see reference below, developed an approach to produce conditional forecasts for VAR models with hard restrictions on the variables using Gibbs Sampling. As an example, they provided a VAR where one of the variables was restricted to a specific value (Fed Funds Rate) and then looked at the effects this had on the other endogenous variables.

Given a VAR-MVGARCH (doesn't matter which one, I prefer a DCC or Copula-GARCH), is there a similar approach? I was not able to find one or anything that could lead to a correct solution.

Reference:

Waggoner, D. F., and T. Zha (1999): “Conditional forecasts in dynamic multivariate models,” The Review of Economics and Statistics, 81(4), 639–651

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