Using Forecast instruction - model stability

After computing with Dynare the second order approximation of a DSGE model, and using the instruction FORECAST where the path of the exogenous deterministic shock is specified to be zero at all periods, I assume the model should converge to a finite number for all endogenous variables.

  1. Is this assumption correct? When solving an open economy model, a large number of specifications diverges when performing the exercise described above. I am puzzled - I see that this problem can arise with stochastic simulations, but I am perplexed that it would occur when the exogenous shocks are shut off. What am I missing?

In the absence of shocks (all shocks realization are zero) although that the agents expected future volatility, the true non-linear model should converge towards a steady state. The later is in general different from the deterministic steady state returned by STEADY.
The problem is that we have no idea about the condition for stability for second order polynomial AR processes. It is possible that the second order approximation doesn’t converge, particularily if the variances are high and that the stochastic steady state is far from the deterministic one. You can see that if the "correction’ terms are relatively large.
An alternative would be to simulate using Chris Sims’ pruning algorithm, but it isn’t available yet in Dynare.