I have the estimation results. I did the simulation with smoothed shocks and estimated parameters. The start point of simulation: for observed variables, I am using the data of the first period; for the unobserved variables, I am using the first value of corresponding smoothed variables. My problem is that some of the simulated series have big increase or decrease at the beginning which leads to the simulation series deviate from data series a lot. In such a case, does it mean my estimation is bad? I was wondering how to improve this problem. Was it caused by the short time series I am using (36 periods in total)?
Thanks a lot.
There is a conceptual (and quantitative) difference between the deterministic solution and the stochastic solution.
The deterministic solution assumes perfect foresight, i.e. at the beginning of time you know the future path of shocks.
The stochastic solution assumes that all innovations to shocks are unexpected. Hence, the outcomes should be very different.
To get stochastic simulations matching the data you can get the initial state, the steady state as well as the transition and impact matrices from dynare’s output (it sets parameters to the mode estimate when computing these), and you can then manually fit in the “fitted errors” which are among the output of dynare as well. This way, you can recover the data exactly. I have implemented this procedure in the past, and it does return the data exactly.