Fan Chart (Predictive Density) - Forecast from a State-Space

Estimation ML/Bayesian estimation
1

Hello dear all,
I want to use the state space representation from a DSGE model to get fan charts (predictives densities) using dynare.
In order to do this, I need one state space, like this:

y_t = Z*alpha_t + eps_t,                 eps_ t ~ N(0,H)                     observation equation
apha_t+1 = T*alpha_t + R*eta_t,              eta_t ~ N(0,Q)             state equation

I am using notation from Koopman and Durbin: “Filtering and smoothing of state vector for difuse state space models”.
With this representation I will get several paths of forecasts by simulation, and after that I will compute percentiles of simulations to plot fan charts.

Also I am needing alpha_0 which must be the smoothed estimate in end of the sample.

My questions are:

  1. How could I retrieve Z, H, T, R and Q?, and How could I check order of variables in y_t and alpha_t? I hope to get in y_t (alpha_t) variables in the same order of declared observed variables (declared endogenous variables) in .mod.

I saw github.com/JohannesPfeifer/DSGE_mod/tree/master/FV_et_al_2007. I guess it works when it is needed decomposition in states and shocks, but I need work with observed variables too.

  1. How could I retrieve alpha_0 (smoothed estimate of alpha_t in end of the sample)?

  2. Is there another ideas to get predictive densities in dynare?

Thanks

Aldo

2
  1. Isn’t the forecast option of the estimation command already what you are looking for?
  2. For building the transition matrix, you are on the right track. See [How to build transition and measurement equations)
  3. For retrieving the smoothed states: they are stored in oo_.SmoothedVariables. Alternatively, you may be able to use smoother2histval (see the manual).
3

Thanks dear jpfeifer,
I saw the manual, and I after run my .mod I see output oo_.PointForecast.deciles. In order to plot my fan chart I would like to have output of complete simulation and not only deciles, for example I would like to compute percentiles.

I have another question, what is the dynare function which compute deciles of forecast?

And finally, I am running a DSGE-VAR, and I include forecast option in estimation command.
I would like to know if oo_.PointForecast.deciles is output of DSGE or DSGE-VAR? I ask this because I am not sure if dynare computes forecast for DSGE-VAR?

Thanks

Aldo

4

This is tricky.

prior_posterior_statistics_core.m

creates the forecasts.

pm3.m

computes the deciles. In principle, you can easily access the saved forecasts across draws in the metropolis-subfolder in the FILENAME_forc_point*.mat-files.

At the current stage, forecasts are from the DSGE-model, not the VAR. It is on our to-do list, but we haven’t managed to do it yet. See github.com/DynareTeam/dynare/issues/819. A year ago a user started working on it, but it went nowhere as far as I know. But maybe it is helpful: [Writtng a dsgevar_forecast function)

5

Thanks a lot dear jpfeifer,
Your help solve my problem.

Cheers!!

Aldo

6

Dear all,

Im having a hard time trying solve question 1 by Aldo - retrieving Z, H, T, R and Q (Durbin Koopman DK notation) from dynare output

I was reading all the state space representation posts, but Im still confused about the ABCD form and the one of DK notation. In ABCD_test.m, the matrix D is returned, but in my case it would be a just a identity matrix (or just a zero matrix in some cases). How to solve this issue? writing the state space matrix as DK notation using dynare output?

[A,B] = kalman_transition_matrix(oo_.dr,ipred,1:M_.nspred); works for the transition equation. but what about the observation equation

Thanks!

7

Have a look at

8

That’s it! thanks jpfeifer