I wanted to test whether Dynare could estimate a non-invertible MA process, in particular y=eps-theta*eps(-1), where theta>1. I generated this process, and then estimated the parameters using the modfile below. The process was generated for 1000 periods using theta=0.5 and var(eps)=1.

First of all, the result is that it did estimate the non-invertible process (although using different priors I could get Dynare to estimate the equivalent invertible process).

However, what I would have anticipated is that since I used a flat prior (the uniform distribution) for the standard error, that the posterior would have been bimodal, with approximately equal likelihoods at theta and 1/theta. Instead the posterior was almost vertical at theta.

I have recently been wondering why it is that I so rarely see bimodal or indeed multimodal priors, and this adds to the mystery.

MODFILE:

//Simple MA(1) model

var y x;

varexo eps;

parameters rho;

rho = 0.90;

model;

x = eps;

y = -rho*x(-1)+eps;

end;

shocks;

var eps; stderr 1;

end;

steady;

check;

estimated_params;

//stderr eps, INV_GAMMA_PDF,1,200; //technology

stderr eps, UNIFORM_PDF,0.001,5; //technology

//rho, BETA_PDF, 0.4,0.2; //AR1 technology

rho, NORMAL_PDF, 1.25,2; //AR1 technology

end;

//stoch_simul(irf=10) x y;

varobs y;

estimation(datafile=y,mode_compute=4,nobs=1000,

prefilter=0,mh_replic=5000,mh_nblocks=2,mh_jscale=0.40,mh_drop=0.2);