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.
//Simple MA(1) model
var y x;
rho = 0.90;
x = eps;
y = -rho*x(-1)+eps;
var eps; stderr 1;
//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
//stoch_simul(irf=10) x y;