I have a model with an exponential random walk plus drift trend in many of the variables, including output. I read in the log of output (lnY_obs) as
lnY_obs - lnY_obs(-1) = dA + y - y(-1);
dA = exp(gam + e_a);
with gam the growth drift>), e_a the disturbance term, and y=output/A, A=A(-1)exp(gam + e_a).
I use the option smoother in the estimation command to obtain the smoothed estimated of the endogenous variables, including lnY_obs. The plots of the stationary variables are fine, but the non-stationary lnY_obs is downward sloping (and gam>0), which is wrong. Without the smoother option, the plot of lnY_obs looks fine. Is there something wrong with the way the smoother option calculates the smoothed values for non-stationary series?
p.s. Can someone tell me what the various rows of oo_.SmoothedVariables.Distribution.endogenousvariable correspond to? I assume quantiles for the posterior distribution of endogenousvarible, but which ones? Is the posterior mean included?