Bayesian Estimation and shock sign


From what I understand, with x = (1-rho)*x(-1) + (rho)*x_bar + eps & shocking eps, we will have a positive shock and in order to have a negative one I have to change the equation to x = (1-rho)*x(-1) + (rho)*x_bar - eps. If I am correct that this is the only way to implement a negative shock, how should I know whether I should write my shock equations with + or - sign in the model for Bayesian estimation? Does it affect the estimation whether their sign changes?

The specified sign of the shock does not matter for estimation. It’s just a matter of normalization. If you implement your model with the opposite sign in front of \varepsilon, then your new shocks \tilde \varepsilon will simply be \tilde \varepsilon=-\varepsilon
so that you will get exactly the same series for x, which is all that matters.

Oh, I got it. Thank you for your answer.