The RATS Software Forum

Hi, I am trying to fit a transfer function model to estimate the impact of a shock on an exogenous variable (z) on the “endogenous” variable (y). The model has the general form described in Enders book (3er ed) pg 285: y_t = A(L)y_t-1+C(L)z_t+B(L)e_t.
I used the “boxjenk” instruction to fit the z’s and y’s ARMA best equations based on the steps mentioned on the same book. I think I already have a fairly good model for both for the z and the y variables. By using the “impulse” instruction I get the response of the y variable to a unit shock on z. This was fairly straightforward, but now I want the confidence intervals of the “impulse” output. This is what I don’t know how to get. May I get some help?

When you say you have a model for Z, does that mean that you're doing the impulse responses on a two equation system---the transfer function model for Y plus a separate ARIMA model for Z?

That is correct Sir. My equation for z is an AR(1), estimated with:
“boxjenk(define=z_eq, AR=1) z”,

and my equation for y is an ARMA(2,1), and I am estimating it with:
“boxjenk(define=y_eq,ar=2,ma=||1||,inputs=1) y
# z 0 0 1”

This allows me to get the response of y (and z) to a unit shock on z with:
"group modelo z_eq y_eq
impulse(model=modelo,shocks=||1.0,0.0||,steps=12,results=IRF)"

The output of this is a (12,2) array containing the response of z and y for 12 periods, but I need also the confidence interval of those responses.

Unfortunately, that will be rather complicated---you would have to do either importance sampling or Metropolis-Gibbs to handle the transfer function.