I have two questions concerning correlated shocks and impulse response functions (irf).
Suppose I have two stationary AR(1)-processes a=rhoa(-1)+u and b=thetab(-1)+e and corr u, e = 0. When running irf, why do I get non-zero values for variables a_e and b_u. They are really small (in the range of 10^-15), yet they are non-zero and the irf (in the range of 10^-15) looks as if b was shocked by u and a by e, respectively .
I always observe this in the case of 2nd order approximation and sometimes in the case of 1st order approximation as well.
Can somebody explain this to me?
Now suppose corr u,e > 0. What does this imply for my irf? I observe that b is not shocked by the standard deviation of e, but by a smaller value, a_e is zero (or almost zero) and b is shocked by a value equal to (stdderr.e * corr e,u), i.e b_u is non-zero.
Did I do something wrong?
Thanks for the help in advance,