When I change my parameter values (OMEGA from 0.37 to 0.15), the stochastic value changes even though the standard deviation value remain unchanged. test2.mod (1.6 KB) The impulses responses from OMEGA=0.15 look kinda abnormal compared to OMEGA = 0.37. Could anyone tell me why the stochastic value changes when I update the parameter values despite it does not affect the standard deviation of the shock?

What do you mean? That the shocked interest rate r moves differently? It is an endogenous object that reacts to other variables in the model. If you change the parameter, if affects the response of output and inflation and therefore the interest rate.

I understand the shocked interest rate r should move differently due to different parameter value. But, why would the initial shocked value at time 1 be different? I thought the initial shocked value should equal to the 100*standard deviation.

No, the interest rate has an exogenous component that you shock and an endogenous component that reacts differently to shocks depending on the parameter values. Please have a look at