I think the persistence parameter of a shock controls the duration of an event. In most publications, the persistence parameter is estimated by bayesian estimation. If I want to know the impact of an event lasting for five years, can I assign a value to this parameter instead of estimation?
What is your definition of “lasting for five years”? The half-life? Generally, one does not know the specific endogenous propagation to the endogenous variables. Only if you are considering exogenous AR processes could you compute something analytically.