But how do I simulate such a shock? The only way in my mind is to add two different shocks up( one is temporary and one is permanent ). So my question is, can I simulate two shocks simultaneously? Or, is there any other way to simulate the shock I need?
In the context of perfect foresight, all shock values are known, not just the stochastic processes underlying them. Thus, there is not point in specifying process, you simply need to specify the values you just plotted above. Of course, if you have a way to specify the values as the combination of two processes as you said, that should also work an may make the math easier.