Comparing the impulse response functions of different models

The problem we want to solve in this paper is that of finding a statistical test that pennits us to compare the impulse response function (JRF) of a linear model with that of a nonlinear one. We achieve our goal starting with a simple case where the comparison is between two VAR models of different order. Next, we briefly extend the results to VARs of the same order but with a different structuralization. A Monte Carlo simulation is performed to evaluate power and size of the test. We then give some insights for comparing VAR with mulrivariate SETAR IRFs. Finally, we present an alternative procedure (a variation of the encompassing test) for comparing linear and complicated nonlinear IRFs.