A matrix unified framework for deriving various impulse responses in Markov switching VAR: Evidence from oil and gas markets

Abstract

We propose a new method to compute various impulse response functions (IRF) for a Markov switching VAR model in terms of neat matrix expressions in closed form. The key is to derive a suitable closed form representation for Markov switching VAR models using a state-space representation. By this representation, the IRF analysis can be processed with respect to either an asymmetric discrete or a symmetric continuous shocks. A simulation study demonstrates the actual advantages of the proposed matrix methodology. To illustrate the feasibility and the usefulness of our approach, we present empirical applications to oil and natural gas markets showing the relevance of accommodating asymmetries in the relationship between their price shocks and economic activities.