Nonparanormal Structural VAR for Non-Gaussian Data

The vector autoregression (VAR) model profoundly uses the lagged causal relationships among variables. It is well known that VAR models say little about contemporaneous time correlation of these variables. However, ignoring causal orderings among VAR endogenous variables in contemporaneous time may produce not representative impulse response functions. The recent advances in Machine/Statistical Learning literature initiated the use of conditional independence test based directed acyclic graph algorithms to impose structure on VAR by exploiting Gaussianity, where tests of conditional independence are usually based on Pearson correlation. In this paper, we propose a new, computationally efficient algorithm to impose structure on VAR when the data does not follow a Gaussian distribution. The algorithm uses a broader class of Gaussian copula or nonparanormal models, where correlation is estimated using rank-based measures. As well, for the structural VAR estimation we derive the likelihood function when the Gaussian assumption is not satisfied. The performance of our method on capturing the contemporaneous time ordering of VAR model was shown using simulation studies and a real Macroeconomic dataset.