Encompassing Univariate Models in Multivariate Time-Series - A Case-Study

Abstract

Through the encompassing principle, univariate ARIMA analysis could provide an important tool for diagnosis of VAR models: The univariate ARIMA models implied by the VAR should explain the results from univariate analysis. This comparison is seldom performed, possibly due to the paradox that, while the implied ARIMA models typically contain a very large number of parameters, univariate analysis yields highly parsimonious models. Using a VAR application to six French macro-economic variables, it is seen how the encompassing check is straight-forward to perform, and surprisingly accurate.