Vector autoregressive moving average identification for macroeconomic modeling: A new methodology

This paper develops a new methodology for identifying the structure of VARMA time series models. The analysis proceeds by examining the echelon form and presents a fully automatic, strongly consistent, data driven approach to model specification. A novel feature of the inferential procedures developed here is that they work in terms of a canonical representation based on the Kronecker invariants in which the variables are expressed in the form of scalar dynamic structural equations derived from the VARMA system. This feature facilitates the construction of procedures which, from the perspective of macroeconomic modeling, can be efficacious in that they do not rely on VAR approximations. Techniques that are applicable to both asymptotically stationary and unit-root, partially nonstationary (cointegrated) time series models are presented. The inferential potential of the techniques is illustrated via simulation experiments that use data generating mechanisms based on real world examples drawn from the time series literature. Aspects of the Kronecker invariants that impinge on practical application and that have not hitherto been discussed in the literature are explored.