Applications of Vector Autoregressions in Their Scalar Autoregressive Component Form

The eigenvalue/eigenvector structure underlying a standard N-variable P -lag vector autoregression (VAR) may be transformed into a system of NP scalar AR1 processes, each with an eigenvalue as its coefficient. This perspective allows a VAR to be assessed, analyzed, and manipulated using the mathematical and statistical convenience of elementary AR1 processes. Illustrative empirical applications demonstrate the inherent benefits: (1) the persistence of a VAR’s dynamics is interpreted from its AR1 processes; (2) closed-form VAR forecasts are obtained from AR1 forecasts; (3) equality or zero constraints on selected AR1 coefficients are tested and imposed for VAR parsimony; (4) a median-unbiased estimate of the largest AR1 coefficient is generated and imposed to produce a more persistent VAR; (5) a unit root for the largest AR1 coefficient is tested and imposed to produce a cointegrated VAR, which also produces an estimate of the associated cointegrating vector.