Applications of Vector Autoregressions in Their Scalar Autoregressive Component Form

Leo Krippner

CAMA Working Papers from Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University

Abstract: 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.

Keywords: vector autoregression; VAR; companion matrix; eigenvalues; eigenvectors (search for similar items in EconPapers)
JEL-codes: C13 C32 C53 (search for similar items in EconPapers)
Pages: 32 pages
Date: 2024-12
New Economics Papers: this item is included in nep-ecm and nep-ets
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Persistent link: https://EconPapers.repec.org/RePEc:een:camaaa:2024-71

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