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Applications of Vector Autoregressions in Their Scalar Autoregressive Component Form

Author

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  • Leo Krippner

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.

Suggested Citation

  • Leo Krippner, 2024. "Applications of Vector Autoregressions in Their Scalar Autoregressive Component Form," CAMA Working Papers 2024-71, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    • Handle: RePEc:een:camaaa:2024-71
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    File URL: https://crawford-prod.anu.edu.au/sites/default/files/2024-12/71_2024_Krippner_0.pdf
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    More about this item

    Keywords

    vector autoregression; VAR; companion matrix; eigenvalues; eigenvectors;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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