Empirical forecasting models · Sources
Bayesian VAR (BVAR) sources, papers, and evidence trail
Primary papers, model variants, source notes, and review signals behind the Bayesian VAR (BVAR) page.
References
Academic and research sources
Peer-reviewed papers, books, and research used to ground model mechanisms or contested interpretations.
[S1] Journal of Business and Economic Statistics
Forecasting with Bayesian Vector Autoregressions
Litterman's Bayesian VAR forecast framework.
Academic - Journal of Business and Economic Statistics - dated 1986
[S2] Journal of Applied Econometrics
Large Bayesian Vector Auto Regressions
Banbura, Giannone, and Reichlin on shrinkage for larger systems.
Academic - Journal of Applied Econometrics - dated 2010
Reference sources
Reference material used for orientation; read primary and academic sources first when claims conflict.
[S3] Reference
Litterman (1986) 'Forecasting with Bayesian Vector Autoregressions -- Five Years of Experience': established the Minnesota prior and demonstrated consistent out-of-sample forecast improvements over unrestricted VARs for U.S. macro variables.
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[S4] Reference
Doan, Litterman, and Sims (1984): introduced the sum-of-coefficients prior to handle unit roots in BVARs without differencing, preserving cointegrating relationships.
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[S5] Reference
Giannone, Lenza, and Primiceri (2015) 'Prior Selection for Vector Autoregressions': closed the loop on hyperparameter choice by maximizing marginal likelihood, making the BVAR fully automatic.
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[S6] Reference
Banbura, Giannone, and Reichlin (2010) 'Large Bayesian Vector Auto Regressions': showed that BVARs scale to 130+ variables with appropriate shrinkage, matching factor model forecast accuracy.
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[S7] Reference
Primiceri (2005) 'Time Varying Structural Vector Autoregressions and Monetary Policy': introduced the TVP-BVAR with stochastic volatility, the standard tool for studying evolving macro dynamics.
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Research footing
Evidence and data
Evaluate forecasts out of sample and report posterior uncertainty rather than only the posterior mean.
Calibration or measurement
Prior tightness, lag length, variable scaling, and dummy observations define the practical model.
Boundaries
- Shrinkage can hide misspecification.
- Priors matter more in short samples.
- Structural interpretation still requires identification.
Use guidance
- When sufficient
- Forecasting and conditional projections with a moderate-to-large variable set when shrinkage priors discipline overparameterization. The Minnesota prior (Litterman 1986 JBES) and its extensions (Banbura-Giannone-Reichlin 2010 JAE) keep the VAR tractable as the variable count grows, improving out-of-sample forecast accuracy over OLS estimation when the sample is short relative to the number of parameters. The right tool for large-system forecasting where the BVAR dominates smaller specification-searched VARs.
- When sketch only
- A BVAR remains a reduced-form forecasting tool. Structural identification still requires a separate assumption block: a sign-restriction or proxy-SVAR layer must be added before impulse responses carry causal content. Also do not use the posterior mean alone as the point forecast without reporting posterior uncertainty; prior tightness can mask genuine parameter uncertainty.
- When to switch
- Switch to a factor-augmented VAR (FAVAR, Bernanke-Boivin-Eliasz 2005 QJE) when a large panel of indicators is relevant but only a few latent factors drive the common variation, making a full BVAR over all indicators unnecessary. Switch to a BVAR with identification when structural shock responses are the object, adding whatever restriction maps the reduced form to the structural form.
- Falsification signal
- Forecast performance that degrades as variables are added to the system, producing higher RMSFE at larger dimensions rather than lower, indicates the prior is misspecified or the prior tightness is too loose to offset the overfitting from additional parameters. A rolling pseudo-real-time comparison of BVARs with 5, 15, and 30 variables showing the 30-variable system losing to the 5-variable version would be the concrete signal.
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