Joshua C. C. Chan, Gary Koop, Xuewen Yu
arXiv 14 Nov 2021 · Econometrics · publishedJournal of Business and Economic Statistics (2023) · 42 citations (OpenAlex)
arXiv:2111.07225 · PDF · DOI · OpenAlex · Extracted main text
Many popular specifications for Vector Autoregressions (VARs) with multivariate stochastic volatility are not invariant to the way the variables are ordered due to the use of a Cholesky decomposition for the error covariance matrix. We show that the order invariance problem in existing approaches is likely to become more serious in large VARs. We propose the use of a specification which avoids the use of this Cholesky decomposition. We show that the presence of multivariate stochastic volatility allows for identification of the proposed model and prove that it is invariant to ordering. We develop a Markov Chain Monte Carlo algorithm which allows for Bayesian estimation and prediction. In exercises involving artificial and real macroeconomic data, we demonstrate that the choice of variable ordering can have non-negligible effects on empirical results. In a macroeconomic forecasting exercise involving VARs with 20 variables we find that our order-invariant approach leads to the best forecasts and that some choices of variable ordering can lead to poor forecasts using a conventional, non-order invariant, approach.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Cogley and Sargent (2005) Drifts and volatilities: Monetary policies and outcomes in the post WWII US | 1.000 | 14 | 5 | 100% |
| 2 | Bertsche and Braun (2020) Identification of structural vector autoregressions by stochastic volatility | 1.000 | 5 | 3 | 100% |
| 3 | Carriero, Clark, and Marcellino (2019) Large Bayesian vector autoregressions with stochastic volatility and non-conjugate priors | 0.950 | 7 | 6 | 86% |
| 4 | Primiceri (2005) Time varying structural vector autoregressions and monetary policy | 0.928 | 4 | 3 | 100% |
| 5 | Arias, Rubio-Ramirez, and Shin (2021) Macroeconomic forecasting and variable ordering in multivariate stochastic volatility models | 0.737 | 3 | 2 | 100% |
| 6 | Carriero, Chan, Clark, and Marcellino (2021) Corrigendum to: Large Bayesian vector autoregressions with stochastic volatility and non-conjugate priors | 0.737 | 3 | 2 | 100% |
| 7 | Villani (2009) Steady-state priors for vector autoregressions | 0.585 | 3 | 1 | 100% |
| 8 | Waggoner and Zha (2003) A Gibbs sampler for structural vector autoregressions | 0.511 | 2 | 1 | 100% |
| 9 | Kastner (2019) Sparse Bayesian time-varying covariance estimation in many dimensions | 0.511 | 2 | 1 | 100% |
| 10 | Asai and McAleer (2009) The structure of dynamic correlations in multivariate stochastic volatility models | 0.405 | 1 | 1 | 100% |
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