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Large Bayesian Tensor VARs with Stochastic Volatility

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  • Joshua C. C. Chan
  • Yaling Qi

Abstract

We consider Bayesian tensor vector autoregressions (TVARs) in which the VAR coefficients are arranged as a three-dimensional array or tensor, and this coefficient tensor is parameterized using a low-rank CP decomposition. We develop a family of TVARs using a general stochastic volatility specification, which includes a wide variety of commonly-used multivariate stochastic volatility and COVID-19 outlier-augmented models. In a forecasting exercise involving 40 US quarterly variables, we show that these TVARs outperform the standard Bayesian VAR with the Minnesota prior. The results also suggest that the parsimonious common stochastic volatility model tends to forecast better than the more flexible Cholesky stochastic volatility model.

Suggested Citation

  • Joshua C. C. Chan & Yaling Qi, 2024. "Large Bayesian Tensor VARs with Stochastic Volatility," Papers 2409.16132, arXiv.org.
    • Handle: RePEc:arx:papers:2409.16132
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    References listed on IDEAS

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    1. Joshua C. C. Chan & Gary Koop & Xuewen Yu, 2024. "Large Order-Invariant Bayesian VARs with Stochastic Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(2), pages 825-837, April.
    2. Cross, Jamie & Poon, Aubrey, 2016. "Forecasting structural change and fat-tailed events in Australian macroeconomic variables," Economic Modelling, Elsevier, vol. 58(C), pages 34-51.
    3. Di Wang & Yao Zheng & Heng Lian & Guodong Li, 2022. "High-Dimensional Vector Autoregressive Time Series Modeling via Tensor Decomposition," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(539), pages 1338-1356, September.
    4. Todd E. Clark, 2011. "Real-Time Density Forecasts From Bayesian Vector Autoregressions With Stochastic Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(3), pages 327-341, July.
    5. Wang, Di & Zheng, Yao & Li, Guodong, 2024. "High-dimensional low-rank tensor autoregressive time series modeling," Journal of Econometrics, Elsevier, vol. 238(1).
    6. Korobilis, Dimitris & Pettenuzzo, Davide, 2019. "Adaptive hierarchical priors for high-dimensional vector autoregressions," Journal of Econometrics, Elsevier, vol. 212(1), pages 241-271.
    7. Florian Huber & Martin Feldkircher, 2019. "Adaptive Shrinkage in Bayesian Vector Autoregressive Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(1), pages 27-39, January.
    8. James H. Stock & Mark W. Watson, 2016. "Core Inflation and Trend Inflation," The Review of Economics and Statistics, MIT Press, vol. 98(4), pages 770-784, October.
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    Cited by:

    1. Cimadomo, Jacopo & Giannone, Domenico & Lenza, Michele & Monti, Francesca & Sokol, Andrej, 2026. "Fiscal Monitoring with VARs," CEPR Discussion Papers 21160, Centre for Economic Policy Research.
    2. Zheng Fan & Worapree Maneesoonthorn & Yong Song, 2025. "A New Perspective of the Meese-Rogoff Puzzle: Application of Sparse Dynamic Shrinkage," Papers 2507.14408, arXiv.org.

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