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Sequential Bayesian inference for vector autoregressions with stochastic volatility

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  • Bognanni, Mark
  • Zito, John

Abstract

We develop a sequential Monte Carlo (SMC) algorithm for Bayesian inference in vector autoregressions with stochastic volatility (VAR-SV). The algorithm builds particle approximations to the sequence of the model’s posteriors, adapting the particles from one approximation to the next as the window of available data expands. The parallelizability of the algorithm’s computations allows the adaptations to occur rapidly. Our particular algorithm exploits the ability to marginalize many parameters from the posterior analytically and embeds a known Markov chain Monte Carlo (MCMC) algorithm for the model as an effective mutation kernel for fighting particle degeneracy. We show that, relative to using MCMC alone, our algorithm increases the precision of inference while reducing computing time by an order of magnitude when estimating a medium-scale VAR-SV model.

Suggested Citation

  • Bognanni, Mark & Zito, John, 2020. "Sequential Bayesian inference for vector autoregressions with stochastic volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 113(C).
    • Handle: RePEc:eee:dyncon:v:113:y:2020:i:c:s016518892030021x
    DOI: 10.1016/j.jedc.2020.103851
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    1. Pierre Del Moral & Arnaud Doucet & Ajay Jasra, 2006. "Sequential Monte Carlo samplers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 411-436, June.
    2. Walter R. Gilks & Carlo Berzuini, 2001. "Following a moving target—Monte Carlo inference for dynamic Bayesian models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 127-146.
    3. Frank Smets & Rafael Wouters, 2007. "Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach," American Economic Review, American Economic Association, vol. 97(3), pages 586-606, June.
    4. Sims, Christopher A. & Waggoner, Daniel F. & Zha, Tao, 2008. "Methods for inference in large multiple-equation Markov-switching models," Journal of Econometrics, Elsevier, vol. 146(2), pages 255-274, October.
    5. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2016. "Common Drifting Volatility in Large Bayesian VARs," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 375-390, July.
    6. 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.
    7. Joshua C. C. Chan & Eric Eisenstat, 2018. "Bayesian model comparison for time‐varying parameter VARs with stochastic volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(4), pages 509-532, June.
    8. Garland Durham & John Geweke, 2014. "Adaptive Sequential Posterior Simulators for Massively Parallel Computing Environments," Advances in Econometrics, in: Bayesian Model Comparison, volume 34, pages 1-44, Emerald Group Publishing Limited.
    9. Todd E. Clark & Francesco Ravazzolo, 2015. "Macroeconomic Forecasting Performance under Alternative Specifications of Time‐Varying Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(4), pages 551-575, June.
    10. Gary Koop & Simon M. Potter, 2007. "Estimation and Forecasting in Models with Multiple Breaks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(3), pages 763-789.
    11. Mark Bognanni, 2018. "A Class of Time-Varying Parameter Structural VARs for Inference under Exact or Set Identification," Working Papers (Old Series) 1811, Federal Reserve Bank of Cleveland.
    12. Christopher A. Sims & Tao Zha, 2006. "Were There Regime Switches in U.S. Monetary Policy?," American Economic Review, American Economic Association, vol. 96(1), pages 54-81, March.
    13. repec:dau:papers:123456789/1908 is not listed on IDEAS
    14. Casarin, Roberto & Grassi, Stefano & Ravazzolo, Francesco & van Dijk, Herman K., 2015. "Parallel Sequential Monte Carlo for Efficient Density Combination: The DeCo MATLAB Toolbox," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 68(i03).
    15. Giorgio E. Primiceri, 2005. "Time Varying Structural Vector Autoregressions and Monetary Policy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 821-852.
    16. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2015. "Prior Selection for Vector Autoregressions," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 436-451, May.
    17. Fernández-Villaverde, Jesús & Zarruk Valencia , David, 2018. "A Practical Guide to Parallelization in Economics," CEPR Discussion Papers 12890, C.E.P.R. Discussion Papers.
    18. Marco Del Negro & Giorgio E. Primiceri, 2015. "Time Varying Structural Vector Autoregressions and Monetary Policy: A Corrigendum," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(4), pages 1342-1345.
    19. repec:dau:papers:123456789/7305 is not listed on IDEAS
    20. Aruoba, S. Borağan & Fernández-Villaverde, Jesús, 2015. "A comparison of programming languages in macroeconomics," Journal of Economic Dynamics and Control, Elsevier, vol. 58(C), pages 265-273.
    21. Drew Creal, 2012. "A Survey of Sequential Monte Carlo Methods for Economics and Finance," Econometric Reviews, Taylor & Francis Journals, vol. 31(3), pages 245-296.
    22. N. Chopin & P. E. Jacob & O. Papaspiliopoulos, 2013. "SMC-super-2: an efficient algorithm for sequential analysis of state space models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 397-426, June.
    23. Omori, Yasuhiro & Chib, Siddhartha & Shephard, Neil & Nakajima, Jouchi, 2007. "Stochastic volatility with leverage: Fast and efficient likelihood inference," Journal of Econometrics, Elsevier, vol. 140(2), pages 425-449, October.
    24. Garland Durham & John Geweke & Susan Porter‐Hudak & Fallaw Sowell, 2019. "Bayesian Inference for ARFIMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 40(4), pages 388-410, July.
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    Cited by:

    1. Chan, Joshua C.C., 2023. "Comparing stochastic volatility specifications for large Bayesian VARs," Journal of Econometrics, Elsevier, vol. 235(2), pages 1419-1446.
    2. Joshua Chan, 2023. "BVARs and Stochastic Volatility," Papers 2310.14438, arXiv.org.
    3. Edward P. Herbst & Fabian Winkler, 2021. "The Factor Structure of Disagreement," Finance and Economics Discussion Series 2021-046, Board of Governors of the Federal Reserve System (U.S.).
    4. Bognanni, Mark, 2022. "Comment on “Large Bayesian vector autoregressions with stochastic volatility and non-conjugate priors”," Journal of Econometrics, Elsevier, vol. 227(2), pages 498-505.

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