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Bayesian model comparison for time-varying parameter VARs with stochastic volatility

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  • Joshua C.C. Chan
  • Eric Eisenstat

Abstract

We develop importance sampling methods for computing two popular Bayesian model comparison criteria, namely, the marginal likelihood and deviance information criterion (DIC) for TVP-VARs with stochastic volatility. The proposed estimators are based on the integrated likelihood, which are substantially more reliable than alternatives. Specifically, integrated likelihood evaluation is achieved by integrating out the time-varying parameters analytically, while the log-volatilities are integrated out numerically via importance sampling. Using US and Australian data, we find overwhelming support for the TVPVAR with stochastic volatility compared to a conventional constant coefficients VAR with homoscedastic innovations. Most of the gains, however, appear to have come from allowing for stochastic volatility rather than time variation in the VAR coefficients or contemporaneous relationships. Indeed, according to both criteria, a constant coefficients VAR with stochastic volatility receives similar support as the more general model with time-varying parameters.

Suggested Citation

  • Joshua C.C. Chan & Eric Eisenstat, 2015. "Bayesian model comparison for time-varying parameter VARs with stochastic volatility," CAMA Working Papers 2015-32, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  • Handle: RePEc:een:camaaa:2015-32
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    References listed on IDEAS

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    Cited by:

    1. Cross, Jamie & Nguyen, Bao H., 2017. "The relationship between global oil price shocks and China's output: A time-varying analysis," Energy Economics, Elsevier, vol. 62(C), pages 79-91.
    2. Jamie L. Cross & Chenghan Hou & Bao H. Nguyen, 2018. "On the China factor in international oil markets: A regime switching approach," Working Papers No 11/2018, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    3. Markus Heinrich & Magnus Reif, 2018. "Forecasting using mixed-frequency VARs with time-varying parameters," ifo Working Paper Series 273, ifo Institute - Leibniz Institute for Economic Research at the University of Munich.
    4. Deborah Gefang & Gary Koop & Aubrey Poon, 2019. "Variational Bayesian Inference in Large Vector Autoregressions with Hierarchical Shrinkage," Economic Statistics Centre of Excellence (ESCoE) Discussion Papers ESCoE DP-2019-07, Economic Statistics Centre of Excellence (ESCoE).
    5. Gary Koop & Stuart McIntyre & James Mitchell & Aubrey Poon, 2018. "Regional Output Growth in the United Kingdom: More Timely and Higher Frequency Estimates, 1970-2017," Economic Statistics Centre of Excellence (ESCoE) Discussion Papers ESCoE DP-2018-14, Economic Statistics Centre of Excellence (ESCoE).
    6. repec:spr:empeco:v:55:y:2018:i:2:d:10.1007_s00181-017-1280-z is not listed on IDEAS
    7. Karlsson, Sune & Österholm, Pär, 2018. "Is the US Phillips Curve Stable? Evidence from Bayesian VARs," Working Papers 2018:5, Örebro University, School of Business.
    8. Joshua C.C. Chan & Eric Eisenstat & Chenghan Hou & Gary Koop, 2018. "Composite Likelihood Methods for Large Bayesian VARs with Stochastic Volatility," Working Paper Series 44, Economics Discipline Group, UTS Business School, University of Technology, Sydney.
    9. repec:eee:intfor:v:33:y:2017:i:4:p:1025-1043 is not listed on IDEAS
    10. Karlsson, Sune & Österholm, Pär, 2018. "A Note on the Stability of the Swedish Philips Curve," Working Papers 2018:6, Örebro University, School of Business.
    11. Eric Eisenstat & Joshua C.C. Chan & Rodney W. Strachan, 2018. "Reducing Dimensions in a Large TVP-VAR," Working Paper series 18-37, Rimini Centre for Economic Analysis.
    12. Joshua C. C. Chan & Liana Jacobi & Dan Zhu, 2019. "An automated prior robustness analysis in Bayesian model comparison," CAMA Working Papers 2019-45, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    13. Dorra Zouari & Achraf Ghorbel & Sonia Ghorbel-Zouari & Younes Boujelbène, 2014. "Volatility spillovers and dynamic correlation between liquidity risk factors in Tunisian banks," International Journal of Managerial and Financial Accounting, Inderscience Enterprises Ltd, vol. 6(1), pages 1-26.
    14. Wang, Mu-Chun, 2018. "Choosing Prior Hyperparameters: With Applications To Time-Varying Parameter Models," Annual Conference 2018 (Freiburg, Breisgau): Digital Economy 181621, Verein für Socialpolitik / German Economic Association.
    15. repec:onb:oenbfi:y:2019:i:q1/19:b:2 is not listed on IDEAS
    16. Legrand, Romain, 2018. "Time-Varying Vector Autoregressions: Efficient Estimation, Random Inertia and Random Mean," MPRA Paper 88925, University Library of Munich, Germany.
    17. Chan, Joshua C.C. & Eisenstat, Eric, 2018. "Comparing hybrid time-varying parameter VARs," Economics Letters, Elsevier, vol. 171(C), pages 1-5.
    18. 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.
    19. Dieppe, Alistair & van Roye, Björn & Legrand, Romain, 2016. "The BEAR toolbox," Working Paper Series 1934, European Central Bank.
    20. repec:bla:ecorec:v:94:y:2018:i:307:p:372-390 is not listed on IDEAS

    More about this item

    Keywords

    Bayesian; state space; marginal likelihood; deviance information criterion; great moderation;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy

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