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Common Drifting Volatility in Large Bayesian VARs

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  • Andrea CARRIERO
  • Todd E. CLARK
  • Massimiliano MARCELLINO

Abstract

The estimation of large Vector Autoregressions with stochastic volatility using standard methods is computationally very demanding. In this paper we propose to model conditional volatilities as driven by a single common unobserved factor. This is justified by the observation that the pattern of estimated volatilities in empirical analyses is often very similar across variables. Using a combination of a standard natural conjugate prior for the VAR coefficients, and an independent prior on a common stochastic volatility factor, we derive the posterior densities for the parameters of the resulting BVAR with common stochastic volatility (BVAR-CSV). Under the chosen prior the conditional posterior of the VAR coefficients features a Kroneker structure that allows for fast estimation, even in a large system. Using US and UK data, we show that, compared to a model with constant volatilities, our proposed common volatility model significantly improves model fit and forecast accuracy. The gains are comparable to or as great as the gains achieved with a conventional stochastic volatility specification that allows independent volatility processes for each variable. But our common volatility specification greatly speeds computations.

Suggested Citation

  • Andrea CARRIERO & Todd E. CLARK & Massimiliano MARCELLINO, 2012. "Common Drifting Volatility in Large Bayesian VARs," Economics Working Papers ECO2012/08, European University Institute.
  • Handle: RePEc:eui:euiwps:eco2012/08
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    References listed on IDEAS

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    Cited by:

    1. Christine Garnier & Elmar Mertens & Edward Nelson, 2015. "Trend Inflation in Advanced Economies," International Journal of Central Banking, International Journal of Central Banking, vol. 11(4), pages 65-136, September.
    2. Rossi, Barbara, 2013. "Advances in Forecasting under Instability," Handbook of Economic Forecasting, Elsevier.
    3. Berg, Tim O. & Henzel, Steffen R., 2015. "Point and density forecasts for the euro area using Bayesian VARs," International Journal of Forecasting, Elsevier, vol. 31(4), pages 1067-1095.
    4. Dovern, Jonas & Feldkircher, Martin & Huber, Florian, 2016. "Does joint modelling of the world economy pay off? Evaluating global forecasts from a Bayesian GVAR," Journal of Economic Dynamics and Control, Elsevier, vol. 70(C), pages 86-100.
    5. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2015. "Realtime nowcasting with a Bayesian mixed frequency model with stochastic volatility," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 178(4), pages 837-862, October.
    6. Todd E. Clark & Francesco Ravazzolo, 2012. "The macroeconomic forecasting performance of autoregressive models with alternative specifications of time-varying volatility," Working Paper 1218, Federal Reserve Bank of Cleveland.
    7. Mumtaz, Haroon & Theodoridis, Konstantinos, 2017. "Common and country specific economic uncertainty," Journal of International Economics, Elsevier, vol. 105(C), pages 205-216.
    8. Kyle Jurado & Sydney C. Ludvigson & Serena Ng, 2015. "Measuring Uncertainty," American Economic Review, American Economic Association, vol. 105(3), pages 1177-1216, March.
    9. Bańbura, Marta & Giannone, Domenico & Lenza, Michele, 2015. "Conditional forecasts and scenario analysis with vector autoregressions for large cross-sections," International Journal of Forecasting, Elsevier, vol. 31(3), pages 739-756.
    10. Koop, Gary & Korobilis, Dimitris, 2013. "Large time-varying parameter VARs," Journal of Econometrics, Elsevier, vol. 177(2), pages 185-198.
    11. Carriero, Andrea & Clark, Todd & Marcellino, Massimiliano, 2014. "No Arbitrage Priors, Drifting Volatilities, and the Term Structure of Interest Rates," CEPR Discussion Papers 9848, C.E.P.R. Discussion Papers.
    12. Florian Huber, 2014. "Density Forecasting using Bayesian Global Vector Autoregressions with Common Stochastic Volatility," Department of Economics Working Papers wuwp179, Vienna University of Economics and Business, Department of Economics.
    13. Clark, Todd E. & Carriero, Andrea & Marcellino, Massimiliano, 2016. "Large Vector Autoregressions with Stochastic Volatility and Flexible Priors," Working Paper 1617, Federal Reserve Bank of Cleveland.
    14. Carriero, Andrea & Mumtaz, Haroon & Theophilopoulou, Angeliki, 2015. "Macroeconomic information, structural change, and the prediction of fiscal aggregates," International Journal of Forecasting, Elsevier, vol. 31(2), pages 325-348.
    15. Pettenuzzo, Davide & Timmermann, Allan & Valkanov, Rossen, 2016. "A MIDAS approach to modeling first and second moment dynamics," Journal of Econometrics, Elsevier, vol. 193(2), pages 315-334.
    16. David Reifschneider & Peter Tulip, 2017. "Gauging the Uncertainty of the Economic Outlook Using Historical Forecasting Errors: The Federal Reserve's Approach," RBA Research Discussion Papers rdp2017-01, Reserve Bank of Australia.
    17. Irina Zviadadze, 2014. "Term-structure of consumption risk premia in the cross-section of currency returns," 2014 Meeting Papers 1075, Society for Economic Dynamics.
    18. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2015. "Large Vector Autoregressions with Asymmetric Priors," Working Papers 759, Queen Mary University of London, School of Economics and Finance.
    19. Chauvet, Marcelle & Potter, Simon, 2013. "Forecasting Output," Handbook of Economic Forecasting, Elsevier.

    More about this item

    Keywords

    Bayesian VARs; stochastic volatility; forecasting; prior specification;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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