IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Common drifting volatility in large Bayesian VARs

  • Andrea Carriero
  • Todd E. Clark
  • Massimiliano Marcellino

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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: https://www.clevelandfed.org/~/media/Files/Working%20Papers/wp2012/wp1206-common-drifting-volatility-in-large-bayesian-vars.pdf?la=en
File Function: Full text
Download Restriction: no

Paper provided by Federal Reserve Bank of Cleveland in its series Working Paper with number 1206.

as
in new window

Length:
Date of creation: 2012
Date of revision:
Handle: RePEc:fip:fedcwp:1206
Contact details of provider: Postal: 1455 East 6th St., Cleveland OH 44114
Phone: 216.579.2000
Web page: http://www.clevelandfed.org/

More information through EDIRC

Order Information: Email:


References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Koop, Gary & Korobilis, Dimitris, 2013. "Large time-varying parameter VARs," Journal of Econometrics, Elsevier, vol. 177(2), pages 185-198.
  2. Christopher A. Sims, 2002. "The Role of Models and Probabilities in the Monetary Policy Process," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 33(2), pages 1-62.
  3. Clements, Michael P. & Hendry, David F. (ed.), 2011. "The Oxford Handbook of Economic Forecasting," OUP Catalogue, Oxford University Press, number 9780195398649, March.
  4. Nelson, Daniel B, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comment," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 403-06, October.
  5. Stark, Tom & Croushore, Dean, 2002. "Forecasting with a real-time data set for macroeconomists," Journal of Macroeconomics, Elsevier, vol. 24(4), pages 507-531, December.
  6. Kadiyala, K. Rao & Karlsson, Sune, 1994. "Numerical Aspects of Bayesian VAR-modeling," SSE/EFI Working Paper Series in Economics and Finance 12, Stockholm School of Economics.
  7. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 371-89, October.
  8. Geweke, John & Amisano, Gianni, 2008. "Comparing and evaluating Bayesian predictive distributions of assets returns," Working Paper Series 0969, European Central Bank.
  9. Marco Del Negro & Frank Schorfheide, 2004. "Priors from General Equilibrium Models for VARS," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(2), pages 643-673, 05.
  10. Geweke, John, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comment," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 397-99, October.
  11. Harvey, Andrew C & Ruiz, Esther, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comment," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 402-03, October.
  12. Eric Jacquier & Nicholas G. Polson & Peter Rossi, . "Stochastic Volatility: Univariate and Multivariate Extensions," Rodney L. White Center for Financial Research Working Papers 19-95, Wharton School Rodney L. White Center for Financial Research.
  13. Marta Bańbura, 2008. "Large Bayesian VARs," 2008 Meeting Papers 334, Society for Economic Dynamics.
  14. Giorgio E. Primiceri, 2005. "Time Varying Structural Vector Autoregressions and Monetary Policy," Review of Economic Studies, Oxford University Press, vol. 72(3), pages 821-852.
  15. Danielsson, Jon, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comment," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 393-95, October.
  16. Croushore, Dean, 2006. "Forecasting with Real-Time Macroeconomic Data," Handbook of Economic Forecasting, Elsevier.
  17. Todd E. Clark & Michael W. McCracken, 2009. "Nested forecast model comparisons: a new approach to testing equal accuracy," Working Papers 2009-050, Federal Reserve Bank of St. Louis.
  18. Andersen, Torben G, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comment," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 389-92, October.
  19. Harvey, David & Leybourne, Stephen & Newbold, Paul, 1997. "Testing the equality of prediction mean squared errors," International Journal of Forecasting, Elsevier, vol. 13(2), pages 281-291, June.
  20. Engle, Robert F, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comment," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 395-96, October.
  21. Andrea Carriero & George Kapetanios & Massimiliano Marcellino, 2009. "Forecasting Large Datasets with Bayesian Reduced Rank Multivariate Models," Economics Working Papers ECO2009/31, European University Institute.
  22. Clark, Todd E. & Davig, Troy, 2011. "Decomposing the declining volatility of long-term inflation expectations," Journal of Economic Dynamics and Control, Elsevier, vol. 35(7), pages 981-999, July.
  23. Clark, Todd E., 2011. "Real-Time Density Forecasts From Bayesian Vector Autoregressions With Stochastic Volatility," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(3), pages 327-341.
  24. Diebold, Francis X & Mariano, Roberto S, 1995. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 253-63, July.
  25. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2006. "Analysis of high dimensional multivariate stochastic volatility models," Journal of Econometrics, Elsevier, vol. 134(2), pages 341-371, October.
  26. Ben S. Bernanke & Jean Boivin & Piotr Eliasz, 2004. "Measuring the effects of monetary policy: a factor-augmented vector autoregressive (FAVAR) approach," Finance and Economics Discussion Series 2004-03, Board of Governors of the Federal Reserve System (U.S.).
  27. Christopher A. Sims, 1992. "A Nine Variable Probabilistic Macroeconomic Forecasting Model," Cowles Foundation Discussion Papers 1034, Cowles Foundation for Research in Economics, Yale University.
  28. Croushore, Dean & Stark, Tom, 2001. "A real-time data set for macroeconomists," Journal of Econometrics, Elsevier, vol. 105(1), pages 111-130, November.
  29. Faust, Jon & Wright, Jonathan H., 2009. "Comparing Greenbook and Reduced Form Forecasts Using a Large Realtime Dataset," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(4), pages 468-479.
  30. Gianni Amisano & Raffaella Giacomini, 2005. "Comparing Density Forecsts via Weighted Likelihood Ratio Tests," Working Papers ubs0504, University of Brescia, Department of Economics.
  31. David H. Romer & Christina D. Romer, 2000. "Federal Reserve Information and the Behavior of Interest Rates," American Economic Review, American Economic Association, vol. 90(3), pages 429-457, June.
  32. Christopher A. Sims & Tao Zha, 1996. "Bayesian methods for dynamic multivariate models," Working Paper 96-13, Federal Reserve Bank of Atlanta.
  33. Uhlig, Harald, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comment," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 410-12, October.
  34. Shephard, Neil & Kim, Sangjoon, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comment," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 406-10, October.
  35. Malin Adolfson & Jesper Linde & Mattias Villani, 2007. "Forecasting Performance of an Open Economy DSGE Model," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 289-328.
  36. Marco Del Negro & Christopher Otrok, 2008. "Dynamic factor models with time-varying parameters: measuring changes in international business cycles," Staff Reports 326, Federal Reserve Bank of New York.
  37. Todd E. Clark & Michael W. McCracken, 2010. "Testing for unconditional predictive ability," Working Papers 2010-031, Federal Reserve Bank of St. Louis.
  38. Jacek Osiewalski & Anna Pajor, 2009. "Bayesian Analysis for Hybrid MSF-SBEKK Models of Multivariate Volatility," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 1(2), pages 179-202, November.
  39. Domenico Giannone & Martha Banbura & Lucrezia Reichlin, 2008. "Bayesian VARs with large panels," ULB Institutional Repository 2013/13388, ULB -- Universite Libre de Bruxelles.
  40. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-17, October.
  41. Anna Pajor, 2006. "Bayesian Analysis of the Conditional Correlation Between Stock Index Returns with Multivariate SV Models," Papers physics/0607176, arXiv.org.
  42. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2002. "Markov chain Monte Carlo methods for stochastic volatility models," Journal of Econometrics, Elsevier, vol. 108(2), pages 281-316, June.
  43. Ghysels, Eric & Jasiak, Joanna, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comment," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 399-401, October.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:fip:fedcwp:1206. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Lee Faulhaber)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.