Advanced Search
MyIDEAS: Login

Time-varying combinations of predictive densities using nonlinear filtering

Contents:

Author Info

  • Billio, Monica
  • Casarin, Roberto
  • Ravazzolo, Francesco
  • van Dijk, Herman K.

Abstract

We propose a Bayesian combination approach for multivariate predictive densities which relies upon a distributional state space representation of the combination weights. Several specifications of multivariate time-varying weights are introduced with a particular focus on weight dynamics driven by the past performance of the predictive densities and the use of learning mechanisms. In the proposed approach the model set can be incomplete, meaning that all models can be individually misspecified. A Sequential Monte Carlo method is proposed to approximate the filtering and predictive densities. The combination approach is assessed using statistical and utility-based performance measures for evaluating density forecasts of simulated data, US macroeconomic time series and surveys of stock market prices. Simulation results indicate that, for a set of linear autoregressive models, the combination strategy is successful in selecting, with probability close to one, the true model when the model set is complete and it is able to detect parameter instability when the model set includes the true model that has generated subsamples of data. Also, substantial uncertainty appears in the weights when predictors are similar; residual uncertainty reduces when the model set is complete; and learning reduces this uncertainty. For the macro series we find that incompleteness of the models is relatively large in the 1970’s, the beginning of the 1980’s and during the recent financial crisis, and lower during the Great Moderation; the predicted probabilities of recession accurately compare with the NBER business cycle dating; model weights have substantial uncertainty attached. With respect to returns of the S&P 500 series, we find that an investment strategy using a combination of predictions from professional forecasters and from a white noise model puts more weight on the white noise model in the beginning of the 1990’s and switches to giving more weight to the professional forecasts over time. Information on the complete predictive distribution and not just on some moments turns out to be very important, above all during turbulent times such as the recent financial crisis. More generally, the proposed distributional state space representation offers great flexibility in combining densities.

Download Info

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: http://www.sciencedirect.com/science/article/pii/S0304407613000869
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 177 (2013)
Issue (Month): 2 ()
Pages: 213-232

as in new window
Handle: RePEc:eee:econom:v:177:y:2013:i:2:p:213-232

Contact details of provider:
Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Density forecast combination; Survey forecast; Bayesian filtering; Sequential Monte Carlo;

Other versions of this item:

Find related papers by JEL classification:

References

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. Dimitris Korobilis, 2013. "Var Forecasting Using Bayesian Variable Selection," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(2), pages 204-230, 03.
  2. Creal, D., 2009. "A survey of sequential Monte Carlo methods for economics and finance," Serie Research Memoranda 0018, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  3. Dangl, Thomas & Halling, Michael, 2012. "Predictive regressions with time-varying coefficients," Journal of Financial Economics, Elsevier, vol. 106(1), pages 157-181.
  4. Antonello D'Agostino & Luca Gambetti & Domenico Giannone, 2009. "Macroeconomic Forecasting and Structural Change," Working Papers ECARES 2009_020, ULB -- Universite Libre de Bruxelles.
  5. repec:att:wimass:9417 is not listed on IDEAS
  6. Boero,Gianna & Smith,Jeremy & Wallis,Kenneth F, 2006. "Uncertainty and disagreement in economic prediction : the Bank of England Survey of External Forecasters," The Warwick Economics Research Paper Series (TWERPS) 811, University of Warwick, Department of Economics.
  7. Massimo Guidolin & Allan Timmerman, 2007. "Forecasts of U.S. short-term interest rates: a flexible forecast combination approach," Working Papers 2005-059, Federal Reserve Bank of St. Louis.
  8. Terui, N. & van Dijk, H.K., 1999. "Combined forecasts from linear and nonlinear time series models," Econometric Institute Research Papers EI 9949-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  9. Lennart Hoogerheide & Richard Kleijn & Francesco Ravazzolo & Herman K. van Dijk & Marno Verbeek, 2009. "Forecast Accuracy and Economic Gains from Bayesian Model Averaging using Time Varying Weights," Tinbergen Institute Discussion Papers 09-061/4, Tinbergen Institute.
  10. Anne Sofie Jore & James Mitchell & Shaun P. Vahey, 2010. "Combining forecast densities from VARs with uncertain instabilities," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 621-634.
  11. Andrew Ang & Geert Bekaert & Min Wei, 2005. "Do Macro Variables, Asset Markets or Surveys Forecast Inflation Better?," NBER Working Papers 11538, National Bureau of Economic Research, Inc.
  12. Todd E. Clark & Francesco Ravazzolo, 2012. "The macroeconomic forecasting performance of autoregressive models with alternative specifications of time-varying volatility," Working Paper 2012/09, Norges Bank.
  13. Amisano, Gianni & Giacomini, Raffaella, 2007. "Comparing Density Forecasts via Weighted Likelihood Ratio Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 177-190, April.
  14. 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.
  15. Amit Goval & Ivo Welch, 2004. "A Comprehensive Look at the Empirical Performance of Equity Premium Prediction," NBER Working Papers 10483, National Bureau of Economic Research, Inc.
  16. Geweke, John & Amisano, Gianni, 2010. "Comparing and evaluating Bayesian predictive distributions of asset returns," International Journal of Forecasting, Elsevier, vol. 26(2), pages 216-230, April.
  17. Gary Koop & Dimitris Korobilis, 2012. "Forecasting Inflation Using Dynamic Model Averaging," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(3), pages 867-886, 08.
  18. Victor Zarnowitz, 1992. "Consensus and Uncertainty in Economic Prediction," NBER Chapters, in: Business Cycles: Theory, History, Indicators, and Forecasting, pages 492-518 National Bureau of Economic Research, Inc.
  19. Lennart F. Hoogerheide & Francesco Ravazzolo & Herman K. van Dijk, 2011. "Backtesting Value-at-Risk using Forecasts for Multiple Horizons, a Comment on the Forecast Rationality Tests of A.J. Patton and A. Timmermann," Tinbergen Institute Discussion Papers 11-131/4, Tinbergen Institute.
  20. Hall, Stephen G. & Mitchell, James, 2007. "Combining density forecasts," International Journal of Forecasting, Elsevier, vol. 23(1), pages 1-13.
  21. Yash P. Mehra, 2002. "Survey measures of expected inflation : revisiting the issues of predictive content and rationality," Economic Quarterly, Federal Reserve Bank of Richmond, issue Sum, pages 17-36.
  22. Christian Kascha & Francesco Ravazzolo, 2008. "Combining inflation density forecasts," Working Paper 2008/22, Norges Bank.
  23. Sloughter, J. McLean & Gneiting, Tilmann & Raftery, Adrian E., 2010. "Probabilistic Wind Speed Forecasting Using Ensembles and Bayesian Model Averaging," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 25-35.
  24. Hansen, Bruce E., 2008. "Least-squares forecast averaging," Journal of Econometrics, Elsevier, vol. 146(2), pages 342-350, October.
  25. Kajal Lahiri & Xuguang Sheng, 2010. "Measuring forecast uncertainty by disagreement: The missing link," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 514-538.
  26. William A. Branch, 2004. "The Theory of Rationally Heterogeneous Expectations: Evidence from Survey Data on Inflation Expectations," Economic Journal, Royal Economic Society, vol. 114(497), pages 592-621, 07.
  27. Nicholas Barberis, 2000. "Investing for the Long Run when Returns Are Predictable," Journal of Finance, American Finance Association, vol. 55(1), pages 225-264, 02.
  28. repec:taf:jnlbes:v:30:y:2012:i:1:p:1-17 is not listed on IDEAS
  29. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
  30. Markku Lanne, 2009. "Properties of Market-Based and Survey Macroeconomic Forecasts for Different Data Releases," Economics Bulletin, AccessEcon, vol. 29(3), pages 2231-2240.
  31. Francis X. Diebold & Robert S. Mariano, 1994. "Comparing Predictive Accuracy," NBER Technical Working Papers 0169, National Bureau of Economic Research, Inc.
  32. Francis X. Diebold & Peter Pauly, 1987. "The use of prior information in forecast combination," Special Studies Papers 218, Board of Governors of the Federal Reserve System (U.S.).
  33. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-84, September.
  34. Clements,Michael & Hendry,David, 1998. "Forecasting Economic Time Series," Cambridge Books, Cambridge University Press, number 9780521634809, December.
  35. Koop, Gary & Korobilis, Dimitris, 2012. "Large Time-Varying Parameter VARs," SIRE Discussion Papers 2012-14, Scottish Institute for Research in Economics (SIRE).
  36. Gneiting, Tilmann & Ranjan, Roopesh, 2011. "Comparing Density Forecasts Using Threshold- and Quantile-Weighted Scoring Rules," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(3), pages 411-422.
  37. Lloyd B. Thomas, 1999. "Survey Measures of Expected U.S. Inflation," Journal of Economic Perspectives, American Economic Association, vol. 13(4), pages 125-144, Fall.
  38. Clark, Todd E. & West, Kenneth D., 2007. "Approximately normal tests for equal predictive accuracy in nested models," Journal of Econometrics, Elsevier, vol. 138(1), pages 291-311, May.
  39. Jeff Fleming, 2001. "The Economic Value of Volatility Timing," Journal of Finance, American Finance Association, vol. 56(1), pages 329-352, 02.
  40. Jan J. J. Groen & Richard Paap & Francesco Ravazzolo, 2013. "Real-Time Inflation Forecasting in a Changing World," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 29-44, January.
  41. Francesco Ravazzolo & Shaun P. Vahey, 2010. "Forecast densities for economic aggregates from disaggregate ensembles," Working Paper 2010/02, Norges Bank.
  42. Monica Billio & Roberto Casarin, 2010. "Identifying business cycle turning points with sequential Monte Carlo methods: an online and real-time application to the Euro area," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(1-2), pages 145-167.
  43. Roberto Casarin & Jean-Michel Marin, 2007. "Online data processing: comparison of Bayesian regularized particle filters," Working Papers 0703, University of Brescia, Department of Economics.
  44. Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, 07.
  45. Geweke, John & Whiteman, Charles, 2006. "Bayesian Forecasting," Handbook of Economic Forecasting, Elsevier.
  46. James Mitchell & Stephen G. Hall, 2005. "Evaluating, Comparing and Combining Density Forecasts Using the KLIC with an Application to the Bank of England and NIESR 'Fan' Charts of Inflation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(s1), pages 995-1033, December.
  47. Robert L. Winkler, 1981. "Combining Probability Distributions from Dependent Information Sources," Management Science, INFORMS, vol. 27(4), pages 479-488, April.
  48. Kenneth D. West & Hali J. Edison & Dongchul Cho, 1992. "A Utility Based Comparison of Some Models of Exchange Rate Volatility," NBER Technical Working Papers 0128, National Bureau of Economic Research, Inc.
  49. Monica Billio & Domenico Sartore & Carlo Toffano, 2000. "Combining forecasts: some results on exchange and interest rates," The European Journal of Finance, Taylor & Francis Journals, vol. 6(2), pages 126-145.
  50. Francesco Ravazzolo & Shaun P. Vahey, 2010. "Forecast Densities for Economic Aggregates from Disaggregate Ensembles," CAMA Working Papers 2010-10, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  51. Fama, Eugene F. & Gibbons, Michael R., 1984. "A comparison of inflation forecasts," Journal of Monetary Economics, Elsevier, vol. 13(3), pages 327-348, May.
  52. Billio Monica & Casarin Roberto, 2011. "Beta Autoregressive Transition Markov-Switching Models for Business Cycle Analysis," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(4), pages 1-32, September.
  53. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-74, October.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Marco Jacopo Lombardi, 2013. "On the correlation between commodity and equity returns: implications for portfolio allocation," BIS Working Papers 420, Bank for International Settlements.
  2. Francesco Ravazzolo & Marco J. Lombardi, 2012. "Oil price density forecasts: Exploring the linkages with stock markets," Working Papers 0008, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
  3. Monica Billio & Roberto Casarin & Francesco Ravazzolo & Herman K. van Dijk, 2013. "Interactions between eurozone and US booms and busts: A Bayesian panel Markov-switching VAR model," Working Paper 2013/20, Norges Bank.
  4. Lukasz Gatarek & Lennart Hoogerheide & Koen Hooning & Herman K. van Dijk, 2013. "Censored Posterior and Predictive Likelihood in Left-Tail Prediction for Accurate Value at Risk Estimation," Tinbergen Institute Discussion Papers 13-060/III, Tinbergen Institute, revised 06 Mar 2014.
  5. Roberto Casarin & Stefano Grassi & Francesco Ravazzolo & Herman K. van Dijk, 2013. "Parallel Sequential Monte Carlo for Efficient Density Combination: The DeCo Matlab Toolbox," Working Papers 2013:08, Department of Economics, University of Venice "Ca' Foscari".

Lists

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

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:177:y:2013:i:2:p:213-232. 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: (Zhang, Lei).

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.