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Combining Multivariate Density Forecasts Using Predictive Criteria

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Author Info

  • Hugo Gerard

    (Reserve Bank of Australia)

  • Kristoffer Nimark

    (Reserve Bank of Australia)

Abstract

This paper combines multivariate density forecasts of output growth, inflation and interest rates from a suite of models. An out-of-sample weighting scheme based on the predictive likelihood as proposed by Eklund and Karlsson (2007) and Andersson and Karlsson (2007) is used to combine the models. Three classes of models are considered: a Bayesian vector autoregression (BVAR), a factor-augmented vector autoregression (FAVAR) and a medium-scale dynamic stochastic general equilibrium (DSGE) model. Using Australian data over the inflation-targeting period, we find that, at short forecast horizons, the Bayesian VAR model is assigned the most weight, while at intermediate and longer horizons the factor model is preferred. The DSGE model is assigned little weight at all horizons, a result that can be attributed to the DSGE model producing density forecasts that are very wide when compared with the actual distribution of observations. While a density forecast evaluation exercise reveals little formal evidence that the optimally combined densities are superior to those from the best-performing individual model, or a simple equal-weighting scheme, this may be a result of the short sample available.

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Bibliographic Info

Paper provided by Reserve Bank of Australia in its series RBA Research Discussion Papers with number rdp2008-02.

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Date of creation: May 2008
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Handle: RePEc:rba:rbardp:rdp2008-02

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Keywords: density forecasts; combining forecasts; predictive criteria;

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References

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  1. Kadiyala, K. Rao & Karlsson, Sune, 1994. "Numerical Aspects of Bayesian VAR-modeling," Working Paper Series in Economics and Finance 12, Stockholm School of Economics.
  2. Francis X. Diebold & Jinyong Hahn & Anthony S. Tay, 1999. "Multivariate Density Forecast Evaluation And Calibration In Financial Risk Management: High-Frequency Returns On Foreign Exchange," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 661-673, November.
  3. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-62, April.
  4. 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.).
  5. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-83, November.
  6. Adolfson, Malin & Laséen, Stefan & Lindé, Jesper & Villani, Mattias, 2005. "Bayesian Estimation of an Open Economy DSGE Model with Incomplete Pass-Through," Working Paper Series 179, Sveriges Riksbank (Central Bank of Sweden).
  7. George Kapetanios & Vincent Labhard & Simon Price, 2006. "Forecasting using Bayesian and Information Theoretic Model Averaging: An Application to UK Inflation," Working Papers 566, Queen Mary, University of London, School of Economics and Finance.
  8. Jean Boivin & Serena Ng, 2005. "Understanding and Comparing Factor-Based Forecasts," NBER Working Papers 11285, National Bureau of Economic Research, Inc.
  9. Lawrence J. Christiano & Martin Eichenbaum & Charles L. Evans, 2001. "Nominal rigidities and the dynamic effects of a shock to monetary policy," Working Paper Series WP-01-08, Federal Reserve Bank of Chicago.
  10. 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.
  11. Litterman, Robert B, 1986. "Forecasting with Bayesian Vector Autoregressions-Five Years of Experience," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(1), pages 25-38, January.
  12. Hall, Stephen G. & Mitchell, James, 2007. "Combining density forecasts," International Journal of Forecasting, Elsevier, vol. 23(1), pages 1-13.
  13. Eklund, Jana & Karlsson, Sune, 2005. "Forecast Combination and Model Averaging using Predictive Measures," Working Paper Series 191, Sveriges Riksbank (Central Bank of Sweden).
  14. Christian Gillitzer & Jonathan Kearns, 2007. "Forecasting with Factors: The Accuracy of Timeliness," RBA Research Discussion Papers rdp2007-03, Reserve Bank of Australia.
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Citations

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Cited by:
  1. David Norman & Anthony Richards, 2012. "The Forecasting Performance of Single Equation Models of Inflation," The Economic Record, The Economic Society of Australia, vol. 88(280), pages 64-78, 03.
  2. Sean Langcake & Tim Robinson, 2013. "An Empirical BVAR-DSGE Model of the Australian Economy," RBA Research Discussion Papers rdp2013-07, Reserve Bank of Australia.
  3. Francesco Ravazzolo & Shaun P Vahey, 2010. "Measuring Core Inflation in Australia with Disaggregate Ensembles," RBA Annual Conference Volume, in: Renée Fry & Callum Jones & Christopher Kent (ed.), Inflation in an Era of Relative Price Shocks Reserve Bank of Australia.
  4. Wolters, Maik Hendrik, 2012. "Evaluating point and density forecasts of DSGE models," IMFS Working Paper Series 59, Institute for Monetary and Financial Stability (IMFS), Goethe University Frankfurt.
  5. Jakub Ryšánek, 2010. "Combining VAR Forecast Densities Using Fast Fourier Transform," Acta Oeconomica Pragensia, University of Economics, Prague, vol. 2010(5), pages 72-88.
  6. Peter Tulip & Stephanie Wallace, 2012. "Estimates of Uncertainty around the RBA's Forecasts," RBA Research Discussion Papers rdp2012-07, Reserve Bank of Australia.
  7. Wolters, Maik H., 2011. "Forecasting under Model Uncertainty," Annual Conference 2011 (Frankfurt, Main): The Order of the World Economy - Lessons from the Crisis 48723, Verein für Socialpolitik / German Economic Association.
  8. Andrew Hodge & Tim Robinson & Robyn Stuart, 2008. "A Small BVAR-DSGE Model for Forecasting the Australian Economy," RBA Research Discussion Papers rdp2008-04, Reserve Bank of Australia.

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