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Combining Multivariate Density Forecasts Using Predictive Criteria

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  • 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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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. Litterman, Robert B, 1986. "Forecasting with Bayesian Vector Autoregressions-Five Years of Experience," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 4(1), pages 25-38, January.
  2. 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, Board of Governors of the Federal Reserve System (U.S.) 2004-03, Board of Governors of the Federal Reserve System (U.S.).
  3. Jana Eklund & Sune Karlsson, 2007. "Forecast Combination and Model Averaging Using Predictive Measures," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 26(2-4), pages 329-363.
  4. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 19(4), pages 465-74, October.
  5. Kapetanios, G. & Labhard, V. & Price, S., 2007. "Forecasting using Bayesian and information theoretic model averaging: an application to UK inflation," Working Papers, Department of Economics, City University London 07/15, Department of Economics, City University London.
  6. Lawrence J. Christiano & Martin Eichenbaum & Charles Evans, 2001. "Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy," NBER Working Papers 8403, National Bureau of Economic Research, Inc.
  7. 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.
  8. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(2), pages 147-62, April.
  9. Kadiyala, K. Rao & Karlsson, Sune, 1994. "Numerical Aspects of Bayesian VAR-modeling," Working Paper Series in Economics and Finance 12, Stockholm School of Economics.
  10. Hall, Stephen G. & Mitchell, James, 2007. "Combining density forecasts," International Journal of Forecasting, Elsevier, Elsevier, vol. 23(1), pages 1-13.
  11. Boivin, Jean & Ng, Serena, 2005. "Understanding and Comparing Factor-Based Forecasts," MPRA Paper 836, University Library of Munich, Germany.
  12. Adolfson, Malin & Laseen, Stefan & Linde, Jesper & Villani, Mattias, 2007. "Bayesian estimation of an open economy DSGE model with incomplete pass-through," Journal of International Economics, Elsevier, vol. 72(2), pages 481-511, July.
  13. Christian Gillitzer & Jonathan Kearns, 2007. "Forecasting with Factors: The Accuracy of Timeliness," RBA Research Discussion Papers, Reserve Bank of Australia rdp2007-03, Reserve Bank of Australia.
  14. 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.
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Cited by:
  1. 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.
  2. Sean Langcake & Tim Robinson, 2013. "An Empirical BVAR-DSGE Model of the Australian Economy," RBA Research Discussion Papers, Reserve Bank of Australia rdp2013-07, Reserve Bank of Australia.
  3. Andrew Hodge & Tim Robinson & Robyn Stuart, 2008. "A Small BVAR-DSGE Model for Forecasting the Australian Economy," RBA Research Discussion Papers, Reserve Bank of Australia rdp2008-04, Reserve Bank of Australia.
  4. 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.
  5. Peter Tulip & Stephanie Wallace, 2012. "Estimates of Uncertainty around the RBA's Forecasts," RBA Research Discussion Papers, Reserve Bank of Australia rdp2012-07, Reserve Bank of Australia.
  6. Jakub Ryšánek, 2010. "Combining VAR Forecast Densities Using Fast Fourier Transform," Acta Oeconomica Pragensia, University of Economics, Prague, vol. 2010(5), pages 72-88.
  7. 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.
  8. 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.

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