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Combining multivariate density forecasts using predictive criteria

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  • Hugo Gerard
  • Kristoffer Nimark

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 (2005) 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, 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.

Suggested Citation

  • Hugo Gerard & Kristoffer Nimark, 2008. "Combining multivariate density forecasts using predictive criteria," Economics Working Papers 1117, Department of Economics and Business, Universitat Pompeu Fabra, revised Oct 2008.
    • Handle: RePEc:upf:upfgen:1117
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    References listed on IDEAS

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    2. 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, March.
    3. Maik H. Wolters, 2015. "Evaluating Point and Density Forecasts of DSGE Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(1), pages 74-96, January.
    4. Bjørnland, Hilde C. & Gerdrup, Karsten & Jore, Anne Sofie & Smith, Christie & Thorsrud, Leif Anders, 2011. "Weights and pools for a Norwegian density combination," The North American Journal of Economics and Finance, Elsevier, vol. 22(1), pages 61-76, January.
    5. Kirdan Lees, 2009. "Overview of a recent Reserve Bank workshop: nowcasting with model combination," Reserve Bank of New Zealand Bulletin, Reserve Bank of New Zealand, vol. 72, pages 31-33, March.
    6. Knotek, Edward S. & Zaman, Saeed, 2023. "Real-time density nowcasts of US inflation: A model combination approach," International Journal of Forecasting, Elsevier, vol. 39(4), pages 1736-1760.
    7. 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.
    8. Magnus Reif, 2020. "Macroeconomics, Nonlinearities, and the Business Cycle," ifo Beiträge zur Wirtschaftsforschung, ifo Institute - Leibniz Institute for Economic Research at the University of Munich, number 87.
    9. Valeriu Nalban, 2015. "Do Bayesian Vector Autoregressive models improve density forecasting accuracy? The case of the Czech Republic and Romania," International Journal of Economic Sciences, International Institute of Social and Economic Sciences, vol. 4(1), pages 60-74, March.
    10. Tomáš Jeřábek & Radka Šperková, 2015. "A Predictive Likelihood Approach to Bayesian Averaging," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 63(4), pages 1269-1276.
    11. Jakub Ryšánek, 2010. "Combining VAR Forecast Densities Using Fast Fourier Transform," Acta Oeconomica Pragensia, Prague University of Economics and Business, vol. 2010(5), pages 72-88.
    12. Cardani, Roberta & Paccagnini, Alessia & Villa, Stefania, 2019. "Forecasting with instabilities: An application to DSGE models with financial frictions," Journal of Macroeconomics, Elsevier, vol. 61(C), pages 1-1.
    13. James Bishop & Peter Tulip, 2017. "Anticipatory Monetary Policy and the 'Price Puzzle'," RBA Research Discussion Papers rdp2017-02, Reserve Bank of Australia.
    14. Ida Wolden Bache & James Mitchell & Francesco Ravazzolo & Shaun P. Vahey, 2009. "Macro modelling with many models," Working Paper 2009/15, Norges Bank.
    15. Farooq Akram & Andrew Binning & Junior Maih, 2016. "Joint prediction bands for macroeconomic risk management," Working Paper 2016/7, Norges Bank.
    16. Sean Langcake & Tim Robinson, 2013. "An Empirical BVAR-DSGE Model of the Australian Economy," RBA Research Discussion Papers rdp2013-07, Reserve Bank of Australia.
    17. Reif Magnus, 2021. "Macroeconomic uncertainty and forecasting macroeconomic aggregates," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 25(2), pages 1-20, April.
    18. Roberta Cardani & Alessia Paccagnini & Stefania Villa, 2015. "Forecasting in a DSGE Model with Banking Intermediation: Evidence from the US," Working Papers 292, University of Milano-Bicocca, Department of Economics, revised Feb 2015.
    19. Farooq Akram & Andrew Binning & Junior Maih, 2016. "Joint prediction bands for macroeconomic risk management," Working Paper 2016/7, Norges Bank.
    20. Francesco Ravazzolo & Shaun P Vahey, 2010. "Measuring Core Inflation in Australia with Disaggregate Ensembles," RBA Annual Conference Volume (Discontinued), in: Renée Fry & Callum Jones & Christopher Kent (ed.),Inflation in an Era of Relative Price Shocks, Reserve Bank of Australia.
    21. Peter Tulip & Stephanie Wallace, 2012. "Estimates of Uncertainty around the RBA's Forecasts," RBA Research Discussion Papers rdp2012-07, Reserve Bank of Australia.

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    More about this item

    Keywords

    Density forecasts; combining forecasts; predictive criteria;
    All these keywords.

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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