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Constructing Optimal Density Forecasts from Point Forecast Combinations

Author

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  • Luiz Renato Regis de Oliveira Lima
  • Wagner Piazza Gaglianone

Abstract

Decision makers often observe point forecasts of the same variable computed, for instance, by commercial banks, IMF, World Bank, but the econometric models used by such institutions are unknown. This paper shows how to use the information available at point forecasts to compute optimal density forecasts. Our idea builds upon the combination of point forecasts under general loss functions and unknonwn forecast error distributions. We use real-time data to forecast the density of future in‡ation in the U.S. and our results indicate that the proposed method materially improves the real-time accuracy of density forecasts vis-à-vis the ones obtained from the (unknown) individual. econometric models.

Suggested Citation

  • Luiz Renato Regis de Oliveira Lima & Wagner Piazza Gaglianone, 2012. "Constructing Optimal Density Forecasts from Point Forecast Combinations," Série Textos para Discussão (Working Papers) 5, Programa de Pós-Graduação em Economia - PPGE, Universidade Federal da Paraíba.
  • Handle: RePEc:ppg:ppgewp:5
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    File URL: http://www.ccsa.ufpb.br/ppge/arquivos/ensaios/QC5f.pdf
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    References listed on IDEAS

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    1. Issler, João Victor & Lima, Luiz Renato, 2009. "A panel data approach to economic forecasting: The bias-corrected average forecast," Journal of Econometrics, Elsevier, vol. 152(2), pages 153-164, October.
    2. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-474, October.
    3. 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.
    4. Marcellino, Massimiliano & Stock, James H. & Watson, Mark W., 2006. "A comparison of direct and iterated multistep AR methods for forecasting macroeconomic time series," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 499-526.
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    6. Christoffersen, Peter F. & Diebold, Francis X., 1997. "Optimal Prediction Under Asymmetric Loss," Econometric Theory, Cambridge University Press, vol. 13(06), pages 808-817, December.
    7. Hall, Stephen G. & Mitchell, James, 2007. "Combining density forecasts," International Journal of Forecasting, Elsevier, vol. 23(1), pages 1-13.
    8. Christian Kascha & Francesco Ravazzolo, 2010. "Combining inflation density forecasts," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(1-2), pages 231-250.
    9. 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.
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    14. Giordani, Paolo & Villani, Mattias, 2010. "Forecasting macroeconomic time series with locally adaptive signal extraction," International Journal of Forecasting, Elsevier, vol. 26(2), pages 312-325, April.
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    17. Clemen, Robert T., 1989. "Combining forecasts: A review and annotated bibliography," International Journal of Forecasting, Elsevier, vol. 5(4), pages 559-583.
    18. Todd E. Clark, 2011. "Real-Time Density Forecasts From Bayesian Vector Autoregressions With Stochastic Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(3), pages 327-341, July.
    19. Mattias Villani & Malin Adolfson & Jesper Linde, 2005. "Forecasting Performance of an Open Economy Dynamic Stochastic General Equilibrium Model," Money Macro and Finance (MMF) Research Group Conference 2005 32, Money Macro and Finance Research Group.
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    Citations

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    Cited by:

    1. Korobilis, Dimitris, 2015. "Quantile forecasts of inflation under model uncertainty," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-72, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    2. Wagner Piazza Gaglianone & Waldyr Dutra Areosa, 2016. "Financial Conditions Indicators for Brazil," Working Papers Series 435, Central Bank of Brazil, Research Department.
    3. Erik Figueiredo & Luiz Renato Lima & Gianluca Orefice, 2016. "Migration and Regional Trade Agreements: A (New) Gravity Estimation," Review of International Economics, Wiley Blackwell, vol. 24(1), pages 99-125, February.
    4. Giovanni Bonaccolto & Massimiliano Caporin, 2016. "The Determinants of Equity Risk and Their Forecasting Implications: A Quantile Regression Perspective," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 9(3), pages 1-25, July.
    5. Korobilis, Dimitris, 2015. "Quantile forecasts of inflation under model uncertainty," MPRA Paper 64341, University Library of Munich, Germany.
    6. repec:spr:empeco:v:53:y:2017:i:1:d:10.1007_s00181-016-1163-8 is not listed on IDEAS
    7. Wagner Piazza Gaglianone & João Victor Issler, 2014. "Microfounded Forecasting," Working Papers Series 372, Central Bank of Brazil, Research Department.
    8. Fabio Busetti & Michele Caivano & Lisa Rodano, 2015. "On the conditional distribution of euro area inflation forecast," Temi di discussione (Economic working papers) 1027, Bank of Italy, Economic Research and International Relations Area.
    9. Korobilis, Dimitris, 2017. "Quantile regression forecasts of inflation under model uncertainty," International Journal of Forecasting, Elsevier, vol. 33(1), pages 11-20.
    10. Wagner Piazza Gaglianone & Osmani Teixeira de Carvalho Guillén & Francisco Marcos Rodrigues Figueiredo, 2015. "Local Unit Root and Inflationary Inertia in Brazil," Working Papers Series 406, Central Bank of Brazil, Research Department.
    11. Wagner Piazza Gaglianone & João Victor Issler & Silvia Maria Matos, 2017. "Applying a microfounded-forecasting approach to predict Brazilian inflation," Empirical Economics, Springer, vol. 53(1), pages 137-163, August.
    12. repec:eee:intfor:v:33:y:2017:i:3:p:707-728 is not listed on IDEAS
    13. Gaglianone, Wagner Piazza & Marins, Jaqueline Terra Moura, 2017. "Evaluation of exchange rate point and density forecasts: An application to Brazil," International Journal of Forecasting, Elsevier, vol. 33(3), pages 707-728.

    More about this item

    Keywords

    forecast combination; quantile regression; density forecast;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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