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The Recalibrated and Copula Opinion Pools

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  • Mitchell, James

    (Warwick Business School)

Abstract

This paper develops methods for combining density forecasts which accommodate stochastic dependence between different experts’ predictions. Previous work combining density forecasts, using so-called “opinion pools”, has essentially ignored dependence. The proposed basis for modelling the dependence among di.erent experts’ densities is a recalibration function, based on the probability integral transforms of the expert densities. We show that this reduces to a copula function in a special case. We explore the properties of various approximations to the recalibration function both via Monte Carlo simulations and in an application density forecasting U.K. inflation using the Bank of England’s “fan” chart. We find that the copula opinion pool can deliver more accurate densities than traditional linear and logarithmic opinion pools in many realistic situations when historical data on expert performance are available.

Suggested Citation

  • Mitchell, James, 2013. "The Recalibrated and Copula Opinion Pools," EMF Research Papers 02, Economic Modelling and Forecasting Group.
    • Handle: RePEc:wrk:wrkemf:02
    as

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    File URL: http://www2.warwick.ac.uk/fac/soc/wbs/subjects/emf/research/papers/the_recalibrated_and_copula_opinion_pools.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. Kapetanios, George & Labhard, Vincent & Price, Simon, 2008. "Forecast combination and the Bank of England's suite of statistical forecasting models," Economic Modelling, Elsevier, vol. 25(4), pages 772-792, July.
    3. Dr. James Mitchell, 2005. "Evaluating, comparing and combining density forecasts using the KLIC with an application to the Bank of England and NIESR ÔfanÕ charts of inflation," National Institute of Economic and Social Research (NIESR) Discussion Papers 253, National Institute of Economic and Social Research.
    4. Chen, Xiaohong & Fan, Yanqin & Patton, Andrew J., 2004. "Simple tests for models of dependence between multiple financial time series, with applications to U.S. equity returns and exchange rates," LSE Research Online Documents on Economics 24681, London School of Economics and Political Science, LSE Library.
    5. Clements,Michael & Hendry,David, 1998. "Forecasting Economic Time Series," Cambridge Books, Cambridge University Press, number 9780521632423.
    6. Yanqin Fan & Xiaohong Chen & Andrew Patton, 2004. "(IAM Series No 003) Simple Tests for Models of Dependence Between Multiple Financial Time Series, with Applications to U.S. Equity Returns and Exchange Rates," FMG Discussion Papers dp483, Financial Markets Group.
    7. 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.
    8. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    9. Robert L. Winkler, 1981. "Combining Probability Distributions from Dependent Information Sources," Management Science, INFORMS, vol. 27(4), pages 479-488, April.
    10. Garratt, Anthony & Mitchell, James & Vahey, Shaun P. & Wakerly, Elizabeth C., 2011. "Real-time inflation forecast densities from ensemble Phillips curves," The North American Journal of Economics and Finance, Elsevier, vol. 22(1), pages 77-87, January.
    11. Stephen C. Hora, 2010. "An Analytic Method for Evaluating the Performance of Aggregation Rules for Probability Densities," Operations Research, INFORMS, vol. 58(5), pages 1440-1449, October.
    12. 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.
    13. James Mitchell & Kenneth F. Wallis, 2011. "Evaluating density forecasts: forecast combinations, model mixtures, calibration and sharpness," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(6), pages 1023-1040, September.
    14. Dr. James Mitchell, 2005. "Evaluating, comparing and combining density forecasts using the KLIC with an application to the Bank of England and NIESR ÔfanÕ charts of inflation," National Institute of Economic and Social Research (NIESR) Discussion Papers 253, National Institute of Economic and Social Research.
    15. Jeremy Smith & Kenneth F. Wallis, 2009. "A Simple Explanation of the Forecast Combination Puzzle," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(3), pages 331-355, June.
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    Cited by:

    1. Knut Are Aastveit & James Mitchell & Francesco Ravazzolo & Herman van Dijk, 2018. "The Evolution of Forecast Density Combinations in Economics," Tinbergen Institute Discussion Papers 18-069/III, Tinbergen Institute.
    2. Jared A. Beekman & Ronald F. A. Woodaman & Dennis M. Buede, 2020. "A Review of Probabilistic Opinion Pooling Algorithms with Application to Insider Threat Detection," Decision Analysis, INFORMS, vol. 17(1), pages 39-55, March.

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