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Measuring Uncertainty of a Combined Forecast and Some Tests for Forecaster Heterogeneity

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  • Kajal Lahiri
  • Huaming Peng
  • Xuguang Sheng

Abstract

We have argued that from the standpoint of a policy maker, the uncertainty of using the average forecast is not the variance of the average, but rather the average of the variances of the individual forecasts that incorporate idiosyncratic risks. With a slight reformulation of the loss function and a standard factor decomposition of a panel of forecasts, we show that the uncertainty of the average forecast can be expressed as the disagreement among the forecasters plus the volatility of the common shock. Using new statistics to test for the homogeneity of idiosyncratic errors under the joint limits with both T and n approaching infinity simultaneously, we show that some previously used measures significantly underestimate the conceptually correct benchmark forecast uncertainty.

Suggested Citation

  • Kajal Lahiri & Huaming Peng & Xuguang Sheng, 2015. "Measuring Uncertainty of a Combined Forecast and Some Tests for Forecaster Heterogeneity," CESifo Working Paper Series 5468, CESifo.
    • Handle: RePEc:ces:ceswps:_5468
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    Cited by:

    1. Kajal Lahiri & Huaming Peng & Xuguang Simon Sheng, 2022. "Measuring Uncertainty of a Combined Forecast and Some Tests for Forecaster Heterogeneity," Advances in Econometrics, in: Essays in Honor of M. Hashem Pesaran: Prediction and Macro Modeling, volume 43, pages 29-50, Emerald Group Publishing Limited.
    2. Clements, Michael P., 2018. "Are macroeconomic density forecasts informative?," International Journal of Forecasting, Elsevier, vol. 34(2), pages 181-198.
    3. Philip Hans Franses, 2021. "Modeling Judgment in Macroeconomic Forecasts," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 401-417, December.
    4. Jonas Dovern & Matthias Hartmann, 2017. "Forecast performance, disagreement, and heterogeneous signal-to-noise ratios," Empirical Economics, Springer, vol. 53(1), pages 63-77, August.
    5. Siklos, Pierre, 2017. "What Has Publishing Inflation Forecasts Accomplished? Central Banks And Their Competitors," LCERPA Working Papers 0098, Laurier Centre for Economic Research and Policy Analysis, revised 01 Apr 2017.
    6. Issler, João Victor & Soares, Ana Flávia, 2019. "Central Bank credibility and inflation expectations: a microfounded forecasting approach," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 812, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    7. Alexander Glas & Matthias Hartmann, 2022. "Uncertainty measures from partially rounded probabilistic forecast surveys," Quantitative Economics, Econometric Society, vol. 13(3), pages 979-1022, July.
    8. Malte Knüppel & Guido Schultefrankenfeld, 2017. "Interest rate assumptions and predictive accuracy of central bank forecasts," Empirical Economics, Springer, vol. 53(1), pages 195-215, August.
    9. Qian, Wei & Rolling, Craig A. & Cheng, Gang & Yang, Yuhong, 2022. "Combining forecasts for universally optimal performance," International Journal of Forecasting, Elsevier, vol. 38(1), pages 193-208.
    10. 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.
    11. Wagner Piazza Gaglianone & João Victor Issler, 2014. "Microfounded Forecasting," Working Papers Series 372, Central Bank of Brazil, Research Department.
    12. Monique Reid & Pierre Siklos, 2024. "Firm level expectations and macroeconomic conditions underpinnings and disagreement," Working Papers 11058, South African Reserve Bank.
    13. Malte Knüppel & Fabian Krüger, 2022. "Forecast uncertainty, disagreement, and the linear pool," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(1), pages 23-41, January.
    14. Reifschneider, David & Tulip, Peter, 2019. "Gauging the uncertainty of the economic outlook using historical forecasting errors: The Federal Reserve’s approach," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1564-1582.
    15. Pierre L. Siklos, 2016. "Forecast Disagreement and the Inflation Outlook: New International Evidence," IMES Discussion Paper Series 16-E-03, Institute for Monetary and Economic Studies, Bank of Japan.

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    More about this item

    Keywords

    forecast combination; forecast uncertainty; model averaging; panel data;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

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