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Forecast Encompassing Tests and Probability Forecasts

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  • Clements, Michael P

    (Department of Economics, University of Warwick)

  • Harvey, David I

    (School of Economics, University of Nottingham)

Abstract

We consider tests of forecast encompassing for probability forecasts, for both quadratic and logarithmic scoring rules. We propose test statistics for the null of forecast encompassing, present the limiting distributions of the test statistics, and investigate the impact of estimating the forecasting models’ parameters on these distributions. The small-sample performance of the various statistics is investigated, both in terms of small numbers of forecasts and model estimation sample sizes. Two empirical applications show the usefulness of the tests for the evaluation of recession probability forecasts from logit models with different leading indicators as explanatory variables, and for evaluating survey-based probability forecasts. Probability forecasts ; encompassing tests ; recession probabilities

Suggested Citation

  • Clements, Michael P & Harvey, David I, 2006. "Forecast Encompassing Tests and Probability Forecasts," The Warwick Economics Research Paper Series (TWERPS) 774, University of Warwick, Department of Economics.
    • Handle: RePEc:wrk:warwec:774
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    Cited by:

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    2. Rodrigues, Bruno Dore & Stevenson, Maxwell J., 2013. "Takeover prediction using forecast combinations," International Journal of Forecasting, Elsevier, vol. 29(4), pages 628-641.
    3. Lahiri, Kajal & Peng, Huaming & Zhao, Yongchen, 2015. "Testing the value of probability forecasts for calibrated combining," International Journal of Forecasting, Elsevier, vol. 31(1), pages 113-129.
    4. Lahiri, Kajal & Wang, J. George, 2013. "Evaluating probability forecasts for GDP declines using alternative methodologies," International Journal of Forecasting, Elsevier, vol. 29(1), pages 175-190.
    5. Oliver Hülsewig & Johannes Mayr & Stéphane Sorbe, 2007. "Assessing the Forecast Properties of the CESifo World Economic Climate Indicator: Evidence for the Euro Area," ifo Working Paper Series 46, ifo Institute - Leibniz Institute for Economic Research at the University of Munich.
    6. Michael P. Clements, 2011. "An Empirical Investigation of the Effects of Rounding on the SPF Probabilities of Decline and Output Growth Histograms," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 43(1), pages 207-220, February.
    7. Dimitriadis, Timo & Schnaitmann, Julie, 2021. "Forecast encompassing tests for the expected shortfall," International Journal of Forecasting, Elsevier, vol. 37(2), pages 604-621.
    8. Michał Rubaszek & Paweł Skrzypczyński & Grzegorz Koloch, 2010. "Forecasting the Polish Zloty with Non-Linear Models," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 2(2), pages 151-167, March.
    9. Timmermann, Allan, 2006. "Forecast Combinations," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 4, pages 135-196, Elsevier.
    10. Dimitriadis, Timo & Liu, Xiaochun & Schnaitmann, Julie, 2020. "Encompassing tests for value at risk and expected shortfall multi-step forecasts based on inference on the boundary," Hohenheim Discussion Papers in Business, Economics and Social Sciences 11-2020, University of Hohenheim, Faculty of Business, Economics and Social Sciences.
    11. Rendon-Sanchez, Juan F. & de Menezes, Lilian M., 2019. "Structural combination of seasonal exponential smoothing forecasts applied to load forecasting," European Journal of Operational Research, Elsevier, vol. 275(3), pages 916-924.
    12. Cepni, Oguzhan & Clements, Michael P., 2024. "How local is the local inflation factor? Evidence from emerging European countries," International Journal of Forecasting, Elsevier, vol. 40(1), pages 160-183.
    13. Turgut Kisinbay & Chikako Baba, 2011. "Predicting Recessions: A New Approach for Identifying Leading Indicators and Forecast Combinations," IMF Working Papers 2011/235, International Monetary Fund.
    14. Clements, Michael P., 2016. "Long-run restrictions and survey forecasts of output, consumption and investment," International Journal of Forecasting, Elsevier, vol. 32(3), pages 614-628.
    15. Clements, Michael P., 2008. "Consensus and uncertainty: Using forecast probabilities of output declines," International Journal of Forecasting, Elsevier, vol. 24(1), pages 76-86.
    16. Timo Dimitriadis & Julie Schnaitmann, 2019. "Forecast Encompassing Tests for the Expected Shortfall," Papers 1908.04569, arXiv.org, revised Aug 2020.
    17. David G. McMillan & Mark E. Wohar, 2010. "Stock return predictability and dividend-price ratio: a nonlinear approach," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 15(4), pages 351-365.
    18. Tsyplakov, Alexander, 2014. "Theoretical guidelines for a partially informed forecast examiner," MPRA Paper 55017, University Library of Munich, Germany.
    19. Guizzardi, Andrea & Stacchini, Annalisa, 2015. "Real-time forecasting regional tourism with business sentiment surveys," Tourism Management, Elsevier, vol. 47(C), pages 213-223.
    20. Xiao, Liye & Wang, Jianzhou & Hou, Ru & Wu, Jie, 2015. "A combined model based on data pre-analysis and weight coefficients optimization for electrical load forecasting," Energy, Elsevier, vol. 82(C), pages 524-549.
    21. Stahl, Dale O., 2018. "Assessing the forecast performance of models of choice," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 73(C), pages 86-92.
    22. Michael P. Clements, 2020. "Are Some Forecasters’ Probability Assessments of Macro Variables Better Than Those of Others?," Econometrics, MDPI, vol. 8(2), pages 1-16, May.
    23. Lu Wang & Shan Li & Chao Liang, 2024. "Exploring the impact of oil security attention on oil volatility: A new perspective," International Finance, Wiley Blackwell, vol. 27(1), pages 61-80, April.

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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