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Asymptotic Variance of Brier (Skill) Score in the Presence of Serial Correlation


  • Kajal Lahiri
  • Liu Yang


We derive autocorrelation-robust asymptotic variances of the Brier score and Brier skill score, which are generally applicable in circumstances with weak serial correlation. A simulation experiment and an empirical application from macroeconomics underscore the importance of taking care of serial correlation. We find that the conventional variances are too conservative to account for the sampling variability in estimating the Brier (skill) score.

Suggested Citation

  • Kajal Lahiri & Liu Yang, 2015. "Asymptotic Variance of Brier (Skill) Score in the Presence of Serial Correlation," CESifo Working Paper Series 5290, CESifo.
  • Handle: RePEc:ces:ceswps:_5290

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    1. Gad Levanon & Jean-Claude Manini & Ataman Ozyildirim & Brian Schaitkin & Jennelyn Tanchua, 2011. "Using a Leading Credit Index to Predict Turning Points in the U.S. Business Cycle," Economics Program Working Papers 11-05, The Conference Board, Economics Program.
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    3. Lahiri, Kajal & Monokroussos, George & Zhao, Yongchen, 2013. "The yield spread puzzle and the information content of SPF forecasts," Economics Letters, Elsevier, vol. 118(1), pages 219-221.
    4. Lahiri, Kajal & Yang, Liu, 2013. "Forecasting Binary Outcomes," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1025-1106, Elsevier.
    5. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    6. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-966, July.
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    Cited by:

    1. Lahiri, Kajal & Yang, Liu, 2016. "Asymptotic variance of Brier (skill) score in the presence of serial correlation," Economics Letters, Elsevier, vol. 141(C), pages 125-129.

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    More about this item


    probability forecasts; serial correlation; Brier score; Brier skill score; survey of professional forecasters;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods


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