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Evaluating the calibration of multi-step-ahead density forecasts using raw moments

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  • Knüppel, Malte

Abstract

The evaluation of multi-step-ahead density forecasts is complicated by the serial correlation of the corresponding probability integral transforms. In the literature, three testing approaches can be found which take this problem into account. However, these approaches can be computationally burdensome, ignore important information and therefore lack power, or suffer from size distortions even asymptotically. In this work, a fourth testing approach based on raw moments is proposed. It is easy to implement, uses standard critical values, can include all moments regarded as important, and has correct asymptotic size. It is found to have good size and power properties if it is based directly on the (standardized) probability integral transforms.

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  • Knüppel, Malte, 2011. "Evaluating the calibration of multi-step-ahead density forecasts using raw moments," Discussion Paper Series 1: Economic Studies 2011,32, Deutsche Bundesbank.
  • Handle: RePEc:zbw:bubdp1:201132
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    Cited by:

    1. Buncic, Daniel & Müller, Oliver, 2017. "Measuring the output gap in Switzerland with linear opinion pools," Economic Modelling, Elsevier, vol. 64(C), pages 153-171.
    2. Delle Monache, Davide & Petrella, Ivan, 2017. "Adaptive models and heavy tails with an application to inflation forecasting," International Journal of Forecasting, Elsevier, vol. 33(2), pages 482-501.
    3. Clements, Michael P., 2018. "Are macroeconomic density forecasts informative?," International Journal of Forecasting, Elsevier, vol. 34(2), pages 181-198.
    4. Horatio Cuesdeanu & Jens Carsten Jackwerth, 2018. "The pricing kernel puzzle in forward looking data," Review of Derivatives Research, Springer, vol. 21(3), pages 253-276, October.
    5. Rossi, Barbara & Sekhposyan, Tatevik, 2019. "Alternative tests for correct specification of conditional predictive densities," Journal of Econometrics, Elsevier, vol. 208(2), pages 638-657.
    6. Rodríguez, Gabriel, 2017. "Modeling Latin-American stock and Forex markets volatility: Empirical application of a model with random level shifts and genuine long memory," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 393-420.
    7. Clements, Michael P, 2012. "Subjective and Ex Post Forecast Uncertainty : US Inflation and Output Growth," The Warwick Economics Research Paper Series (TWERPS) 995, University of Warwick, Department of Economics.
    8. Knut Are Aastveit & Claudia Foroni & Francesco Ravazzolo, 2017. "Density Forecasts With Midas Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(4), pages 783-801, June.
    9. Knut Are Aastveit & Francesco Ravazzolo & Herman K. van Dijk, 2018. "Combined Density Nowcasting in an Uncertain Economic Environment," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 131-145, January.
    10. Cardani, Roberta & Paccagnini, Alessia & Villa, Stefania, 2019. "Forecasting with instabilities: An application to DSGE models with financial frictions," Journal of Macroeconomics, Elsevier, vol. 61(C), pages 1-1.
    11. Gelain, Paolo & Iskrev, Nikolay & J. Lansing, Kevin & Mendicino, Caterina, 2019. "Inflation dynamics and adaptive expectations in an estimated DSGE model," Journal of Macroeconomics, Elsevier, vol. 59(C), pages 258-277.
    12. 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.
    13. Fabio Busetti, 2017. "Quantile Aggregation of Density Forecasts," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 79(4), pages 495-512, August.
    14. Roberta Cardani & Alessia Paccagnini & Stefania Villa, 2015. "Forecasting in a DSGE Model with Banking Intermediation: Evidence from the US," Working Papers 292, University of Milano-Bicocca, Department of Economics, revised Feb 2015.
    15. 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

    density forecast evaluation; normality tests;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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