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Moment tests for density forecast evaluation in the presence of parameter estimation uncertainty

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  • Yi‐Ting Chen

Abstract

Density forecast (DF) possesses appealing properties when it is correctly specified for the true conditional distribution. Although a number of parametric specification tests have been introduced for the DF evaluation (DFE) in the parameter-free context, econometric DF models are typically parameter‐dependent. In this paper, we first use a generalized probability integral transformation‐based moment test to unify these existing tests, and then apply the Newey–Tauchen method (the West–McCracken method) to correct this unified test as a generalized full‐sample (out‐of‐sample) test in the parameter‐dependent context. Unlike the corrected tests, the uncorrected tests could be substantially undersized (oversized) when they are directly applied to the full‐sample (out‐of‐sample) DFE in the presence of parameter estimation uncertainty. We also use a simulation to show the usefulness of the corrected tests in rectifying the size distortion problem, and apply the corrected tests to an empirical study of stock index returns. Copyright (C) 2010 John Wiley & Sons, Ltd.

Suggested Citation

  • Yi‐Ting Chen, 2011. "Moment tests for density forecast evaluation in the presence of parameter estimation uncertainty," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(4), pages 409-450, July.
    • Handle: RePEc:jof:jforec:v:30:y:2011:i:4:p:409-450
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    File URL: http://hdl.handle.net/10.1002/for.1178
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    Citations

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    Cited by:

    1. Jonas Dovern & Hans Manner, 2020. "Order‐invariant tests for proper calibration of multivariate density forecasts," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(4), pages 440-456, June.
    2. Clark, Todd & McCracken, Michael, 2013. "Advances in Forecast Evaluation," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1107-1201, Elsevier.
    3. Malte Knuppel & Fabian Kruger & Marc-Oliver Pohle, 2022. "Score-based calibration testing for multivariate forecast distributions," Papers 2211.16362, arXiv.org, revised Dec 2023.
    4. Yang, Lu & Yang, Lei & Ho, Kung-Cheng & Hamori, Shigeyuki, 2020. "Dependence structures and risk spillover in China’s credit bond market: A copula and CoVaR approach," Journal of Asian Economics, Elsevier, vol. 68(C).
    5. Malte Knüppel, 2015. "Evaluating the Calibration of Multi-Step-Ahead Density Forecasts Using Raw Moments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 270-281, April.
    6. Yi-Ting Chen, 2016. "Testing for Granger Causality in Moments," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 78(2), pages 265-288, April.
    7. Chen, Yi-Ting, 2012. "A simple approach to standardized-residuals-based higher-moment tests," Journal of Empirical Finance, Elsevier, vol. 19(4), pages 427-453.
    8. Tsyplakov, Alexander, 2014. "Theoretical guidelines for a partially informed forecast examiner," MPRA Paper 55017, University Library of Munich, Germany.
    9. González-Rivera, Gloria & Yoldas, Emre, 2012. "Autocontour-based evaluation of multivariate predictive densities," International Journal of Forecasting, Elsevier, vol. 28(2), pages 328-342.
    10. Jorge Fornero & Andrés Gatty, 2020. "Back testing fan charts of activity and inflation: the Chilean case," Working Papers Central Bank of Chile 881, Central Bank of Chile.
    11. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    12. Patton, Andrew, 2013. "Copula Methods for Forecasting Multivariate Time Series," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 899-960, Elsevier.

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