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Moment-Based Tests under Parameter Uncertainty

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  • Christian Bontemps

    (University of Toulouse, ENAC, and Toulouse School of Economics)

Abstract

This paper considers moment-based tests applied to estimated quantities. We propose a general class of transforms of moments to handle the parameter uncertainty problem. The construction requires only a linear correction that can be implemented in sample and remains valid for some extended families of nonsmooth moments. We reemphasize the attractiveness of working with robust moments, which lead to testing procedures that do not depend on the estimator. Furthermore, no correction is needed when considering the implied test statistic in the out-of-sample case. We apply our methodology to various examples with an emphasis on the backtesting of value-at-risk forecasts.

Suggested Citation

  • Christian Bontemps, 2019. "Moment-Based Tests under Parameter Uncertainty," The Review of Economics and Statistics, MIT Press, vol. 101(1), pages 146-159, March.
  • Handle: RePEc:tpr:restat:v:101:y:2019:i:1:p:146-159
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    2. Peter Horvath & Jia Li & Zhipeng Liao & Andrew J. Patton, 2022. "A consistent specification test for dynamic quantile models," Quantitative Economics, Econometric Society, vol. 13(1), pages 125-151, January.

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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