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Testing distributional assumptions using a continuum of moments

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  • Amengual, Dante
  • Carrasco, Marine
  • Sentana, Enrique

Abstract

We propose specification tests for parametric distributions that compare the potentially complex theoretical and empirical characteristic functions using the continuum of moment conditions analogue to an overidentifying restrictions test, which takes into account the correlation between influence functions for different argument values. We derive its asymptotic distribution for fixed regularization parameter and when this vanishes with the sample size. We show its consistency against any deviation from the null, study its local power and compare it with existing tests. An extensive Monte Carlo exercise confirms that our proposed tests display good power in finite samples against a variety of alternatives.

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  • Amengual, Dante & Carrasco, Marine & Sentana, Enrique, 2020. "Testing distributional assumptions using a continuum of moments," Journal of Econometrics, Elsevier, vol. 218(2), pages 655-689.
    • Handle: RePEc:eee:econom:v:218:y:2020:i:2:p:655-689
    DOI: 10.1016/j.jeconom.2020.04.033
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    Cited by:

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    3. Guay, Alain & Pelgrin, Florian, 2023. "Structural VAR models in the Frequency Domain," Journal of Econometrics, Elsevier, vol. 236(1).
    4. Gabriele Fiorentini & Enrique Sentana, 2021. "Specification tests for non‐Gaussian maximum likelihood estimators," Quantitative Economics, Econometric Society, vol. 12(3), pages 683-742, July.
    5. Ron Mittelhammer & George Judge & Miguel Henry, 2022. "An Entropy-Based Approach for Nonparametrically Testing Simple Probability Distribution Hypotheses," Econometrics, MDPI, vol. 10(1), pages 1-19, January.
    6. Antoine, Bertille & Sun, Wenqian, 2025. "Simulation-based estimation with many auxiliary statistics applied to long-run dynamic analysis," Journal of Econometrics, Elsevier, vol. 248(C).

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    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • 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

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