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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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    More about this item

    Keywords

    Characteristic function; Complex Gaussian process; Consistent tests; Continuum of moment conditions; Goodness-of-fit; GMM; Tikhonov regularization;
    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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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