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A martingale-difference-divergence-based test for specification

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  • Su, Liangjun
  • Zheng, Xin

Abstract

In this paper we propose a novel consistent model specification test based on the martingale difference divergence (MDD) of the error term given the covariates. The MDD equals zero if and only if error term is conditionally mean independent of the covariates. Our MDD test does not require any nonparametric estimation under the alternative and it is applicable even if we have many covariates in the regression model. We establish the asymptotic distributions of our test statistic under the null and a sequence of Pitman local alternatives converging to the null at the usual parametric rate. Simulations suggest that our MDD test has superb performance in terms of both size and power and it generally dominates several competitors. In particular, it is the only test that has well controlled size in the presence of many covariates and reasonable power against high frequency alternatives as well.

Suggested Citation

  • Su, Liangjun & Zheng, Xin, 2017. "A martingale-difference-divergence-based test for specification," Economics Letters, Elsevier, vol. 156(C), pages 162-167.
    • Handle: RePEc:eee:ecolet:v:156:y:2017:i:c:p:162-167
    DOI: 10.1016/j.econlet.2017.05.002
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    References listed on IDEAS

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    1. Su, Liangjun & White, Halbert, 2007. "A consistent characteristic function-based test for conditional independence," Journal of Econometrics, Elsevier, vol. 141(2), pages 807-834, December.
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    3. Lai, Tingyu & Zhang, Zhongzhan & Wang, Yafei, 2021. "A kernel-based measure for conditional mean dependence," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    4. Emmanuel Selorm Tsyawo & Abdul-Nasah Soale, 2021. "A Distance Covariance-based Estimator," Papers 2102.07008, arXiv.org, revised Sep 2024.

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    More about this item

    Keywords

    Distance covariance; Integrated conditional moment test; Martingale difference divergence; Martingale difference correlation; Specification test;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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