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A Consistent ICM-based $\chi^2$ Specification Test

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  • Feiyu Jiang
  • Emmanuel Selorm Tsyawo

Abstract

In spite of the omnibus property of Integrated Conditional Moment (ICM) specification tests, they are not commonly used in empirical practice owing to, e.g., the non-pivotality of the test and the high computational cost of available bootstrap schemes especially in large samples. This paper proposes specification and mean independence tests based on a class of ICM metrics termed the generalized martingale difference divergence (GMDD). The proposed tests exhibit consistency, asymptotic $\chi^2$-distribution under the null hypothesis, and computational efficiency. Moreover, they demonstrate robustness to heteroskedasticity of unknown form and can be adapted to enhance power towards specific alternatives. A power comparison with classical bootstrap-based ICM tests using Bahadur slopes is also provided. Monte Carlo simulations are conducted to showcase the proposed tests' excellent size control and competitive power.

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  • Feiyu Jiang & Emmanuel Selorm Tsyawo, 2022. "A Consistent ICM-based $\chi^2$ Specification Test," Papers 2208.13370, arXiv.org, revised May 2024.
    • Handle: RePEc:arx:papers:2208.13370
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    References listed on IDEAS

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    1. Escanciano, J. Carlos, 2009. "On The Lack Of Power Of Omnibus Specification Tests," Econometric Theory, Cambridge University Press, vol. 25(1), pages 162-194, February.
    2. Yoshihiko Maesono, 1998. "Asymptotic Comparisons of Several Variance Estimators and their Effects for Studentizations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(3), pages 451-470, September.
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