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On the Size Control of the Hybrid Test for Predictive Ability

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  • Deborah Kim

Abstract

We analyze theoretical properties of the hybrid test for superior predictability. We demonstrate with a simple example that the test may not be pointwise asymptotically of level $\alpha$ at commonly used significance levels and may lead to rejection rates over $11\%$ when the significance level $\alpha$ is $5\%$. Generalizing this observation, we provide a formal result that pointwise asymptotic invalidity of the hybrid test persists in a setting under reasonable conditions. As an easy alternative, we propose a modified hybrid test based on the generalized moment selection method and show that the modified test enjoys pointwise asymptotic validity. Monte Carlo simulations support the theoretical findings.

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  • Deborah Kim, 2020. "On the Size Control of the Hybrid Test for Predictive Ability," Papers 2008.02318, arXiv.org, revised Sep 2021.
    • Handle: RePEc:arx:papers:2008.02318
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    References listed on IDEAS

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    1. Oliver Linton & Esfandiar Maasoumi & Yoon-Jae Whang, 2005. "Consistent Testing for Stochastic Dominance under General Sampling Schemes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 735-765.
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    4. Andrews, Donald W.K. & Guggenberger, Patrik, 2010. "ASYMPTOTIC SIZE AND A PROBLEM WITH SUBSAMPLING AND WITH THE m OUT OF n BOOTSTRAP," Econometric Theory, Cambridge University Press, vol. 26(2), pages 426-468, April.
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    6. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
    7. Donald W. K. Andrews & Gustavo Soares, 2010. "Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection," Econometrica, Econometric Society, vol. 78(1), pages 119-157, January.
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