Hostname: page-component-7479d7b7d-m9pkr Total loading time: 0 Render date: 2024-07-15T03:44:05.488Z Has data issue: false hasContentIssue false

ON THE SIZE CONTROL OF THE HYBRID TEST FOR SUPERIOR PREDICTIVE ABILITY

Published online by Cambridge University Press:  02 May 2023

Deborah Kim*
Affiliation:
Northwestern University
*
Address correspondence to Deborah Kim, Department of Economics, Northwestern University, Evanston, IL 60208, USA; e-mail: deborahkim@u.northwestern.edu.

Abstract

This article analyzes the theoretical properties of the hybrid test for superior predictive ability. A simple example reveals that the test may not be size-controlled at common significance levels with rejection rates exceeding $11\%$ at a $5\%$ nominal level. Generalizing this observation, the main results show the pointwise asymptotic invalidity of the hybrid test under reasonable conditions. Monte Carlo simulations support these theoretical findings.

Type
MISCELLANEA
Copyright
© The Author(s), 2023. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

I would like to thank the Editor, the Co-Editor, and the two anonymous referees for their helpful comments on the earlier version. I am indebted to Ivan Canay for his invaluable guidance and support. Thanks also go to Yoon-Jae Whang who guided my Master’s thesis, from which this project originated, as well as Joel Horowitz, Eric Auerbach, Myungkou Shin, Yong Cai, and participants of the Econometrics Reading Group at Northwestern for their helpful comments. I would also like to thank Carl Hallmann for proofreading the article. All errors are my own.

References

REFERENCES

Andrews, D.W.K. & Soares, G. (2010) Inference for parameters defined by moment inequalities using generalized moment selection. Econometrica 78, 119157.Google Scholar
Canay, I. & Shaikh, A. (2017) Practical and theoretical advances in inference for partially identified models. In Honor, B., Pakes, A., & Piazzesi, M. (eds.), Advances in Economics and Econometrics: Eleventh World Congress , vol. 2, pp. 271–230. Cambridge University Press.CrossRefGoogle Scholar
Hansen, P.R. (2005) A test for superior predictive ability. Journal of Business & Economic Statistics 23, 365380.CrossRefGoogle Scholar
Kim, D. (2021) On the size control of the hybrid test for predictive ability. Preprint, arXiv:2008.02318.Google Scholar
Kosorok, M.R. (2008) Introduction to Empirical Processes and Semiparametric Inference . Springer.CrossRefGoogle Scholar
Lehmann, E.L.& Romano, J.P. (2006) Testing Statistical Hypotheses . Springer Texts in Statistics. Springer.Google Scholar
Linton, O., Maasoumi, E., & Whang, Y.-J. (2005) Consistent testing for stochastic dominance under general sampling schemes. Review of Economic Studies 72, 735765.CrossRefGoogle Scholar
Politis, D.N. & Romano, J.P. (1994) The stationary bootstrap. Journal of the American Statistical Association 89, 13031313.CrossRefGoogle Scholar
Song, K. (2012) Testing predictive ability and power robustification. Journal of Business & Economic Statistics 30, 288296.CrossRefGoogle Scholar
White, H. (2000) A reality check for data snooping. Econometrica 68, 10971126.CrossRefGoogle Scholar