Inference for Nonparametric High-Frequency Estimators with an Application to Time Variation in Betas

Abstract

We consider the problem of conducting inference on nonparametric high-frequency estimators without knowing their asymptotic variances. We prove that a multivariate subsampling method achieves this goal under general conditions that were not previously available in the literature. By construction, the subsampling method delivers estimates of the variance-covariance matrices that are always positive semidefinite. Our simulation study indicates that the subsampling method is more robust than the plug-in method based on the asymptotic expression for the variance. We use our subsampling method to study the dynamics of financial betas of six stocks on the NYSE. We document significant variation in betas, and find that tick data captures more variation in betas than the data sampled at moderate frequencies such as every 5 or 20 min. To capture this variation we estimate a simple dynamic model for betas. The variance estimation is also important for the correction of the errors-in-variables bias in such models. We find that the bias corrections are substantial, and that betas are more persistent than the naive estimators would lead one to believe.

KEYWORDS:

• Market microstructure noise
• Realized volatility
• Subsampling

Supplementary Materials

All proofs are collected in the Appendices A–C in the supplementary materials. Appendix D in the supplementary materials contains the tables and figures for the summary statistics of data. Appendix E in the supplementary materials contains the tables and figures for the empirical illustration in Section 6. Appendix M in the supplementary materials contains the tables for the simulations in Section 5. Appendix R in the supplementary materials contains an additional simulation study.

Acknowledgments

I would like to thank an associate editor and four referees for many helpful suggestions. I would also like to thank Kirill Evdokimov, Vasyl Golosnoy, Silvia Gonçalves, Christian Gourieroux, Benoit Perron, Myung Hwan Seo, and Kevin Sheppard for helpful comments, as well as the participants of various seminars and conferences. Earlier drafts of this article were previously circulated under the title “Nonparametric Tests of Time Variation in Betas.”

Funding

I gratefully acknowledge financial support from Institut de finance mathématique de Montréal, SSHRC, and FQRSC.