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UNIT ROOT TEST WITH HIGH-FREQUENCY DATA

Published online by Cambridge University Press:  08 April 2021

Sébastien Laurent  and
Shuping Shi
Sébastien Laurent
Affiliation:
Aix-Marseille University (Aix-Marseille School of Economics) CNRS & EHESS Aix-Marseille Graduate School of Management–IAE, France
Shuping Shi*
Affiliation:
Macquarie University
*
Address correspondence to Shuping Shi, Department of Economics, Macquarie University, Sydney, NSW, Australia; e-mail: shuping.shi@mq.edu.au.
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Abstract

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Deviations of asset prices from the random walk dynamic imply the predictability of asset returns and thus have important implications for portfolio construction and risk management. This paper proposes a real-time monitoring device for such deviations using intraday high-frequency data. The proposed procedures are based on unit root tests with in-fill asymptotics but extended to take the empirical features of high-frequency financial data (particularly jumps) into consideration. We derive the limiting distributions of the tests under both the null hypothesis of a random walk with jumps and the alternative of mean reversion/explosiveness with jumps. The limiting results show that ignoring the presence of jumps could potentially lead to severe size distortions of both the standard left-sided (against mean reversion) and right-sided (against explosiveness) unit root tests. The simulation results reveal satisfactory performance of the proposed tests even with data from a relatively short time span. As an illustration, we apply the procedure to the Nasdaq composite index at the 10-minute frequency over two periods: around the peak of the dot-com bubble and during the 2015–2106 stock market sell-off. We find strong evidence of explosiveness in asset prices in late 1999 and mean reversion in late 2015. We also show that accounting for jumps when testing the random walk hypothesis on intraday data is empirically relevant and that ignoring jumps can lead to different conclusions.

Type
ARTICLES
Information
Econometric Theory , Volume 38 , Issue 1 , February 2022 , pp. 113 - 171
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Footnotes

The authors gratefully acknowledge Peter C.B. Phillips, Jun Yu, Olivier Scaillet, Xiaohu Wang, and participants at the QFFE 2019 conference in Marseille for helpful discussions. We thank the coeditor Eric Renault and three anonymous referees for very useful comments. Shi acknowledges research support from the Australian Research Council under project No. DE190100840. Laurent acknowledges research support from the French National Research Agency Grant ANR-17-EURE-0020.

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