Abstract

This paper proposes a novel variation-ratio test for the presence of volatility

jumps using high frequency data with microstructure noise. Under the null hypothesis

that there are no volatility jumps, the test statistic is asymptotically normal. Under the

alternative hypothesis that volatility jumps are present, the test statistic diverges at a

rate of n1/4−ι (for arbitrarily small ι > 0), which is faster than the best rate available

in the literature (approximately n1/8), where n denotes the number of observed returns

per unit time. Simulation results corroborate our theoretical findings. Empirical results

show that, while modeling volatility as a continuous semimartingale is appropriate for

a substantial subset of the 90 U.S. stocks analyzed, a notable portion exhibits features

indicative of volatility jumps.

Key words and phrases: Volatility Jumps, Central Limit Theorem, High Frequency Data, Microstructure Noise, Semimartingale

Information

Preprint No.SS-2025-0126
Manuscript IDSS-2025-0126
Complete AuthorsGuangying Liu, Kewen Shi, Zhiyuan Zhang
Corresponding AuthorsGuangying Liu
Emailsliugying@nau.edu.cn

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Acknowledgments

GL was partially supported by Natural Science Foundation of China (72342019,

12371267); National social science fund major project of China (23&ZD036); National Science Foundation of Jiangsu Province of China (BK20221348); Jiangsu

Province College Science Key Foundation (25KJA110002); open project of Joint

Lab for Statistics and Finance (2025JLSF205); Priority Academic Program Development of Jiangsu Higher Education Institutions (Statistics). KS was partially

supported by Postgraduate Research & Practice Innovation Program of Jiangsu

Province (KYCX25_2449). ZZ was supported by the National Natural Science

Foundation of China (No. 72373086). Partial support from Shanghai Research

Center for Data Science and Decision Technology is also gratefully acknowledged.

Supplementary Materials

The supplementary material provides the proofs of the theoretical results and

related lemmas.

Supplementary materials are available for download.