Testing for Jumps in a Discretely Observed Price Process with Endogenous Sampling Times

69 Pages Posted: 14 Nov 2021 Last revised: 10 Oct 2022

See all articles by Yifan Li

Yifan Li

The University of Manchester - Alliance Manchester Business School; Lancaster University - Department of Accounting and Finance

Ingmar Nolte

Lancaster University - Department of Accounting and Finance

Sandra Nolte (Lechner)

Lancaster University Management School

Shifan Yu

Lancaster University Management School

Date Written: October 6, 2022

Abstract

We propose a new nonparametric test to determine whether finite-activity jumps are present in a discretely observed price process. For a univariate Itô semimartingale, we introduce the concept of censored increments for observations recursively sampled at exit times with a symmetric double barrier, and design a standardized test statistic to compare the sample moments of censored and uncensored increments. Simulation results show that our test has better finite-sample performance than other commonly used calendar-time-based jump tests with similar levels of sampling frequencies, and is fairly robust to measurement errors including market microstructure noise and price staleness. Our empirical study provides strong evidence for the presence of jumps, but jump activity is much less frequent with the new test compared to some alternative tests.

Keywords: high-frequency data, jump test, market microstructure noise, stochastic sampling scheme, first exit time, price staleness

JEL Classification: C12, C14, C22, C58

Suggested Citation

Li, Yifan and Nolte, Ingmar and Nolte (Lechner), Sandra and Yu, Shifan, Testing for Jumps in a Discretely Observed Price Process with Endogenous Sampling Times (October 6, 2022). Available at SSRN: https://ssrn.com/abstract=3943203 or http://dx.doi.org/10.2139/ssrn.3943203

Yifan Li

The University of Manchester - Alliance Manchester Business School ( email )

Booth Street West
Manchester, M15 6PB
United Kingdom

Lancaster University - Department of Accounting and Finance ( email )

The Management School
Lancaster LA1 4YX
United Kingdom

Ingmar Nolte

Lancaster University - Department of Accounting and Finance ( email )

Lancaster, Lancashire LA1 4YX
United Kingdom

Sandra Nolte (Lechner)

Lancaster University Management School ( email )

Lancaster, Lancashire LA1 4YX
United Kingdom

Shifan Yu (Contact Author)

Lancaster University Management School ( email )

Department of Accounting and Finance
Lancaster University Management School
Lancaster, LA1 4YX
United Kingdom

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