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

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