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

Abstract

This paper introduces a novel nonparametric high-frequency jump test for discretely observed Itô semimartingales. Based on observations sampled recursively at first exit times from a symmetric double barrier, our method distinguishes between threshold exceedances caused by the Brownian component and jumps, which enables the construction of a feasible, noise-robust statistical test. Simulation results demonstrate superior finite-sample performance of our test compared to classical methods. An empirical analysis of NYSE-traded stocks provides clear statistical evidence for jumps, with the results highly robust to spurious detections.

Keywords: High-Frequency Data, Jump Test, Market Microstructure Noise, Stochastic Sampling Scheme, First Exit Time

JEL Classification: C12, C14, C22, C58