Testing for jumps in a discretely observed process

TL;DR

This paper introduces a new statistical test to detect the presence of jumps in discretely observed asset return processes, which is robust, does not depend on process coefficients, and works for various jump activities.

Contribution

The paper presents a novel jump detection test that is valid for all Itô semimartingales, independent of process law or coefficients, and applicable to both finite and infinite activity jumps.

Findings

Test statistic converges to 1 if jumps are present.

Test statistic converges to a known value if no jumps.

Successful implementation on simulations and asset data.

Abstract

We propose a new test to determine whether jumps are present in asset returns or other discretely sampled processes. As the sampling interval tends to 0, our test statistic converges to 1 if there are jumps, and to another deterministic and known value (such as 2) if there are no jumps. The test is valid for all It\^{o} semimartingales, depends neither on the law of the process nor on the coefficients of the equation which it solves, does not require a preliminary estimation of these coefficients, and when there are jumps the test is applicable whether jumps have finite or infinite-activity and for an arbitrary Blumenthal--Getoor index. We finally implement the test on simulations and asset returns data.