Open Access
February 2009 Testing for jumps in a discretely observed process
Yacine Aït-Sahalia, Jean Jacod
Ann. Statist. 37(1): 184-222 (February 2009). DOI: 10.1214/07-AOS568


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 Itô 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.


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Yacine Aït-Sahalia. Jean Jacod. "Testing for jumps in a discretely observed process." Ann. Statist. 37 (1) 184 - 222, February 2009.


Published: February 2009
First available in Project Euclid: 16 January 2009

zbMATH: 1155.62057
MathSciNet: MR2488349
Digital Object Identifier: 10.1214/07-AOS568

Primary: 62F12 , 62M05
Secondary: 60H10 , 60J60

Keywords: discrete sampling , high-frequency , jumps , Test

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 1 • February 2009
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