The Annals of Statistics

Testing for jumps in a discretely observed process

Yacine Aït-Sahalia and Jean Jacod

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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 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.

Article information

Source
Ann. Statist., Volume 37, Number 1 (2009), 184-222.

Dates
First available in Project Euclid: 16 January 2009

Permanent link to this document
https://projecteuclid.org/euclid.aos/1232115932

Digital Object Identifier
doi:10.1214/07-AOS568

Mathematical Reviews number (MathSciNet)
MR2488349

Zentralblatt MATH identifier
1155.62057

Subjects
Primary: 62F12: Asymptotic properties of estimators 62M05: Markov processes: estimation
Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60J60: Diffusion processes [See also 58J65]

Keywords
Jumps test discrete sampling high-frequency

Citation

Aït-Sahalia, Yacine; Jacod, Jean. Testing for jumps in a discretely observed process. Ann. Statist. 37 (2009), no. 1, 184--222. doi:10.1214/07-AOS568. https://projecteuclid.org/euclid.aos/1232115932


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