Testing for Jumps in a Discretely Observed Process

36 Pages Posted: 12 Dec 2007

See all articles by Yacine Ait-Sahalia

Yacine Ait-Sahalia

Princeton University - Department of Economics; National Bureau of Economic Research (NBER)

Jean Jacod

Université Paris VI Pierre et Marie Curie


We propose a new test to determine whether jumps are present in asset returns or other discretelly sampled processses. 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.

Keywords: jumps, test, discrete, sampling, high frequency

Suggested Citation

Ait-Sahalia, Yacine and Jacod, Jean, Testing for Jumps in a Discretely Observed Process. Paris December 2007 Finance International Meeting AFFI. Available at SSRN: https://ssrn.com/abstract=1069872 or http://dx.doi.org/10.2139/ssrn.1069872

Yacine Ait-Sahalia (Contact Author)

Princeton University - Department of Economics ( email )

Fisher Hall
Princeton, NJ 08544
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National Bureau of Economic Research (NBER)

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Jean Jacod

Université Paris VI Pierre et Marie Curie ( email )

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Laboratoire de Probabilites
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