Testing for jumps in a discretely observed process

Details Testing for jumps in a discretely observed process Testing for jumps in a discretely observed process

2009-03-02

arxiv.org/abs/0903.0226v1

Annals of Statistics 2009, Vol. 37, No. 1, 184-222

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/07-AOS568 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

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 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.

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