%0 Journal Article
%T Testing for jumps in a discretely observed process
%A Yacine A£¿t-Sahalia
%A Jean Jacod
%J Mathematics
%D 2009
%I arXiv
%R 10.1214/07-AOS568
%X 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.
%U http://arxiv.org/abs/0903.0226v1