Testing for Jumps in a Discretely Observed Process

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Abstract
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.