TESTING FOR JUMPS IN A DISCRETELY OBSERVED PROCESS

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 I if there are jumps, and to another deterministic and known value (such as 2) if there are no jumps. The test is valid 4 for all Ito semi martingales, 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.