|Testing for jumps in a discretely observed process
Yacine Ait-Sahalia* (Princeton University), Jean Jacod (Universit¨¦ Paris)
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 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.