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arXiv · 0908.1847

Testing for common arrivals of jumps for discretely observed multidimensional processes

Jean Jacod·Viktor Todorov
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Abstract

We consider a bivariate process $X_t=(X^1_t,X^2_t)$, which is observed on a finite time interval $[0,T]$ at discrete times $0,Δ_n,2Δ_n,....$ Assuming that its two components $X^1$ and $X^2$ have jumps on $[0,T]$, we derive tests to decide whether they have at least one jump occurring at the same time ("common jumps") or not ("disjoint jumps"). There are two different tests for the two possible null hypotheses (common jumps or disjoint jumps). Those tests have a prescribed asymptotic level, as the mesh $Δ_n$ goes to 0. We show on some simulations that these tests perform reasonably well even in the finite sample case, and we also put them in use for some exchange rates data.

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Jean Jacod, Viktor Todorov. 2009-08-13. Testing for common arrivals of jumps for discretely observed multidimensional processes. https://doi.org/10.1214/08-aos624

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