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August 2009 Testing for common arrivals of jumps for discretely observed multidimensional processes
Jean Jacod, Viktor Todorov
Ann. Statist. 37(4): 1792-1838 (August 2009). DOI: 10.1214/08-AOS624


We consider a bivariate process Xt=(Xt1, Xt2), which is observed on a finite time interval [0, T] at discrete times 0, Δn, 2Δn, …. Assuming that its two components X1 and X2 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 Δn 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. "Testing for common arrivals of jumps for discretely observed multidimensional processes." Ann. Statist. 37 (4) 1792 - 1838, August 2009.


Published: August 2009
First available in Project Euclid: 18 June 2009

zbMATH: 1168.62075
MathSciNet: MR2533472
Digital Object Identifier: 10.1214/08-AOS624

Primary: 62F12 , 62M05
Secondary: 60H10 , 60J60

Keywords: Common jumps , discrete sampling , high-frequency data , tests

Rights: Copyright © 2009 Institute of Mathematical Statistics


Vol.37 • No. 4 • August 2009
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