TESTING FOR COMMON ARRIVALS OF JUMPS FOR DISCRETELY OBSERVED MULTIDIMENSIONAL PROCESSES
成果类型：
Article
署名作者：
Jacod, Jean; Todorov, Viktor
署名单位：
Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Northwestern University
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/08-AOS624
发表日期：
2009
页码：
1792-1838
关键词：
摘要：
We consider a bivariate process X-t = (X-t(1), X-t(2)), which is observed on a finite time interval [0, T] at discrete times 0, Delta(n), 2 Delta(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 Delta(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.