多维离散观测过程跳跃共同到达的检验
Testing for common arrivals of jumps for discretely observed multidimensional processes
摘要：
我们考虑一个二元过程$X_t=(X^1_t,X^2_t)$，这是观察到一个有限的时间间隔$[0,T]$在离散时间$0,Δ_n,2Δ_n,....$假设它的两个组件$X^1$和$X^2$有跳跃$[0,T]$，我们得到测试，以决定是否有至少一个跳跃发生在同一时间（“共同跳跃”）或没有（“不相交跳跃”）。对于两个可能的零假设有两种不同的检验（共同跳跃或不相交跳跃）。这些检验具有规定的渐近水平，因为网格$Δ_n$变为0。我们在一些模拟中表明，即使在有限样本的情况下，这些测试也表现得相当好，我们也把它们用于一些汇率数据。
英文摘要：
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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