Articlegreen2009

Testing for common arrivals of jumps for discretely observed multidimensional processes

194 citations0/0 files storedThe Annals of Statistics

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Stochastic processes and financial applications Probability and Statistical Research Financial Risk and Volatility Modeling

Abstract

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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References

1976Option pricing when underlying stock returns are discontinuous 2004Power and Bipower Variation with Stochastic Volatility and Jumps 2007Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility 2005Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation 2005The Relative Contribution of Jumps to Total Price Variance 2009Testing for jumps in a discretely observed process 1998Asymptotic error distributions for the Euler method for stochastic differential equations 2007Asymptotic properties of realized power variations and related functionals of semimartingales

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