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Testing for jumps in a discretely observed process. (English) Zbl 1155.62057

Summary: We propose a new test to determine whether jumps are present in asset returns or other discretely sampled processes. As the sampling interval tends to 0, our test statistic converges to 1 if there are jumps, and to another deterministic and known value (such as 2) if there are no jumps. The test is valid for all Itô semimartingales, depends neither on the law of the process nor on the coefficients of the equation which it solves, does not require a preliminary estimation of these coefficients, and when there are jumps the test is applicable whether the jumps have finite or infinite-activity and for an arbitrary Blumenthal-Getoor index. We finally implement the test on simulations and asset returns data.

MSC:

62M02 Markov processes: hypothesis testing
62F12 Asymptotic properties of parametric estimators
60G48 Generalizations of martingales
62M05 Markov processes: estimation; hidden Markov models
60F05 Central limit and other weak theorems
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J60 Diffusion processes
62P05 Applications of statistics to actuarial sciences and financial mathematics
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References:

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