Testing whether jumps have finite or infinite activity. (English) Zbl 1234.62117

Summary: We propose statistical tests to discriminate between the finite and infinite activity of jumps in a semimartingale discretely observed at high frequency. The two statistics allow for a symmetric treatment of the problem: we can either take the null hypothesis to be finite activity, or infinite activity. When implemented on high-frequency stock returns, both tests point toward the presence of infinite-activity jumps in the data.


62M07 Non-Markovian processes: hypothesis testing
62M02 Markov processes: hypothesis testing
60G48 Generalizations of martingales
62F05 Asymptotic properties of parametric tests
65C60 Computational problems in statistics (MSC2010)
Full Text: DOI arXiv


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