Aït-Sahalia, Yacine; Jacod, Jean Testing whether jumps have finite or infinite activity. (English) Zbl 1234.62117 Ann. Stat. 39, No. 3, 1689-1719 (2011). 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. Cited in 31 Documents MSC: 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) Keywords:semimartingale; Brownian motion; discrete sampling; high frequency × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] Aït-Sahalia, Y. (2002). Telling from discrete data whether the underlying continuous-time model is a diffusion. J. Finance 57 2075-2112. [2] Aït-Sahalia, Y. and Jacod, J. (2009a). Estimating the degree of activity of jumps in high frequency financial data. Ann. Statist. 37 2202-2244. · Zbl 1173.62060 · doi:10.1214/08-AOS640 [3] Aït-Sahalia, Y. and Jacod, J. (2009b). Testing for jumps in a discretely observed process. Ann. Statist. 37 184-222. · Zbl 1155.62057 · doi:10.1214/07-AOS568 [4] Aït-Sahalia, Y. and Jacod, J. (2011). 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