Open Access
June 2011 Testing whether jumps have finite or infinite activity
Yacine Aït-Sahalia, Jean Jacod
Ann. Statist. 39(3): 1689-1719 (June 2011). DOI: 10.1214/11-AOS873


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.


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Yacine Aït-Sahalia. Jean Jacod. "Testing whether jumps have finite or infinite activity." Ann. Statist. 39 (3) 1689 - 1719, June 2011.


Published: June 2011
First available in Project Euclid: 25 July 2011

zbMATH: 1234.62117
MathSciNet: MR2850217
Digital Object Identifier: 10.1214/11-AOS873

Primary: 62F12 , 62M05
Secondary: 60H10 , 60J60

Keywords: Brownian motion , discrete sampling , finite activity , high frequency , infinite activity , jumps , Semimartingale

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.39 • No. 3 • June 2011
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