Open Access
October 2009 Estimating the degree of activity of jumps in high frequency data
Yacine Aït-Sahalia, Jean Jacod
Ann. Statist. 37(5A): 2202-2244 (October 2009). DOI: 10.1214/08-AOS640


We define a generalized index of jump activity, propose estimators of that index for a discretely sampled process and derive the estimators’ properties. These estimators are applicable despite the presence of Brownian volatility in the process, which makes it more challenging to infer the characteristics of the small, infinite activity jumps. When the method is applied to high frequency stock returns, we find evidence of infinitely active jumps in the data and estimate their index of activity.


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Yacine Aït-Sahalia. Jean Jacod. "Estimating the degree of activity of jumps in high frequency data." Ann. Statist. 37 (5A) 2202 - 2244, October 2009.


Published: October 2009
First available in Project Euclid: 15 July 2009

zbMATH: 1173.62060
MathSciNet: MR2543690
Digital Object Identifier: 10.1214/08-AOS640

Primary: 62F12 , 62M05
Secondary: 60H10

Keywords: discrete sampling , high frequency , index of activity , infinite activity , jumps

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 5A • October 2009
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