The Annals of Statistics

Estimating the degree of activity of jumps in high frequency data

Yacine Aït-Sahalia and Jean Jacod

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Abstract

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.

Article information

Source
Ann. Statist., Volume 37, Number 5A (2009), 2202-2244.

Dates
First available in Project Euclid: 15 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.aos/1247663753

Digital Object Identifier
doi:10.1214/08-AOS640

Mathematical Reviews number (MathSciNet)
MR2543690

Zentralblatt MATH identifier
1173.62060

Subjects
Primary: 62F12: Asymptotic properties of estimators 62M05: Markov processes: estimation
Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05]

Keywords
Jumps index of activity infinite activity discrete sampling high frequency

Citation

Aït-Sahalia, Yacine; Jacod, Jean. Estimating the degree of activity of jumps in high frequency data. Ann. Statist. 37 (2009), no. 5A, 2202--2244. doi:10.1214/08-AOS640. https://projecteuclid.org/euclid.aos/1247663753


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References

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