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