Journal
ANNALS OF STATISTICS
Volume 37, Issue 5A, Pages 2202-2244Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/08-AOS640
Keywords
Jumps; index of activity; infinite activity; discrete sampling; high frequency
Categories
Funding
- NSF [DMS-05-32370]
- Divn Of Social and Economic Sciences
- Direct For Social, Behav & Economic Scie [0850533] Funding Source: National Science Foundation
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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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