Estimating the degree of activity of jumps in high frequency data

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.

arXiv commentPublished in at http://dx.doi.org/10.1214/08-AOS640 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• Testing for jumps in a discretely observed process
• Spectral estimation of the fractional order of a Lévy process

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