Estimating the degree of activity of jumps in high frequency data

Details Estimating the degree of activity of jumps in high frequency data Estimating the degree of activity of jumps in high frequency data

2009-08-21

arxiv.org/abs/0908.3095v1

Annals of Statistics 2009, Vol. 37, No. 5A, 2202-2244

Mathematics

Statistics Theory

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

Scientific paper

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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