Open Access
February 2016 Near-optimal estimation of jump activity in semimartingales
Adam D. Bull
Ann. Statist. 44(1): 58-86 (February 2016). DOI: 10.1214/15-AOS1349


In quantitative finance, we often model asset prices as semimartingales, with drift, diffusion and jump components. The jump activity index measures the strength of the jumps at high frequencies, and is of interest both in model selection and fitting, and in volatility estimation. In this paper, we give a novel estimate of the jump activity, together with corresponding confidence intervals. Our estimate improves upon previous work, achieving near-optimal rates of convergence, and good finite-sample performance in Monte-Carlo experiments.


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Adam D. Bull. "Near-optimal estimation of jump activity in semimartingales." Ann. Statist. 44 (1) 58 - 86, February 2016.


Received: 1 September 2014; Revised: 1 March 2015; Published: February 2016
First available in Project Euclid: 10 December 2015

zbMATH: 1334.62179
MathSciNet: MR3449762
Digital Object Identifier: 10.1214/15-AOS1349

Primary: 62P20
Secondary: 62M02 , 62M05

Keywords: Blumenthal–Getoor index , Infinite variation , jump activity , Lévy process , Semimartingale

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.44 • No. 1 • February 2016
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