The Annals of Statistics

Near-optimal estimation of jump activity in semimartingales

Adam D. Bull

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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.

Article information

Ann. Statist., Volume 44, Number 1 (2016), 58-86.

Received: September 2014
Revised: March 2015
First available in Project Euclid: 10 December 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62P20: Applications to economics [See also 91Bxx]
Secondary: 62M02: Markov processes: hypothesis testing 62M05: Markov processes: estimation

Blumenthal–Getoor index Lévy process infinite variation jump activity semimartingale


Bull, Adam D. Near-optimal estimation of jump activity in semimartingales. Ann. Statist. 44 (2016), no. 1, 58--86. doi:10.1214/15-AOS1349.

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