The Annals of Statistics

Near-optimal estimation of jump activity in semimartingales

Adam D. Bull

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.aos/1449755957

Digital Object Identifier
doi:10.1214/15-AOS1349

Mathematical Reviews number (MathSciNet)
MR3449762

Zentralblatt MATH identifier
1334.62179

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

Keywords
Blumenthal–Getoor index Lévy process infinite variation jump activity semimartingale

Citation

Bull, Adam D. Near-optimal estimation of jump activity in semimartingales. Ann. Statist. 44 (2016), no. 1, 58--86. doi:10.1214/15-AOS1349. https://projecteuclid.org/euclid.aos/1449755957


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