Open Access
2020 Rate-optimal estimation of the Blumenthal–Getoor index of a Lévy process
Fabian Mies
Electron. J. Statist. 14(2): 4165-4206 (2020). DOI: 10.1214/20-EJS1769


The Blumenthal–Getoor (BG) index characterizes the jump measure of an infinitely active Lévy process. It determines sample path properties and affects the behavior of various econometric procedures. If the process contains a diffusion term, existing estimators of the BG index based on high-frequency observations achieve rates of convergence which are suboptimal by a polynomial factor. In this paper, a novel estimator for the BG index and the successive BG indices is presented, attaining the optimal rate of convergence. If an additional proportionality factor needs to be inferred, the proposed estimator is rate-optimal up to logarithmic factors. Furthermore, our method yields a new efficient volatility estimator which accounts for jumps of infinite variation. All parameters are estimated jointly by the generalized method of moments. A simulation study compares the finite sample behavior of the proposed estimators with competing methods from the financial econometrics literature.


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Fabian Mies. "Rate-optimal estimation of the Blumenthal–Getoor index of a Lévy process." Electron. J. Statist. 14 (2) 4165 - 4206, 2020.


Received: 1 August 2019; Published: 2020
First available in Project Euclid: 17 November 2020

zbMATH: 07285583
MathSciNet: MR4175392
Digital Object Identifier: 10.1214/20-EJS1769

Primary: 62M05
Secondary: 60G51

Keywords: Fisher information , high-frequency , jump activity , method of moments , non-diagonal rate matrix

Vol.14 • No. 2 • 2020
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