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May 2019 Low-frequency estimation of continuous-time moving average Lévy processes
Denis Belomestny, Vladimir Panov, Jeannette H.C. Woerner
Bernoulli 25(2): 902-931 (May 2019). DOI: 10.3150/17-BEJ1008

Abstract

In this paper, we study the problem of statistical inference for a continuous-time moving average Lévy process of the form

\[Z_{t}=\int_{\mathbb{R}}\mathcal{K}(t-s)\,dL_{s},\qquad t\in\mathbb{R},\] with a deterministic kernel $\mathcal{K}$ and a Lévy process $L$. Especially the estimation of the Lévy measure $\nu$ of $L$ from low-frequency observations of the process $Z$ is considered. We construct a consistent estimator, derive its convergence rates and illustrate its performance by a numerical example. On the mathematical level, we establish some new results on exponential mixing for continuous-time moving average Lévy processes.

Citation

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Denis Belomestny. Vladimir Panov. Jeannette H.C. Woerner. "Low-frequency estimation of continuous-time moving average Lévy processes." Bernoulli 25 (2) 902 - 931, May 2019. https://doi.org/10.3150/17-BEJ1008

Information

Received: 1 May 2017; Revised: 1 September 2017; Published: May 2019
First available in Project Euclid: 6 March 2019

zbMATH: 07049395
MathSciNet: MR3920361
Digital Object Identifier: 10.3150/17-BEJ1008

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

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Vol.25 • No. 2 • May 2019
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