## Bernoulli

• Bernoulli
• Volume 25, Number 2 (2019), 902-931.

### Low-frequency estimation of continuous-time moving average Lévy processes

#### 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.

#### Article information

Source
Bernoulli, Volume 25, Number 2 (2019), 902-931.

Dates
Revised: September 2017
First available in Project Euclid: 6 March 2019

https://projecteuclid.org/euclid.bj/1551862839

Digital Object Identifier
doi:10.3150/17-BEJ1008

Mathematical Reviews number (MathSciNet)
MR3920361

Zentralblatt MATH identifier
07049395

#### Citation

Belomestny, Denis; Panov, Vladimir; Woerner, Jeannette H.C. Low-frequency estimation of continuous-time moving average Lévy processes. Bernoulli 25 (2019), no. 2, 902--931. doi:10.3150/17-BEJ1008. https://projecteuclid.org/euclid.bj/1551862839

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