### Article

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

In this paper we study the problem of statistical inference for a continuous-time moving average L\'evy process of the form

\[ Z_{t}=\int_{\R}\mathcal{K}(t-s)\, dL_{s},\quad t\in\mathbb{R}, \] with a deterministic kernel \(\K\) and a L{\'e}vy process \(L\). Especially the estimation of the L\'evy 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 L\'evy processes.