In this paper we study the problem of statistical inference for a continuous-time moving average L\'evy process of the form $$Z_{ t} = \int_{ \mathbb{ R}}\mathcal{ K}(t-s)\, dL_{ s},\quad t\in\mathbb{ R}$$ 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 technical level, the main challenge is to establish a kind of exponential mixing for continuous-time moving average L\'evy processes.
Categories: math.ST stat.TH