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Low-frequency estimation of continuous-time moving average Levy processes
Bernoulli: a journal of mathematical statistics and probability. 2019. Vol. 25. No. 2. P. 902–931.
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.
Keywords: low-frequency dataнизкочастотные данныеmoving averageMellin transformпреобразование Меллинаскользящее среднее
Publication based on the results of:
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