Low-frequency estimation of continuous-time moving average Lévy processes
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Date
2016
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Abstract
In this paper we study the problem of statistical inference for a continuoustime
moving average Lévy process of the form
Zt=∫ℝκ(t-s)dLs, t∈ℝ
with a deterministic kernel κ and a Lévy process L. Especially the estimation
of the Lévy measure v 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 Lévy processes.
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Keywords
moving average, low-frequency estimation, Mellin transform