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A Note on Parametric Estimation of Lévy Moving Average Processes

Research output: Contribution to book/anthology/report/proceedingArticle in proceedingsResearchpeer-review

In this paper, we present a new parametric estimation method for a Lévy moving average process driven by a symmetric α -stable Lévy motion L, α∈ (0, 2 ). More specifically, we consider a parametric family of kernel functions g θ with θ∈ Θ ⊆ R and propose an asymptotically normal estimator of the pair (α, θ). The estimation idea is based upon the minimal contrast approach, which compares the empirical characteristic function of the Lévy moving average process with its theoretical counterpart. Our work is related to recent papers (Ljungdahl and Podolskij in A minimal contrast estimator for the linear fractional motion. Working Paper, 2018 [14]; Mazur et al. in Estimation of the linear fractional stable motion. Working Paper, 2018 [16]) that are studying parametric estimation of a linear fractional stable motion.

Original languageEnglish
Title of host publicationStochastic Models, Statistics and Their Applications, 2019 : Dresden, Germany, March 2019
EditorsAnsgar Steland, Ewaryst Rafajłowicz, Ostap Okhrin
Number of pages16
Place of publicationCham
Publication year2019
ISBN (print)978-3-030-28664-4
ISBN (Electronic)978-3-030-28665-1
Publication statusPublished - 2019
SeriesSpringer proceedings in mathematics & statistics

    Research areas

  • Lévy moving average processes, Minimal contrast estimation, Weak limit theorems

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