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Intermittency of trawl processes

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  • Grahovac, Danijel
  • Leonenko, Nikolai N.
  • Taqqu, Murad S.

Abstract

We study the limiting behavior of continuous time trawl processes which are defined using an infinitely divisible random measure of a time dependent set. In this way one is able to define separately the marginal distribution and the dependence structure. One can have long-range dependence or short-range dependence by choosing the time set accordingly. We introduce the scaling function of the integrated process and show that its behavior displays intermittency, a phenomenon associated with an unusual behavior of moments.

Suggested Citation

  • Grahovac, Danijel & Leonenko, Nikolai N. & Taqqu, Murad S., 2018. "Intermittency of trawl processes," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 235-242.
    • Handle: RePEc:eee:stapro:v:137:y:2018:i:c:p:235-242
    DOI: 10.1016/j.spl.2018.01.030
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    References listed on IDEAS

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    1. Ole E. Barndorff-Nielsen & Asger Lunde & Neil Shephard & Almut E.D. Veraart, 2014. "Integer-valued Trawl Processes: A Class of Stationary Infinitely Divisible Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 693-724, September.
    2. Pipiras,Vladas & Taqqu,Murad S., 2017. "Long-Range Dependence and Self-Similarity," Cambridge Books, Cambridge University Press, number 9781107039469, October.
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    Cited by:

    1. Grahovac, Danijel, 2022. "Intermittency in the small-time behavior of Lévy processes," Statistics & Probability Letters, Elsevier, vol. 187(C).

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