, Volume 21, Issue 4, pp 551–579 | Cite as

The tail process revisited

  • Hrvoje Planinić
  • Philippe SoulierEmail author


The tail measure of a regularly varying stationary time series has been recently introduced. It is used in this contribution to reconsider certain properties of the tail process and establish new ones. A new formulation of the time change formula is used to establish identities, some of which were indirectly known and some of which are new.


Regularly varying time series Tail process Tail measure 

AMS 2000 Subject Classifications



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Section 5 owes a lot to Enkelejd Hashorva who brought the references Hashorva (2016) and Dȩbicki and Hashorva (2017) to our attention as well as the formula (3.20). The research of the first author is supported in part by Croatian Science Foundation under the project 3526. The research of the second author is partially supported by LABEX MME-DII.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ZagrebZagrebCroatia
  2. 2.Département de MathématiquesUniversité Paris NanterreNanterreFrance

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