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.
KeywordsRegularly varying time series Tail process Tail measure
AMS 2000 Subject Classifications60G70
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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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