# The tail process revisited

## TL;DR

This paper revisits the tail process of regularly varying stationary time series, providing new formulations and identities that deepen understanding of its properties and introduce novel insights into its behavior.

## Contribution

It introduces a new formulation of the time change formula and establishes both known and new identities related to the tail process.

## Key findings

- New formulation of the time change formula
- Identification of previously unknown properties of the tail process
- Enhanced understanding of the tail measure in stationary time series

## Abstract

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.