# Transformed-Linear Models for Time Series Extremes

arXiv: https://arxiv.org/abs/2012.06705 · HTML: https://mlsanity.com/paper/2012.06705/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Dec 2020.

## Built on by (most cited first, 1 of 1)

- [Principal Component Analysis for Multivariate Extremes](https://mlsanity.com/paper/2606.07213/) (2026)

## Abstract (arXiv)

In order to capture the dependence in the upper tail of a time series, we develop non-negative regularly-varying time series models that are constructed similarly to classical non-extreme ARMA models. Rather than fully characterizing tail dependence of the time series, we define the concept of weak tail stationarity which allows us to describe a regularly-varying time series through the tail pairwise dependence function (TPDF) which is a measure of pairwise extremal dependencies. We state consistency requirements among the finite-dimensional collections of the elements of a regularly-varying time series and show that the TPDF's value does not depend on the dimension being considered. So that our models take nonnegative values, we use transformed-linear operations. We show existence and stationarity of these models, and develop their properties such as the model TPDF's. Additionally, we show the class of transformed-linear MA(∞) models forms an inner product space. Motivated by investigating conditions conducive to the spread of wildfires, we fit models to hourly windspeed data and find that the fitted transformed-linear models produce better estimates of upper tail quantities than traditional ARMA models or than classical linear regularly varying models.