2020/12/12 by Nehali Mhatre, Daniel Cooley, Mhatre, Nehali +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #FOS: Computer and information sciences #Financial Risk and Volatility Modeling #Methodology (stat.ME) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2012.06705
openalex publication_date 2020/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.