P‐min‐Stable Regression Models for Time Series With Extreme Values of Limited Range

Leonardo Brandao Freitas Nascimento, Max Sousa Lima and Luiz H. Duczmal

Environmetrics, 2025, vol. 36, issue 2

Abstract: In this paper, a P‐min‐stable regression model is proposed for a time series of extreme values observed in a limited interval. The model may be useful when the variable or indicator of interest is the minimum value of a series restricted to the unit interval and is related to other variables through a regression structure. The serial extremal dependence is induced through the marginalization of the Kumaraswamy distribution conditioned on a latent α$$ \alpha $$‐stable process. The model is flexible to capture trends, seasonality, and non‐stationarity. Some properties of the model are presented, as well as the extremogram of the series. Procedures for estimation and inference are discussed and implemented via an Expectation‐Maximization algorithm. As an illustration, the model was used to analyze the minimum relative humidity observed in the Brazilian Amazon.

Date: 2025
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