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

Author

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  • Leonardo Brandao Freitas Nascimento
  • Max Sousa Lima
  • Luiz H. Duczmal

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.

Suggested Citation

  • Leonardo Brandao Freitas Nascimento & Max Sousa Lima & Luiz H. Duczmal, 2025. "P‐min‐Stable Regression Models for Time Series With Extreme Values of Limited Range," Environmetrics, John Wiley & Sons, Ltd., vol. 36(2), March.
    • Handle: RePEc:wly:envmet:v:36:y:2025:i:2:n:e2897
    DOI: 10.1002/env.2897
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    References listed on IDEAS

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    1. Qu, Yan & Dassios, Angelos & Zhao, Hongbiao, 2021. "Random variate generation for exponential and gamma tilted stable distributions," LSE Research Online Documents on Economics 108593, London School of Economics and Political Science, LSE Library.
    2. Paola Bortot & Carlo Gaetan, 2014. "A Latent Process Model for Temporal Extremes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 606-621, September.
    3. Francis X. Diebold, 2015. "Comparing Predictive Accuracy, Twenty Years Later: A Personal Perspective on the Use and Abuse of Diebold-Mariano Tests," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(1), pages 1-1, January.
    4. Hall, Peter & Peng, Liang & Yao, Qiwei, 2002. "Moving-maximum models for extrema of time series," LSE Research Online Documents on Economics 6084, London School of Economics and Political Science, LSE Library.
    5. Masarotto, Guido, 1990. "Bootstrap prediction intervals for autoregressions," International Journal of Forecasting, Elsevier, vol. 6(2), pages 229-239, July.
    6. Emma F. Eastoe & Jonathan A. Tawn, 2009. "Modelling non‐stationary extremes with application to surface level ozone," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(1), pages 25-45, February.
    7. Anne‐Laure Fougères & John P. Nolan & Holger Rootzén, 2009. "Models for Dependent Extremes Using Stable Mixtures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 42-59, March.
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