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Combining Generalized Linear Autoregressive Moving Average and Bootstrap Models for Analyzing Time Series of Respiratory Diseases and Air Pollutants

Author

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  • Ana Julia Alves Camara

    (Department of Statistics, Federal University of Espirito Santo, Av. Fernando Ferrari, 514, Vitoria 29075-910, Brazil)

  • Valdério Anselmo Reisen

    (PPGEA (Graduate Program in Environmental Engineering), Federal University of Espirito Santo, Av. Fernando Ferrari, 514, Vitoria 29075-910, Brazil)

  • Glaura Conceicao Franco

    (Department of Statistics, Federal University of Minas Gerais, Av. Antonio Carlos 6627, Belo Horizonte 31270-901, Brazil)

  • Pascal Bondon

    (Laboratoire des Signaux et Systèmes, CentraleSupélec, CNRS, Université Paris-Saclay, 3 Rue Joliot Curie, 91192 Gif-sur-Yvette, France)

Abstract

The generalized linear autoregressive moving-average model (GLARMA) has been used in epidemiology to evaluate the impact of pollutants on health. These effects are quantified through the relative risk (RR) measure, which inference can be based on the asymptotic properties of the maximum likelihood estimator. However, for small series, this can be troublesome. This work studies different types of bootstrap confidence intervals (CIs) for the RR. The simulation study revealed that the model parameter related to the data’s autocorrelation could influence the intervals’ coverage. Problems could arise when covariates present an autocorrelation structure. To solve this, using the vector autoregressive (VAR) filter in the covariates is suggested.

Suggested Citation

  • Ana Julia Alves Camara & Valdério Anselmo Reisen & Glaura Conceicao Franco & Pascal Bondon, 2025. "Combining Generalized Linear Autoregressive Moving Average and Bootstrap Models for Analyzing Time Series of Respiratory Diseases and Air Pollutants," Mathematics, MDPI, vol. 13(5), pages 1-23, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:859-:d:1605724
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    References listed on IDEAS

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