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

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 e...

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Main Authors: Ana Julia Alves Camara, Valdério Anselmo Reisen, Glaura Conceicao Franco, Pascal Bondon
Format: Article
Language:English
Published: MDPI AG 2025-03-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/5/859
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author Ana Julia Alves Camara
Valdério Anselmo Reisen
Glaura Conceicao Franco
Pascal Bondon
author_facet Ana Julia Alves Camara
Valdério Anselmo Reisen
Glaura Conceicao Franco
Pascal Bondon
author_sort Ana Julia Alves Camara
collection DOAJ
description 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.
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spelling doaj-art-fd69faff2e3b48d881a0ee2852166cc62025-08-20T02:59:00ZengMDPI AGMathematics2227-73902025-03-0113585910.3390/math13050859Combining Generalized Linear Autoregressive Moving Average and Bootstrap Models for Analyzing Time Series of Respiratory Diseases and Air PollutantsAna Julia Alves Camara0Valdério Anselmo Reisen1Glaura Conceicao Franco2Pascal Bondon3Department of Statistics, Federal University of Espirito Santo, Av. Fernando Ferrari, 514, Vitoria 29075-910, BrazilPPGEA (Graduate Program in Environmental Engineering), Federal University of Espirito Santo, Av. Fernando Ferrari, 514, Vitoria 29075-910, BrazilDepartment of Statistics, Federal University of Minas Gerais, Av. Antonio Carlos 6627, Belo Horizonte 31270-901, BrazilLaboratoire des Signaux et Systèmes, CentraleSupélec, CNRS, Université Paris-Saclay, 3 Rue Joliot Curie, 91192 Gif-sur-Yvette, FranceThe 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.https://www.mdpi.com/2227-7390/13/5/859time series of countsINAR modelsinteger-valued datarespiratory diseasesair pollution
spellingShingle Ana Julia Alves Camara
Valdério Anselmo Reisen
Glaura Conceicao Franco
Pascal Bondon
Combining Generalized Linear Autoregressive Moving Average and Bootstrap Models for Analyzing Time Series of Respiratory Diseases and Air Pollutants
Mathematics
time series of counts
INAR models
integer-valued data
respiratory diseases
air pollution
title Combining Generalized Linear Autoregressive Moving Average and Bootstrap Models for Analyzing Time Series of Respiratory Diseases and Air Pollutants
title_full Combining Generalized Linear Autoregressive Moving Average and Bootstrap Models for Analyzing Time Series of Respiratory Diseases and Air Pollutants
title_fullStr Combining Generalized Linear Autoregressive Moving Average and Bootstrap Models for Analyzing Time Series of Respiratory Diseases and Air Pollutants
title_full_unstemmed Combining Generalized Linear Autoregressive Moving Average and Bootstrap Models for Analyzing Time Series of Respiratory Diseases and Air Pollutants
title_short Combining Generalized Linear Autoregressive Moving Average and Bootstrap Models for Analyzing Time Series of Respiratory Diseases and Air Pollutants
title_sort combining generalized linear autoregressive moving average and bootstrap models for analyzing time series of respiratory diseases and air pollutants
topic time series of counts
INAR models
integer-valued data
respiratory diseases
air pollution
url https://www.mdpi.com/2227-7390/13/5/859
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