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

Ana Julia Alves Camara, Valdério Anselmo Reisen (), Glaura Conceicao Franco and Pascal Bondon
Additional contact information
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

Mathematics, 2025, vol. 13, issue 5, 1-23

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.

Keywords: time series of counts; INAR models; integer-valued data; respiratory diseases; air pollution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/5/859/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/5/859/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:5:p:859-:d:1605724

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().