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 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.