A periodic and seasonal statistical model for non-negative integer-valued time series with an application to dispensed medications in respiratory diseases

Paulo Prezotti (1, 2, 3) , Valdério Reisen (2, 3) , Pascal Bondon (3) , Márton Ispány (4) , Milena Machado (2) , Faradiba Sarquis (5)

1 IFES - Federal Institute of Education, Science and Technology of Espírito Santo
2 Federal University of Espírito Santo
3 L2S - Laboratoire des signaux et systèmes
4 University of Debrecen Egyetem [Debrecen]
5 EMESCAM - Escola Superior de Ciências da Santa Casa de Misericórdia de Vitória

This paper introduces a new class of models for non-negative integer-valued time series with a periodic and seasonal autoregressive structure. Some properties of the model are discussed and the conditional quasi-maximum likelihood method is used to estimate the parameters. The consistency and asymptotic normality of the estimators are established. Their performances are investigated for finite sample sizes and the empirical results indicate that the method gives accurate estimates. The proposed model is applied to analyse the daily number of antibiotic dispensing medication for the treatment of respiratory diseases, registered in a health center of Vitória, Brazil.

Keywords: Count time series; periodicity; seasonality; consistency; forecast; air pollution problems

Domains: Statistics Theory [stat.TH]

Paulo Prezotti, Valdério Reisen, Pascal Bondon, Márton Ispány, Milena Machado, et al.. A periodic and seasonal statistical model for non-negative integer-valued time series with an application to dispensed medications in respiratory diseases. Applied Mathematical Modelling, 2021, ⟨10.1016/j.apm.2021.03.025⟩. ⟨hal-03185700⟩