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

Abstract

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.