Space-time integer-valued ARMA modelling for time series of counts

Electronic Journal of Statistics , 17 (2023), 3472-3511
https://doi.org/10.1214/23-EJS2183

This paper introduces a new class of space-time integer-valued ARMA models referred to as STINARMA. This class arises as the natural space-time extension of the INARMA models and, simultaneously, as the integer-valued counterpart of the conventional STARMA models. In this work, the moving average subclass STINMA$(q_{m_1, \dots, m_q})$ is studied in detail. Particular attention is given to the derivation of first- and second-order moments, including space-time autocorrelations. Due to its large potential use in real-data applications, the Poisson STINMA($1_1$) process is analyzed in further detail. Estimation methods are also addressed and their performance is demonstrated through a simulation study and by analysing the daily number of hospital admissions observed over time in three Portuguese locations.