Open Access
2023 Space-time integer-valued ARMA modelling for time series of counts
Ana Martins, Manuel G. Scotto, Christian H. Weiß, Sónia Gouveia
Author Affiliations +
Electron. J. Statist. 17(2): 3472-3511 (2023). DOI: 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(qm1,,mq) 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(11) 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.

Funding Statement

This work was partially funded by the Foundation for Science and Technology, FCT (, Portugal through national (MEC) and European structural (FEDER) funds, in the scope of the research projects IEETA/UA (UIDB/00127/2020, and CEMAT/IST/UL (UIDB/04621/2020, This work also benefited from funding of the National Network for Advanced Computing, RNCA (, which is part of the Scientific Computing Unit (FCCN) of the FCT, under the project CPCA/A1/449427/2021. AM acknowledges a PhD grant from the FCT (SFRH/BD/143973/2019) funded by the Portuguese state budget, through the Ministry for Science, Technology and Higher Education and, by the European Social Fund within the Framework of PORTUGAL2020, namely through Programa Operacional Capital Humano (PO CH) and Programa Operacional Regional do Centro (Centro 2020).


The authors thank the Associate Editor and the three reviewers for their valuable comments on an earlier draft of this manuscript. The authors thank Administração Central do Sistema de Saúde for providing hospital admissions data. The authors are also grateful to Dr. Philipp Wittenberg (HSU Hamburg) for the helpful advice on implementing the parameter estimation in R.


Download Citation

Ana Martins. Manuel G. Scotto. Christian H. Weiß. Sónia Gouveia. "Space-time integer-valued ARMA modelling for time series of counts." Electron. J. Statist. 17 (2) 3472 - 3511, 2023.


Received: 1 October 2022; Published: 2023
First available in Project Euclid: 28 November 2023

Digital Object Identifier: 10.1214/23-EJS2183

Primary: 62H11 , 62H12 , 62M10
Secondary: 62P12 , 68T09

Keywords: autoregressive moving-average processes , binomial thinning operator , Poisson distribution , Space-time series of counts , STINARMA models

Vol.17 • No. 2 • 2023
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