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Discrete time series Location: 0.002 Session Chair: Christian H. Weiß | |
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Overview of the STINARMA Class of Models and its STINAR and STINMA Subclasses 1: Institute of Electronics and Informatics Engineering of Aveiro (IEETA) and Department of Electronics, Telecommunications and Informatics (DETI), University of Aveiro, Aveiro, Portugal; Intelligent Systems Associate Laboratory (LASI), University of Aveiro, Portugal.; 2: Center for Computational and Stochastic Mathematics (CEMAT), Department of Mathematics, IST, University of Lisbon, Lisbon, Portugal; 3: Department of Mathematics and Statistics, Helmut Schmidt University, Hamburg, Germany Spatio-temporal count data arise in many applied fields, where observations are collected over time across multiple spatial units. In these settings, it is crucial to jointly capture temporal and spatial dynamics. The spatio-temporal integer-valued autoregressive and moving average (STINARMA) class of models provides a flexible framework to address these challenges within the class of integer-valued processes. This work presents an overview of the STINARMA class of models, together with its main subclasses, those of the STINAR and STINMA models.The STINARMA can be viewed as the natural spatio-temporal extension of univariate INARMA models. Moreover, they are the integer counterpart of the continuous STARMA models, which is achieved by replacing the multiplication operator with the matrix binomial thinning operator and by considering component-wise independent discrete innovations. The general class of STINARMA models is introduced, followed by a discussion of its autoregressive and moving average subclasses. Key probabilistic properties are briefly presented through first- and second-order moments. Estimation approaches based on the method of moments, conditional least squares and conditional maximum likelihood are also outlined. The practical relevance of the STINARMA class is illustrated using spatio-temporal health data from Portugal and Germany, and its performance is compared with multivariate models that do not explicitly account for spatial dependence. References Martins, A., Scotto, M. G., Weiß, C. H., Gouveia, S. Space-time integer-valued ARMA modelling for time series of counts, Electronic Journal of Statistics, 17 (2), (2023), 3472-3511. Franke, J. Subba Rao, T. Multivariate First-Order Integer-Valued Autoregressions, Technical Report, University of Kaiserslaute, (1993). Pfeifer P. E., Deutsch S. J., A Three-Stage Iterative Procedure for Space-Time Modeling, Technometrics, 22 (1), (1980), 35-47. Steutel, F. W., Van Harn, K., Discrete Analogues of Self-Decomposability and Stability, The Annals of Probability, 7 (5), (1979), 893-899 | |
