Conference Agenda

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.
Similarly to the STARMA model, the spatial dependence in the STINARMA is incorporated through a pre-specified weight matrix that reflects the underlying structure of the spatial system.

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

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Steutel, F. W., Van Harn, K., Discrete Analogues of Self-Decomposability and Stability, The Annals of Probability, 7 (5), (1979), 893-899

Ghodsi et al. (2012) have introduced the first-order integer-valued autoregressive model for count random fields as a planar analogue of the classical INAR(1) model, designed for count data observed on a regular lattice. We extend this framework to higher-order dependence structures and derive key stochastic properties of the resulting models.

Building on this approach, we further propose two additional count random field models: the CINAR random field model and the INMA random field model. For each model, we investigate fundamental properties and provide a comparative analysis highlighting their respective strengths and limitations.

Ghodsi, A., Shitan, M., & Bakouch, H. S. (2012). A first-order spatial integer-valued autoregressive SINAR (1, 1) model. Communications in Statistics-Theory and Methods, 41(15), 2773-2787.

Identifying key influencers from time series data without a known prior network structure is a challenging problem in various applications, from crime analysis to social media. While much work has focused on event-based time series (timestamp) data, fewer methods address count data, where event counts are recorded in fixed intervals. We develop network inference methods for both batched and sequential count data. Here the strong network connection represents the key influences among the nodes. We introduce an ensemble-based algorithm, rooted in the expectation-maximization (EM) framework, and demonstrate its utility to identify node dynamics and connections through a discrete-time Cox or Hawkes process. For the linear multidimensional Hawkes model, we employ a minimization-majorization (MM) approach, allowing for parallelized inference of networks.

For sequential inference, we use a second-order approximation of the Bayesian inference problem. Under certain assumptions, a rank-1 update for the covariance matrix reduces computational costs. We validate our methods on synthetic data and real-world datasets, including email communications within European academic communities. Our approach effectively reconstructs underlying networks, accounting for both excitation and diffusion influences. This work advances network reconstruction from count data in real-world scenarios.