Fit spatio-temporal models within a (double) generalized linear modelling framework. The package includes functions for estimation, simulation and inference.
Maintainer: Steffen Maletz maletz@statistik.tu-dortmund.de (ORCID)
Authors:
Konstantinos Fokianos fokianos@ucy.ac.cy (ORCID)
Roland Fried fried@statistik.tu-dortmund.de (ORCID)
Other contributors:
Valerie Weismann [contributor]
The implemented models are based on spatio-temporal autoregressive moving average (STARMA) models. They incorporate spatial and temporal dependencies by spatial lagging, via spatial weight matrices, and temporal lagging via past observations and past values of the linear predictor.
The main functions for fitting such models are glmstarma and dglmstarma.
The main difference between the two functions is that glmstarma fits a model for the (conditional) mean of the spatio-temporal process and dglmstarma fits two models, one for the (conditional) mean and another one for the (conditional) dispersion.
The mean model in both functions generalizes the structure of spatio-temporal Poisson autoregressions, and allows for various distributions from the exponential dispersion family.
The dispersion model can be seen as an generalization of an spatio-temporal GARCH or log-GARCH model.
Data can be simulated with glmstarma.sim and dglmstarma.sim.
For more details on the models see the documentation of the fitting functions glmstarma and dglmstarma.
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Barreto‐Souza, W., Piancastelli, L. S., Fokianos, K., & Ombao, H. (2025). Time‐Varying Dispersion Integer‐Valued GARCH Models. Journal of Time Series Analysis. tools:::Rd_expr_doi("10.1111/jtsa.12838")
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Knight, M., Leeming, K., Nason, G., & Nunes, M. (2020). Generalized Network Autoregressive Processes and the GNAR Package. Journal of Statistical Software, 96(5), 1–36. tools:::Rd_expr_doi("10.18637/jss.v096.i05")
Maletz, S., Fokianos, K., & Fried, R. (2024). Spatio-Temporal Count Autoregression. Data Science in Science, 3(1). tools:::Rd_expr_doi("10.1080/26941899.2024.2425171")
Meyer, S., Held, L., & Höhle, M. (2017). Spatio-Temporal Analysis of Epidemic Phenomena Using the R Package surveillance. Journal of Statistical Software, 77(11), 1–55. tools:::Rd_expr_doi("10.18637/jss.v077.i11")
Otto, P. (2024). A multivariate spatial and spatiotemporal ARCH Model. Spatial Statistics, 60. tools:::Rd_expr_doi("10.1016/j.spasta.2024.100823")
Pfeifer, P. E., & Deutsch, S. J. (1980). A Three-Stage Iterative Procedure for Space-Time Modeling Phillip. Technometrics, 22(1), 35–47. tools:::Rd_expr_doi("10.2307/1268381")
Smyth, G.K. (1989), Generalized Linear Models with Varying Dispersion. Journal of the Royal Statistical Society: Series B (Methodological), 51(1), 47-60. tools:::Rd_expr_doi("10.1111/j.2517-6161.1989.tb01747.x")
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