For the statistical time series analysis of geo-referenced data, two essential requirements must be met by the model:
• Ability to reliably predict events
• Ability to uncover possible procedural relationships.
Semi-parametric, statistical regression models with regularized learning or estimation methods are used to meet these requirements. These enable automatic model selection and serve as the basis for developing specific models for historical geodata. To assess the reliability and accuracy of h-step-ahead forecasts, not only point predictions should be made, but the entire distribution of the size to be described should be predicted. This allows the accuracy and reliability of the forecast as well as possible asymmetries in the distribution to be described.
Generalized additive models for location, scale, and shape (GAMLSS) should be used for distribution predictions. The model's main strength lies in the flexible modelling of the additive components, which penalized B-splines should represent. Finally, the estimates of these functions allow for the interpretation of the following:
(a) temporal relationships of the observed phenomena,
(b) spatial dependencies, and
(c) influence of exogenous features.
