Abstract

Many environmental and climate measures such as temperature, precipitation, air pollutant levels, and vegetation indices are continuously tracked over time at sites distributed throughout the space. These observations can naturally be treated as curves (functional data) tied to spatial locations, with dependence across both space and time. Making use of this functional structure is essential for reliable prediction and classification. Typical uses include estimating values at un-sampled locations, forecasting extreme events, and clustering regions into risk categories.
In this talk, we present nonparametric approaches to supervised learning for both regression and classification with functional spatio-temporal series as predictors. Instead of assuming a predetermined parametric relationship between the response and the observed curves, we estimate the link directly from the data using kernel-based estimators tailored to functional covariates. It incorporates spatial and temporal dependence, so that neighboring observations inform predictions while long-range dependence is controlled. We discuss the main theoretical properties of the estimators, practical choices such as the semi-metric and bandwidth selection, and how the methods compare with classical approaches.
We apply the approach using real-world data and explain how adaptable, data-driven curve-based learning can aid prediction and risk mapping in complex spatio-temporal contexts.