Dynamic models for space-time prediction via Karhunen-Loève expansion

The paper is concerned with the spatio-temporal prediction of spacetime processes. By combining the state-space model with the kriging predictor and Karhunen-Loève Expansion, we present a parsimonious space-time model which is spatially descriptive and temporally dynamic. We consider the difficulties of applying principal component analysis of stochastic processes observed on an irregular network. Using the Voronoi tessellation we make adjustments to the Fredholm integral equation to avoid distorted loading patterns and derive an “adjusted” kriging spatial predictor. This allows for the specification of a space-time model which achieves dimension reduction in the analysis of large spatial and spatio-temporal data sets. As a practical example, the model is applied to study the evolution of the Nitrogen Dioxide (NO2) measurements recorded in the Milan district.