Formalization and Scalable Processing of Spatially-Embedded Time Series

Time series play a crucial role in numerous scientific and technological domains.In many cases, these series do not come from completely independent sensors, but are associated with specific locations in a space—such as geographic space—inducing common spatial patterns. In this work, we study different datasets sharing this characteristic: meteorological records over a spatial grid, traffic sensors distributed across the city of Madrid, and electroencephalograms where sensor positions reflect the distribution of electrodes on the human scalp. We provide a general formalization of the key properties of these datasets with the aim of facilitating their analysis in similar contexts. We evaluate properties such as temporal and spatio-temporal autocorrelation, and propose variants of compact data structures adapted to each domain type. Compared to state-of-the-art approaches, our proposals show competitive results, particularly highlighting spatial efficiency for dense datasets with high spatio-temporal locality, as well as query times for some cases of window-based access.