Spatio-temporal process monitoring using exponentially weighted spatial LASSO

Spatio-temporal process monitoring (STPM) has received a considerable attention recently due to its broad applications in environment monitoring, disease surveillance, streaming image processing, and more. Because spatio-temporal data often have complicated structure, including latent spatio-temporal data correlation, complex spatio-temporal mean structure, and nonparametric data distribution, STPM is a challenging research problem. In practice, if a spatio-temporal process has a distributional shift (e.g., mean shift) started at a specific time point, then the spatial locations with the shift are usually clustered in small regions. This kind of spatial feature of the shift has not been considered in the existing STPM literature yet. In this paper, we develop a new STPM method that takes into account the spatial feature of the shift in its construction. The new method combines the ideas of exponentially weighted moving average in the temporal domain for online process monitoring and spatial LASSO in the spatial domain for accommodating the spatial feature of a future shift. It can also accommodate the complicated spatio-temporal data structure well. Both simulation studies and a real-data application show that it can provide a reliable and effective tool for different STPM applications.