Principal Components and Factor Models for Space-Time Data of Remote Sensing

Time-lapse videos, created with sequences of remotely-sensed images, are widely
available nowadays; their aim is monitoring land transformations, both as regards
natural events (e.g., floods) and human interventions (e.g., urbanizations). The corresponding datasets are represented by multidimensional arrays (at least 3-4D)
and their spectral analysis (eigenvalues, eigenvectors, principal components, factor
models) poses several issues. In particular, one may wonder what are the statistically
meaningful operations and what is the treatment of the space–time autocorrelation
(ACR) across pixels. In this article, we develop principal component analysis (PCA,
useful for data reduction and description) and factor autoregressive models (FAR,
suitable for data analysis and forecasting), for 3D data arrays. An extensive application, to a real case study of a Google Earth video, is carried out to illustrate and check the validity of the numerical solutions.