Spatio-temporal principal component analysis

Principal component analysis (PCA) is a well-established research approach extensively utilised in the quantitative social sciences. The primary objective of the present study is to devise and evaluate a novel methodology that effectively addresses the mathematical and statistical treatment of spatio-temporal dependencies among multivariate datasets within PCA. This approach builds upon recent advancements in multifunctional PCA. The study aims to optimise the product of the variance of functional principal components and the Moran’s $I$I index, thereby enhancing the analytical framework. Both simulation studies and a real example show that positive spatio-temporal principal components should be constructed using a distance-based spatial weight matrix, and negative ones using a border-length-based spatial weight matrix.