Spatio-temporal principal component analysis

M Krzysko, P Nijkamp*, W Ratajczak, W Wolynski, B Wenerska

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


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
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.
Original languageEnglish
Pages (from-to)8-29
Number of pages22
JournalSpatial Economic Analysis
Issue number1
Early online date21 Aug 2023
Publication statusPublished - 2024


  • Moran's I index
  • Spatio-temporal data
  • Functional data
  • Multivariate analysis
  • Spatial weights
  • Spatio-temporal principal components


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