Graph‐Laplacian modeling of spatiotemporal effects for house price estimation

Many variables involve the modeling of spatial effects, and their dynamics over time. This article presents a linear model in which spatiotemporal random effects are modeled by graph‐Laplacians. A graph‐Laplacian flexibly encodes adjacency in both space and time, in our case not depending on unknown parameters. The graph‐Laplacian can be input for a prior in a Bayesian estimation setup, or used as regularization term in a Ridge regression. A spectral decomposition of the graph‐Laplacian significantly reduces computation time for estimation. As an application, we estimate graph‐Laplacian hedonic pricing and repeat‐sales models on sales prices of Australian residential properties in the period from 1990 to 2024. Bayesian and Ridge regression estimation results are very similar, although the computation time for the Ridge regression is orders of magnitude faster, however at the expense of missing posterior density functions. Our results highlight the advantages of graph‐Laplacians for predicting individual property prices and for producing stable, granular price indexes, also in thin markets.