Spatiotemporal patterns and prediction of multi-region house prices via functional mixed effects model

House prices have always been a popular indicator for real estate market monitoring. This study explores the spatiotemporal patterns of house prices at the community level in San Francisco from January 2009 to April 2024. A functional spatiotemporal semiparametric mixed effects (FST-SM) model was proposed to analyze the Zillow Home Value Index (ZHVI), considering spatiotemporal variations. This response is associated with known influences and unknown latent random effects. The random-effects component was expanded using functional principal components. The conditional autoregressive (CAR) structure of the principal component scores was adopted to analyze nonparametric time trends and spatiotemporal correlations. The proposed model was compared with other time-series models in terms of spatiotemporal prediction. The results show that the prediction accuracy of the proposed model is higher than that of other regular models. In summary, a functional mixed effects model was proposed to describe spatiotemporal patterns and forecast house prices. This study can provide valuable references for decision-making by local governments, real estate suppliers, and house buyers.