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This paper examines the predictive power of five linear hedonic pricing models for the residential market with varying complexity in their spatial and temporal structure. In contrast to similar studies, we extend the out-of-sample forecast evaluation to one-day-ahead predictions with a rolling estimation window, which is a reasonable setting for many practical applications. We can show that in-sample fit and cross-validation prediction accuracy improve significantly when we account for spatial heterogeneity. In particular, for one-day-ahead forecasts, the spatiotemporal autoregressive (STAR) model demonstrates its superiority compared to model specifications with alternating spatial and temporal heterogeneity and dependence structures. In addition, sub-market fixed-effects, constructed on the basis of statistical TREE methods, further improve the results of predefined local rental markets.