We examine U.S. housing price forecastability using principal component analysis (PCA), partial least squares (PLS) and sparse PLS (SPLS). We incorporate information from a large panel of 128 economic time series and show that macroeconomic fundamentals have strong predictive power for future movements in housing prices. We find that (S)PLS models systematically dominate PCA models. (S)PLS models also generate significant out‐of‐sample predictive power over and above the predictive power contained by the price–rent ratio, autoregressive benchmarks and regression models based on small datasets.