\section{Econometric and machine learning benchmarks}\label{sec:bench}

Task A benchmarks are a hedonic OLS, ridge and elastic net on the same features, a random forest (150 trees, depth 18), XGBoost (600 trees, depth 8), LightGBM (800 trees, 63 leaves, with five quantile models), support vector regression on a 15{,}000-sale subsample, and a quantile MLP (two GELU layers, 256 and 128 units, pinball loss) without embeddings; the naive reference is the municipality's median log price over the three months before the origin. Task B benchmarks are the no-change forecast, the cell's historical mean $h$-month growth, momentum (the last three-month change scaled to the horizon with a fitted slope), random walk with the twelve-month drift, seasonal naive (the same-calendar change of the previous year), an AR(2) on the cell's monthly changes, a local linear trend (Kalman slope extrapolation), a pooled ridge regression on the panel features, LightGBM on the panel (with quantile models), a panel MLP, LSTM and GRU on the thirteen-month history with the features, a temporal convolutional network, and a TFT-lite with gated variable selection and self-attention over the history. Factor and VAR models are represented by the parent-momentum features (provincial and regional changes enter every pooled model) and by the AR benchmark; a full Bayesian VAR on 82 series with 45 origins is not estimable with any reliability and is not reported. All neural benchmarks output the five quantiles with the pinball loss; the others use residual quantiles. Hyper-parameters are listed in Appendix~\ref{app:hyper}; none was tuned on test origins.