spb/wp23_uqo

1\section{Interpretation and economic mechanisms}\label{sec:interp}23\subsection{What the property-level models use}45Table~\ref{tab:shap} reports the mean absolute SHAP values \citep{lundberglee2017shap,lundberg2020treeexplainer} of the LightGBM sale-price model at three origins. The quality-stripped prices of the ten nearest past sales dominate (\Shapknnq{} log points on average), followed by floor area (\Shaplfa), age (\Shapagef) and lot area; the municipal and regional market features (levels, momentum, volumes) each contribute less than 3.5 log points, and the time index, which carries the market trend during training, loses importance as the history lengthens (\ShaporigintTwoZeroTwoThreeZeroThree{} at the March 2023 origin against \ShaporigintTwoZeroTwoFiveZeroThree{} at the March 2025 origin). The ranking is stable across origins. The accumulated local effect \citep{apleyzhu2020ale} of the neighbour price is monotone and nearly linear over its range (\ALEknnqRange{} log points from the lowest to the highest decile), which is the spatial counterpart of a location fixed effect; the effect of municipal momentum is small and, at the top decile, negative (\ALEmunmomThreeOneTwoTop{} log points): dwellings in municipalities whose recent prices ran ahead of their twelve-month level sell for slightly less than the local level would imply, a mean-reversion pattern of the kind documented by \citet{capozza2004anatomy}, read here as a predictive association rather than a causal one.67\input{tables/tab_shap}89\subsection{What is forecastable at the market level}1011The protocol's eight questions receive the following answers from Sections~\ref{sec:results}, \ref{sec:het} and~\ref{sec:ablation}. (1) \emph{Spatial spillovers} carry no predictive information beyond the parent (regional and provincial) momentum that every pooled model receives: the graph network does not beat the pooled ridge, its attention is diffuse, and removing its graph does not hurt. (2) \emph{Local momentum} persists at one to six months: the cell's own recent changes are the dominant predictors, and AR(2) and mean-growth rules capture most of the gain; but it reverses at twelve months, where no pooled model beats the no-change forecast. (3) \emph{Property characteristics} forecast the value of a dwelling, not the market: the trees halve the error of the municipal median in Task~A, but their horizon profile shows no information about future market movements. (4) \emph{Regimes}: Figure~\ref{fig:regimes} shows the filtered state probabilities of the RAREF hidden Markov model, re-estimated at each origin from the provincial real-time growth known then. The model identifies a high-growth state (mean monthly growth of about $+2.6$ log points at the last origin) that it assigns to the origins of March to June of 2024, 2025 and 2026 (and August 2024), a middle state for the rest of the year, and a low-growth state (mean $-0.2$) that it visits with near certainty only at the September 2025 origin, after the one negative provincial month of the evaluation period. The states are the seasonal cycle, not business-cycle regimes, and the gating therefore reproduces what the calendar-month feature already gives the ridge; separate regime experts cannot be estimated from a sample that contains one slowdown and one recovery, and Table~\ref{tab:regime_b} confirms that the forecast gains are a property of rising windows. (5) \emph{Hierarchical pooling} in small municipalities does not help forecasting once the panel features are pooled: BHPF's municipal intercepts shrink to zero and HSHN's partial pooling matches no pooling. (6) \emph{Uncertainty in low-volume periods}: QANSS, which carries the WP22 filter variance, widens its intervals in thin cells and is the only model with nominal or higher coverage at every horizon. (7) \emph{Quality-adjusted versus median targets}: WP22 showed that the median index embeds composition; here the quality-adjusted index is forecastable at short horizons mainly through its seasonal and momentum structure. (8) \emph{Turning points}: the 2025--2026 slowdown was not anticipated by any model; the twelve-month forecasts issued in 2024 carry the bias of the preceding boom. Predictive importance in these results is not evidence of causality.1213\begin{figure}[htbp]\centering14\includegraphics[width=\textwidth]{figures/fig_regimes.pdf}15\caption{RAREF: filtered probabilities of the three hidden Markov states (ordered by mean growth) at each origin, estimated from the provincial real-time growth known at the origin (houses); the black line is the last observed provincial monthly growth, rescaled.}\label{fig:regimes}16\end{figure}17