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1\begin{table}[htbp]2\centering\footnotesize3\caption{Region-level benchmarks (16 administrative regions): mean standard deviation of monthly log changes (×100) and RMSE of 12-month log changes against the Case–Shiller repeat-sales index (×100)}\label{tab:bench_region}4\begin{threeparttable}56\begin{tabular}{lrrrrrr}7\toprule8Method & H: s.d. $\Delta$ & H: RMSE vs RS & C: s.d. $\Delta$ & C: RMSE vs RS & P: s.d. $\Delta$ & P: RMSE vs RS \\9\midrule10Median price & 7.91 & 13.7 & 9.17 & 13.0 & 13.27 & 27.5 \\11Stratified median & 6.16 & 13.2 & 6.21 & 12.2 & 10.00 & 26.0 \\12Pooled time dummy (Huber) & 4.41 & 12.6 & 4.65 & 11.1 & 7.11 & 24.6 \\13Rolling TD, 13 m, mean splice & 4.87 & 12.8 & 5.11 & 12.0 & 8.91 & 24.7 \\14Hedonic imputation Fisher (chained) & 5.42 & 12.0 & 3.79 & 7.6 & 7.23 & 17.8 \\15GEKS-Fisher, 25 m & 5.19 & 9.7 & 3.69 & 6.5 & 6.30 & 13.7 \\16HMTS, 13 m & 1.59 & 10.1 & 0.95 & 6.2 & 1.09 & 14.2 \\17QHPI v2.1 architecture & 2.33 & 9.9 & 1.48 & 6.6 & 2.20 & 14.5 \\18SHARP-HPI (real-time filtered) & 4.42 & 12.8 & 2.28 & 11.2 & 3.61 & 24.7 \\19SHARP-HPI & 3.75 & 12.7 & 1.60 & 11.0 & 2.56 & 24.8 \\20\bottomrule21\end{tabular}22\begin{tablenotes}\footnotesize\item Repeat sales are an independent (pair-based) arbiter, not the truth: they carry renovation and selection biases. Lower s.d. is not better per se; the Monte Carlo (Section 7) separates noise from signal.\end{tablenotes}23\end{threeparttable}24\end{table}25