\begin{table}[htbp]
\centering\footnotesize
\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}
\begin{threeparttable}

\begin{tabular}{lrrrrrr}
\toprule
Method & H: s.d. $\Delta$ & H: RMSE vs RS & C: s.d. $\Delta$ & C: RMSE vs RS & P: s.d. $\Delta$ & P: RMSE vs RS \\
\midrule
Median price & 7.91 & 13.7 & 9.17 & 13.0 & 13.27 & 27.5 \\
Stratified median & 6.16 & 13.2 & 6.21 & 12.2 & 10.00 & 26.0 \\
Pooled time dummy (Huber) & 4.41 & 12.6 & 4.65 & 11.1 & 7.11 & 24.6 \\
Rolling TD, 13 m, mean splice & 4.87 & 12.8 & 5.11 & 12.0 & 8.91 & 24.7 \\
Hedonic imputation Fisher (chained) & 5.42 & 12.0 & 3.79 & 7.6 & 7.23 & 17.8 \\
GEKS-Fisher, 25 m & 5.19 & 9.7 & 3.69 & 6.5 & 6.30 & 13.7 \\
HMTS, 13 m & 1.59 & 10.1 & 0.95 & 6.2 & 1.09 & 14.2 \\
QHPI v2.1 architecture & 2.33 & 9.9 & 1.48 & 6.6 & 2.20 & 14.5 \\
SHARP-HPI (real-time filtered) & 4.42 & 12.8 & 2.28 & 11.2 & 3.61 & 24.7 \\
SHARP-HPI & 3.75 & 12.7 & 1.60 & 11.0 & 2.56 & 24.8 \\
\bottomrule
\end{tabular}
\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}
\end{threeparttable}
\end{table}