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1\begin{table}[htbp]2\centering\footnotesize3\caption{Province-level benchmark indices, January 2021 to September 2026: cumulative log change (×100) and standard deviation of monthly log changes (×100)}\label{tab:bench_prov}4\begin{threeparttable}5\resizebox{\textwidth}{!}{%6\begin{tabular}{lrrrrrrr}7\toprule8Method & H: total & H: s.d. $\Delta$ & C: total & C: s.d. $\Delta$ & P: total & P: s.d. $\Delta$ & sec. \\9\midrule10Median price & 46.4 & 3.97 & 36.0 & 2.09 & 50.9 & 5.74 & 0 \\11Mean price & 47.8 & 3.79 & 36.3 & 2.47 & 43.9 & 4.16 & 0 \\12Stratified median & 54.0 & 3.35 & 37.3 & 1.88 & 49.6 & 4.61 & 0 \\13Pooled time dummy (OLS) & 58.5 & 2.58 & 40.9 & 1.35 & 48.7 & 2.42 & 1 \\14Pooled time dummy (Huber) & 56.5 & 1.86 & 41.0 & 1.06 & 51.4 & 1.94 & 4 \\15Rolling TD, 7 m, mean splice & 56.1 & 1.89 & 37.3 & 1.01 & 51.0 & 2.06 & 12 \\16Rolling TD, 13 m, mean splice & 55.6 & 1.87 & 37.2 & 1.02 & 50.6 & 1.91 & 18 \\17Rolling TD, 13 m, movement splice & 55.0 & 1.86 & 37.1 & 1.00 & 51.8 & 1.91 & 18 \\18Rolling TD, 13 m, window splice & 56.5 & 1.91 & 38.7 & 1.13 & 52.0 & 2.04 & 18 \\19Rolling TD, 25 m, mean splice & 56.4 & 1.86 & 39.4 & 1.03 & 51.1 & 1.87 & 32 \\20Hedonic imputation Laspeyres (chained) & 56.4 & 2.76 & 45.4 & 1.50 & 55.6 & 2.44 & 5 \\21Hedonic imputation Paasche (chained) & 56.5 & 2.76 & 36.8 & 1.45 & 57.8 & 2.53 & 5 \\22Hedonic imputation Fisher (chained) & 56.5 & 2.75 & 41.1 & 1.45 & 56.7 & 2.44 & 4 \\23Hedonic imputation Fisher (direct) & 59.0 & 2.76 & 41.5 & 1.69 & 50.1 & 2.30 & 4 \\24GEKS-Fisher, 13 m & 58.8 & 2.78 & 41.0 & 1.47 & 52.3 & 2.48 & 16 \\25GEKS-Fisher, 25 m & 59.0 & 2.78 & 41.1 & 1.47 & 51.8 & 2.45 & 27 \\26HMTS, 4 m & 59.2 & 1.93 & 42.4 & 1.06 & 53.2 & 1.56 & — \\27HMTS, 13 m & 60.1 & 1.92 & 42.2 & 0.90 & 54.9 & 1.29 & — \\28Repeat sales (BMN) & 68.6 & 3.02 & 38.6 & 1.71 & 57.9 & 4.58 & 0 \\29Repeat sales (Case–Shiller) & 67.6 & 2.97 & 37.6 & 1.73 & 58.5 & 4.61 & 0 \\30GBM out-of-time residual & 46.9 & 2.54 & 36.0 & 1.46 & 39.3 & 2.32 & 191 \\31QHPI v2.1 architecture & 55.6 & 1.87 & 37.2 & 1.02 & 50.6 & 1.91 & 18 \\32SHARP stage 1 without time-varying prices & 56.7 & 1.91 & 41.0 & 1.06 & 51.3 & 1.98 & 21 \\33SHARP-HPI & 56.9 & 1.91 & 41.5 & 1.04 & 50.9 & 1.97 & 21 \\34\bottomrule35\end{tabular}}36\begin{tablenotes}\footnotesize\item H = houses, C = condominiums, P = plexes. Rolling TD = rolling time dummy; GEKS on bilateral double-imputation Fisher links with movement splice; HMTS = hedonic multilateral time series (Ishaak et al., 2024); QHPI = re-implementation of the QWHPI v2.1 architecture; last column = wall-clock seconds for the house sample on one Apple M-series core.\end{tablenotes}37\end{threeparttable}38\end{table}39