\section{Forecasting Accuracies during Peak Times} \label{peak_results} This appendix shows all tables from the main text with the MASE averages calculated from time steps within peak times that are defined to be from 12 pm to 2 pm (=lunch) or from 6 pm to 8 pm (=dinner). While the exact decimals of the MASEs differ, the relative ranks of the forecasting methods are the same except in rare cases. \begin{center} \captionof{table}{Top-3 models by training weeks and average demand ($1~\text{km}^2$ pixel size, 60-minute time steps)} \label{t:results:a} \begin{tabular}{|c|c|*{12}{c|}} \hline \multirow{3}{*}{\rotatebox{90}{\thead{Training}}} & \multirow{3}{*}{\rotatebox{90}{\thead{Rank}}} & \multicolumn{3}{c|}{\thead{No Demand}} & \multicolumn{3}{c|}{\thead{Low Demand}} & \multicolumn{3}{c|}{\thead{Medium Demand}} & \multicolumn{3}{c|}{\thead{High Demand}} \\ ~ & ~ & \multicolumn{3}{c|}{(0 - 2.5)} & \multicolumn{3}{c|}{(2.5 - 10)} & \multicolumn{3}{c|}{(10 - 25)} & \multicolumn{3}{c|}{(25 - $\infty$)} \\ \cline{3-14} ~ & ~ & Method & MASE & $n$ & Method & MASE & $n$ & Method & MASE & $n$ & Method & MASE & $n$ \\ \hline \hline \multirow{3}{*}{3} & 1 & \textbf{\textit{trivial}} & 0.794 & \multirow{3}{*}{\rotatebox{90}{4586}} & \textbf{\textit{hsma}} & 0.817 & \multirow{3}{*}{\rotatebox{90}{2975}} & \textbf{\textit{hsma}} & 0.838 & \multirow{3}{*}{\rotatebox{90}{2743}} & \textbf{\textit{rtarima}} & 0.871 & \multirow{3}{*}{\rotatebox{90}{2018}} \\ ~ & 2 & \textit{hsma} & 0.808 & ~ & \textit{hses} & 0.847 & ~ & \textit{hses} & 0.851 & ~ & \textit{rtses} & 0.872 & ~ \\ ~ & 3 & \textit{pnaive} & 0.938 & ~ & \textit{hets} & 0.848 & ~ & \textit{hets} & 0.853 & ~ & \textit{rtets} & 0.874 & ~ \\ \hline \multirow{3}{*}{4} & 1 & \textbf{\textit{trivial}} & 0.791 & \multirow{3}{*}{\rotatebox{90}{4532}} & \textbf{\textit{hsma}} & 0.833 & \multirow{3}{*}{\rotatebox{90}{3033}} & \textbf{\textit{hsma}} & 0.839 & \multirow{3}{*}{\rotatebox{90}{2687}} & \textbf{\textit{vrfr}} & 0.848 & \multirow{3}{*}{\rotatebox{90}{2016}} \\ ~ & 2 & \textit{hsma} & 0.794 & ~ & \textit{hses} & 0.838 & ~ & \textit{hses} & 0.847 & ~ & \textbf{\textit{rtarima}} & 0.851 & ~ \\ ~ & 3 & \textit{pnaive} & 0.907 & ~ & \textit{hets} & 0.841 & ~ & \textit{hets} & 0.851 & ~ & \textit{rtses} & 0.857 & ~ \\ \hline \multirow{3}{*}{5} & 1 & \textbf{\textit{trivial}} & 0.782 & \multirow{3}{*}{\rotatebox{90}{4527}} & \textbf{\textit{hsma}} & 0.844 & \multirow{3}{*}{\rotatebox{90}{3055}} & \textbf{\textit{hsma}} & 0.841 & \multirow{3}{*}{\rotatebox{90}{2662}} & \textbf{\textit{vrfr}} & 0.849 & \multirow{3}{*}{\rotatebox{90}{2019}} \\ ~ & 2 & \textit{hsma} & 0.802 & ~ & \textit{hses} & 0.851 & ~ & \textit{hets} & 0.844 & ~ & \textbf{\textit{rtarima}} & 0.851 & ~ \\ ~ & 3 & \textit{pnaive} & 0.888 & ~ & \textit{hets} & 0.863 & ~ & \textit{hses} & 0.845 & ~ & \textit{vsvr} & 0.853 & ~ \\ \hline \multirow{3}{*}{6} & 1 & \textbf{\textit{trivial}} & 0.743 & \multirow{3}{*}{\rotatebox{90}{4470}} & \textbf{\textit{hsma}} & 0.843 & \multirow{3}{*}{\rotatebox{90}{3086}} & \textbf{\textit{hsma}} & 0.841 & \multirow{3}{*}{\rotatebox{90}{2625}} & \textbf{\textit{vrfr}} & 0.844 & \multirow{3}{*}{\rotatebox{90}{2025}} \\ ~ & 2 & \textit{hsma} & 0.765 & ~ & \textit{hses} & 0.853 & ~ & \textit{hses} & 0.844 & ~ & \textbf{\textit{hets}} & 0.847 & ~ \\ ~ & 3 & \textit{pnaive} & 0.836 & ~ & \textit{hets} & 0.861 & ~ & \textit{hets} & 0.844 & ~ & \textit{vsvr} & 0.849 & ~ \\ \hline \multirow{3}{*}{7} & 1 & \textbf{\textit{trivial}} & 0.728 & \multirow{3}{*}{\rotatebox{90}{4454}} & \textbf{\textit{hsma}} & 0.855 & \multirow{3}{*}{\rotatebox{90}{3132}} & \textbf{\textit{hets}} & 0.843 & \multirow{3}{*}{\rotatebox{90}{2597}} & \textbf{\textit{hets}} & 0.839 & \multirow{3}{*}{\rotatebox{90}{2007}} \\ ~ & 2 & \textit{hsma} & 0.744 & ~ & \textit{hses} & 0.862 & ~ & \textit{hsma} & 0.845 & ~ & \textbf{\textit{vrfr}} & 0.842 & ~ \\ ~ & 3 & \textit{pnaive} & 0.812 & ~ & \textit{hets} & 0.868 & ~ & \textbf{\textit{vsvr}} & 0.849 & ~ & \textit{vsvr} & 0.846 & ~ \\ \hline \multirow{3}{*}{8} & 1 & \textbf{\textit{trivial}} & 0.736 & \multirow{3}{*}{\rotatebox{90}{4402}} & \textbf{\textit{hsma}} & 0.865 & \multirow{3}{*}{\rotatebox{90}{3159}} & \textbf{\textit{hets}} & 0.843 & \multirow{3}{*}{\rotatebox{90}{2575}} & \textbf{\textit{hets}} & 0.837 & \multirow{3}{*}{\rotatebox{90}{2002}} \\ ~ & 2 & \textit{hsma} & 0.759 & ~ & \textit{hets} & 0.874 & ~ & \textbf{\textit{vsvr}} & 0.848 & ~ & \textbf{\textit{vrfr}} & 0.841 & ~ \\ ~ & 3 & \textit{pnaive} & 0.820 & ~ & \textit{hses} & 0.879 & ~ & \textit{hsma} & 0.850 & ~ & \textit{vsvr} & 0.847 & ~ \\ \hline \end{tabular} \end{center} \begin{center} \captionof{table}{Ranking of benchmark and horizontal models ($1~\text{km}^2$ pixel size, 60-minute time steps): the table shows the ranks for cases with $2.5 < ADD < 25$ (and $25 < ADD < \infty$ in parentheses if they differ)} \label{t:hori:a} \begin{tabular}{|c|ccc|cccccccc|} \hline \multirow{2}{*}{\rotatebox{90}{\thead{\scriptsize{Training}}}} & \multicolumn{3}{c|}{\thead{Benchmarks}} & \multicolumn{8}{c|}{\thead{Horizontal (whole-day-ahead)}} \\ \cline{2-12} ~ & \textit{naive} & \textit{fnaive} & \textit{paive} & \textit{harima} & \textit{hcroston} & \textit{hets} & \textit{hholt} & \textit{hhwinters} & \textit{hses} & \textit{hsma} & \textit{htheta} \\ \hline \hline 3 & 11 & 7 (2) & 8 (5) & 5 (7) & 4 & 3 & 9 (10) & 10 (9) & 2 (6) & 1 & 6 (8) \\ 4 & 11 & 7 (2) & 8 (3) & 5 (6) & 4 (5) & 3 (1) & 9 (10) & 10 (9) & 2 (8) & 1 (4) & 6 (7) \\ 5 & 11 & 7 (2) & 8 (4) & 5 (3) & 4 (9) & 3 (1) & 9 (10) & 10 (5) & 2 (8) & 1 (6) & 6 (7) \\ 6 & 11 & 8 (5) & 9 (6) & 5 (4) & 4 (7) & 2 (1) & 10 & 7 (2) & 3 (8) & 1 (9) & 6 (3) \\ 7 & 11 & 8 (5) & 10 (6) & 5 (4) & 4 (7) & 2 (1) & 9 (10) & 7 (2) & 3 (8) & 1 (9) & 6 (3) \\ 8 & 11 & 9 (5) & 10 (6) & 5 (4) & 4 (7) & 2 (1) & 8 (10) & 7 (2) & 3 (8) & 1 (9) & 6 (3) \\ \hline \end{tabular} \end{center} \ \begin{center} \captionof{table}{Ranking of classical models on vertical time series ($1~\text{km}^2$ pixel size, 60-minute time steps): the table shows the ranks for cases with $2.5 < ADD < 25$ (and $25 < ADD < \infty$ in parentheses if they differ)} \label{t:vert:a} \begin{tabular}{|c|cc|ccccc|ccccc|} \hline \multirow{2}{*}{\rotatebox{90}{\thead{\scriptsize{Training}}}} & \multicolumn{2}{c|}{\thead{Benchmarks}} & \multicolumn{5}{c|}{\thead{Vertical (whole-day-ahead)}} & \multicolumn{5}{c|}{\thead{Vertical (real-time)}} \\ \cline{2-13} ~ & \textit{hets} & \textit{hsma} & \textit{varima} & \textit{vets} & \textit{vholt} & \textit{vses} & \textit{vtheta} & \textit{rtarima} & \textit{rtets} & \textit{rtholt} & \textit{rtses} & \textit{rttheta} \\ \hline \hline 3 & 2 (10) & 1 (7) & 6 (4) & 8 (6) & 10 (9) & 7 (5) & 11 (12) & 4 (1) & 5 (3) & 9 (8) & 3 (2) & 12 (11) \\ 4 & 2 (7) & 1 (10) & 6 (4) & 8 (6) & 10 (9) & 7 (5) & 12 (11) & 3 (1) & 5 (3) & 9 (8) & 4 (2) & 11 (12) \\ 5 & 2 (3) & 1 (10) & 7 (5) & 8 (7) & 10 (9) & 6 & 11 & 4 (1) & 5 (4) & 9 (8) & 3 (2) & 12 \\ 6 & 2 (1) & 1 (10) & 6 (5) & 8 (7) & 10 (9) & 7 (6) & 11 (12) & 3 (2) & 5 (4) & 9 (8) & 4 (3) & 12 (11) \\ 7 & 2 (1) & 1 (10) & 8 (5) & 7 & 10 (9) & 6 & 11 (12) & 5 (2) & 4 & 9 (8) & 3 & 12 (11) \\ 8 & 2 (1) & 1 (9) & 8 (5) & 7 & 10 (8) & 6 & 12 (10) & 5 (2) & 4 & 9 (6) & 3 & 11 \\ \hline \end{tabular} \end{center} \ \pagebreak \begin{center} \captionof{table}{Ranking of ML models on vertical time series ($1~\text{km}^2$ pixel size, 60-minute time steps): the table shows the ranks for cases with $2.5 < ADD < 25$ (and $25 < ADD < \infty$ in parentheses if they differ)} \label{t:ml:a} \begin{tabular}{|c|cccc|cc|} \hline \multirow{2}{*}{\rotatebox{90}{\thead{\scriptsize{Training}}}} & \multicolumn{4}{c|}{\thead{Benchmarks}} & \multicolumn{2}{c|}{\thead{ML}} \\ \cline{2-7} ~ & \textit{fnaive} & \textit{hets} & \textit{hsma} & \textit{rtarima} & \textit{vrfr} & \textit{vsvr} \\ \hline \hline 3 & 6 & 2 (5) & 1 (3) & 3 (1) & 5 (2) & 4 \\ 4 & 6 (5) & 2 (3) & 1 (6) & 3 (2) & 5 (1) & 4 \\ 5 & 6 (5) & 2 (4) & 1 (6) & 4 (2) & 5 (1) & 3 \\ 6 & 6 (5) & 2 & 1 (6) & 4 & 5 (1) & 3 \\ 7 & 6 (5) & 2 (1) & 1 (6) & 4 & 5 (2) & 3 \\ 8 & 6 (5) & 2 (1) & 1 (6) & 4 & 5 (2) & 3 \\ \hline \end{tabular} \end{center} \