\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}
\
