<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\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}}}
    &amp; \multirow{3}{*}{\rotatebox{90}{\thead{Rank}}}
    &amp; \multicolumn{3}{c|}{\thead{No Demand}}
    &amp; \multicolumn{3}{c|}{\thead{Low Demand}}
    &amp; \multicolumn{3}{c|}{\thead{Medium Demand}}
    &amp; \multicolumn{3}{c|}{\thead{High Demand}} \\
~ &amp; ~
    &amp; \multicolumn{3}{c|}{(0 - 2.5)}
    &amp; \multicolumn{3}{c|}{(2.5 - 10)}
    &amp; \multicolumn{3}{c|}{(10 - 25)}
    &amp; \multicolumn{3}{c|}{(25 - $\infty$)} \\
\cline{3-14}
~ &amp; ~
    &amp; Method &amp; MASE &amp; $n$
    &amp; Method &amp; MASE &amp; $n$
    &amp; Method &amp; MASE &amp; $n$
    &amp; Method &amp; MASE &amp; $n$ \\

\hline \hline
\multirow{3}{*}{3} &amp; 1
    &amp; \textbf{\textit{trivial}}
        &amp; 0.794 &amp; \multirow{3}{*}{\rotatebox{90}{4586}}
    &amp; \textbf{\textit{hsma}}
        &amp; 0.817 &amp; \multirow{3}{*}{\rotatebox{90}{2975}}
    &amp; \textbf{\textit{hsma}}
        &amp; 0.838 &amp; \multirow{3}{*}{\rotatebox{90}{2743}}
    &amp; \textbf{\textit{rtarima}}
        &amp; 0.871 &amp; \multirow{3}{*}{\rotatebox{90}{2018}} \\
~ &amp; 2
    &amp; \textit{hsma}    &amp; 0.808 &amp; ~
    &amp; \textit{hses}    &amp; 0.847 &amp; ~
    &amp; \textit{hses}    &amp; 0.851 &amp; ~
    &amp; \textit{rtses}   &amp; 0.872 &amp; ~ \\
~ &amp; 3
    &amp; \textit{pnaive}  &amp; 0.938 &amp; ~
    &amp; \textit{hets}    &amp; 0.848 &amp; ~
    &amp; \textit{hets}    &amp; 0.853 &amp; ~
    &amp; \textit{rtets}   &amp; 0.874 &amp; ~ \\

\hline
\multirow{3}{*}{4} &amp; 1
    &amp; \textbf{\textit{trivial}}
        &amp; 0.791 &amp; \multirow{3}{*}{\rotatebox{90}{4532}}
    &amp; \textbf{\textit{hsma}}
        &amp; 0.833 &amp; \multirow{3}{*}{\rotatebox{90}{3033}}
    &amp; \textbf{\textit{hsma}}
        &amp; 0.839 &amp; \multirow{3}{*}{\rotatebox{90}{2687}}
    &amp; \textbf{\textit{vrfr}}
        &amp; 0.848 &amp; \multirow{3}{*}{\rotatebox{90}{2016}} \\
~ &amp; 2
    &amp; \textit{hsma}             &amp; 0.794 &amp; ~
    &amp; \textit{hses}             &amp; 0.838 &amp; ~
    &amp; \textit{hses}             &amp; 0.847 &amp; ~
    &amp; \textbf{\textit{rtarima}} &amp; 0.851 &amp; ~ \\
~ &amp; 3
    &amp; \textit{pnaive}  &amp; 0.907 &amp; ~
    &amp; \textit{hets}    &amp; 0.841 &amp; ~
    &amp; \textit{hets}    &amp; 0.851 &amp; ~
    &amp; \textit{rtses}   &amp; 0.857 &amp; ~ \\

\hline
\multirow{3}{*}{5} &amp; 1
    &amp; \textbf{\textit{trivial}}
        &amp; 0.782 &amp; \multirow{3}{*}{\rotatebox{90}{4527}}
    &amp; \textbf{\textit{hsma}}
        &amp; 0.844 &amp; \multirow{3}{*}{\rotatebox{90}{3055}}
    &amp; \textbf{\textit{hsma}}
        &amp; 0.841 &amp; \multirow{3}{*}{\rotatebox{90}{2662}}
    &amp; \textbf{\textit{vrfr}}
        &amp; 0.849 &amp; \multirow{3}{*}{\rotatebox{90}{2019}} \\
~ &amp; 2
    &amp; \textit{hsma}             &amp; 0.802 &amp; ~
    &amp; \textit{hses}             &amp; 0.851 &amp; ~
    &amp; \textit{hets}             &amp; 0.844 &amp; ~
    &amp; \textbf{\textit{rtarima}} &amp; 0.851 &amp; ~ \\
~ &amp; 3
    &amp; \textit{pnaive}  &amp; 0.888 &amp; ~
    &amp; \textit{hets}    &amp; 0.863 &amp; ~
    &amp; \textit{hses}    &amp; 0.845 &amp; ~
    &amp; \textit{vsvr}    &amp; 0.853 &amp; ~ \\

\hline
\multirow{3}{*}{6} &amp; 1
    &amp; \textbf{\textit{trivial}}
        &amp; 0.743 &amp; \multirow{3}{*}{\rotatebox{90}{4470}}
    &amp; \textbf{\textit{hsma}}
        &amp; 0.843 &amp; \multirow{3}{*}{\rotatebox{90}{3086}}
    &amp; \textbf{\textit{hsma}}
        &amp; 0.841 &amp; \multirow{3}{*}{\rotatebox{90}{2625}}
    &amp; \textbf{\textit{vrfr}}
        &amp; 0.844 &amp; \multirow{3}{*}{\rotatebox{90}{2025}} \\
~ &amp; 2
    &amp; \textit{hsma}             &amp; 0.765 &amp; ~
    &amp; \textit{hses}             &amp; 0.853 &amp; ~
    &amp; \textit{hses}             &amp; 0.844 &amp; ~
    &amp; \textbf{\textit{hets}}    &amp; 0.847 &amp; ~ \\
~ &amp; 3
    &amp; \textit{pnaive}  &amp; 0.836 &amp; ~
    &amp; \textit{hets}    &amp; 0.861 &amp; ~
    &amp; \textit{hets}    &amp; 0.844 &amp; ~
    &amp; \textit{vsvr}    &amp; 0.849 &amp; ~ \\

\hline
\multirow{3}{*}{7} &amp; 1
    &amp; \textbf{\textit{trivial}}
        &amp; 0.728 &amp; \multirow{3}{*}{\rotatebox{90}{4454}}
    &amp; \textbf{\textit{hsma}}
        &amp; 0.855 &amp; \multirow{3}{*}{\rotatebox{90}{3132}}
    &amp; \textbf{\textit{hets}}
        &amp; 0.843 &amp; \multirow{3}{*}{\rotatebox{90}{2597}}
    &amp; \textbf{\textit{hets}}
        &amp; 0.839 &amp; \multirow{3}{*}{\rotatebox{90}{2007}} \\
~ &amp; 2
    &amp; \textit{hsma}          &amp; 0.744 &amp; ~
    &amp; \textit{hses}          &amp; 0.862 &amp; ~
    &amp; \textit{hsma}          &amp; 0.845 &amp; ~
    &amp; \textbf{\textit{vrfr}} &amp; 0.842 &amp; ~ \\
~ &amp; 3
    &amp; \textit{pnaive}        &amp; 0.812 &amp; ~
    &amp; \textit{hets}          &amp; 0.868 &amp; ~
    &amp; \textbf{\textit{vsvr}} &amp; 0.849 &amp; ~
    &amp; \textit{vsvr}          &amp; 0.846 &amp; ~ \\

\hline
\multirow{3}{*}{8} &amp; 1
    &amp; \textbf{\textit{trivial}}
        &amp; 0.736 &amp; \multirow{3}{*}{\rotatebox{90}{4402}}
    &amp; \textbf{\textit{hsma}}
        &amp; 0.865 &amp; \multirow{3}{*}{\rotatebox{90}{3159}}
    &amp; \textbf{\textit{hets}}
        &amp; 0.843 &amp; \multirow{3}{*}{\rotatebox{90}{2575}}
    &amp; \textbf{\textit{hets}}
        &amp; 0.837 &amp; \multirow{3}{*}{\rotatebox{90}{2002}} \\
~ &amp; 2
    &amp; \textit{hsma}          &amp; 0.759 &amp; ~
    &amp; \textit{hets}          &amp; 0.874 &amp; ~
    &amp; \textbf{\textit{vsvr}} &amp; 0.848 &amp; ~
    &amp; \textbf{\textit{vrfr}} &amp; 0.841 &amp; ~ \\
~ &amp; 3
    &amp; \textit{pnaive}  &amp; 0.820 &amp; ~
    &amp; \textit{hses}    &amp; 0.879 &amp; ~
    &amp; \textit{hsma}    &amp; 0.850 &amp; ~
    &amp; \textit{vsvr}    &amp; 0.847 &amp; ~ \\

\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 $2.5 &lt; ADD &lt; 25$
                  (and $25 &lt; ADD &lt; \infty$ in parentheses if they differ)}
\label{t:hori:a}
\begin{tabular}{|c|ccc|cccccccc|}
\hline
\multirow{2}{*}{\rotatebox{90}{\thead{\scriptsize{Training}}}}
    &amp; \multicolumn{3}{c|}{\thead{Benchmarks}}
    &amp; \multicolumn{8}{c|}{\thead{Horizontal (whole-day-ahead)}} \\
\cline{2-12}
~ &amp; \textit{naive}     &amp; \textit{fnaive}   &amp; \textit{paive}
  &amp; \textit{harima}    &amp; \textit{hcroston} &amp; \textit{hets} &amp; \textit{hholt}
  &amp; \textit{hhwinters} &amp; \textit{hses}     &amp; \textit{hsma} &amp; \textit{htheta} \\
\hline \hline
3 &amp; 11      &amp;  7 (2) &amp;  8 (5) &amp; 5 (7) &amp; 4     &amp; 3
  &amp;  9 (10) &amp; 10 (9) &amp;  2 (6) &amp; 1     &amp; 6 (8) \\
4 &amp; 11      &amp;  7 (2) &amp;  8 (3) &amp; 5 (6) &amp; 4 (5) &amp; 3 (1)
  &amp;  9 (10) &amp; 10 (9) &amp;  2 (8) &amp; 1 (4) &amp; 6 (7) \\
5 &amp; 11      &amp;  7 (2) &amp;  8 (4) &amp; 5 (3) &amp; 4 (9) &amp; 3 (1)
  &amp;  9 (10) &amp; 10 (5) &amp;  2 (8) &amp; 1 (6) &amp; 6 (7) \\
6 &amp; 11      &amp;  8 (5) &amp;  9 (6) &amp; 5 (4) &amp; 4 (7) &amp; 2 (1)
  &amp; 10      &amp;  7 (2) &amp;  3 (8) &amp; 1 (9) &amp; 6 (3)  \\
7 &amp; 11      &amp;  8 (5) &amp; 10 (6) &amp; 5 (4) &amp; 4 (7) &amp; 2 (1)
  &amp;  9 (10) &amp;  7 (2) &amp;  3 (8) &amp; 1 (9) &amp; 6 (3) \\
8 &amp; 11      &amp;  9 (5) &amp; 10 (6) &amp; 5 (4) &amp; 4 (7) &amp; 2 (1)
  &amp;  8 (10) &amp;  7 (2) &amp;  3 (8) &amp; 1 (9) &amp; 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 $2.5 &lt; ADD &lt; 25$
                  (and $25 &lt; ADD &lt; \infty$ in parentheses if they differ)}
\label{t:vert:a}
\begin{tabular}{|c|cc|ccccc|ccccc|}
\hline
\multirow{2}{*}{\rotatebox{90}{\thead{\scriptsize{Training}}}}
    &amp; \multicolumn{2}{c|}{\thead{Benchmarks}}
    &amp; \multicolumn{5}{c|}{\thead{Vertical (whole-day-ahead)}}
    &amp; \multicolumn{5}{c|}{\thead{Vertical (real-time)}} \\
\cline{2-13}
~ &amp; \textit{hets}  &amp; \textit{hsma}   &amp; \textit{varima} &amp; \textit{vets} 
  &amp; \textit{vholt} &amp; \textit{vses}   &amp; \textit{vtheta} &amp; \textit{rtarima}
  &amp; \textit{rtets} &amp; \textit{rtholt} &amp; \textit{rtses}  &amp; \textit{rttheta} \\
\hline \hline
3 &amp;  2 (10) &amp;  1  (7) &amp; 6 (4) &amp; 8 (6) &amp; 10 (9)
  &amp;  7  (5) &amp; 11 (12) &amp; 4 (1) &amp; 5 (3) &amp;  9 (8) &amp; 3 (2) &amp; 12 (11) \\
4 &amp;  2  (7) &amp;  1 (10) &amp; 6 (4) &amp; 8 (6) &amp; 10 (9)
  &amp;  7  (5) &amp; 12 (11) &amp; 3 (1) &amp; 5 (3) &amp;  9 (8) &amp; 4 (2) &amp; 11 (12) \\
5 &amp;  2  (3) &amp;  1 (10) &amp; 7 (5) &amp; 8 (7) &amp; 10 (9)
  &amp;  6      &amp; 11      &amp; 4 (1) &amp; 5 (4) &amp;  9 (8) &amp; 3 (2) &amp; 12 \\
6 &amp;  2  (1) &amp;  1 (10) &amp; 6 (5) &amp; 8 (7) &amp; 10 (9)
  &amp;  7  (6) &amp; 11 (12) &amp; 3 (2) &amp; 5 (4) &amp;  9 (8) &amp; 4 (3) &amp; 12 (11) \\
7 &amp;  2  (1) &amp;  1 (10) &amp; 8 (5) &amp; 7     &amp; 10 (9)
  &amp;  6      &amp; 11 (12) &amp;	5 (2) &amp; 4     &amp;  9 (8) &amp; 3     &amp; 12 (11) \\
8 &amp;  2  (1) &amp;  1  (9) &amp; 8 (5) &amp; 7     &amp; 10 (8)
  &amp;  6      &amp; 12 (10) &amp; 5 (2) &amp; 4     &amp;  9 (6) &amp; 3     &amp; 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 $2.5 &lt; ADD &lt; 25$
                  (and $25 &lt; ADD &lt; \infty$ in parentheses if they differ)}
\label{t:ml:a}
\begin{tabular}{|c|cccc|cc|}
\hline
\multirow{2}{*}{\rotatebox{90}{\thead{\scriptsize{Training}}}}
    &amp; \multicolumn{4}{c|}{\thead{Benchmarks}}
    &amp; \multicolumn{2}{c|}{\thead{ML}} \\
\cline{2-7}
~ &amp; \textit{fnaive}  &amp; \textit{hets} &amp; \textit{hsma}
  &amp; \textit{rtarima} &amp; \textit{vrfr} &amp; \textit{vsvr} \\
\hline \hline
3 &amp; 6     &amp; 2 (5) &amp; 1 (3) &amp; 3 (1) &amp; 5 (2) &amp; 4 \\
4 &amp; 6 (5) &amp; 2 (3) &amp; 1 (6) &amp; 3 (2) &amp; 5 (1) &amp; 4 \\
5 &amp; 6 (5) &amp; 2 (4) &amp; 1 (6) &amp; 4 (2) &amp; 5 (1) &amp; 3 \\
6 &amp; 6 (5) &amp; 2     &amp; 1 (6) &amp; 4     &amp; 5 (1) &amp; 3 \\
7 &amp; 6 (5) &amp; 2 (1) &amp; 1 (6) &amp; 4     &amp; 5 (2) &amp; 3 \\
8 &amp; 6 (5) &amp; 2 (1) &amp; 1 (6) &amp; 4     &amp; 5 (2) &amp; 3 \\
\hline
\end{tabular}
\end{center}
\
</pre></body></html>