\subsection{Calibration of the Time Series Generation Process}
\label{params}

Independent of the concrete forecasting models, the time series generation
    must be calibrated.
We concentrate our forecasts on the pickup side for two reasons.
First, the restaurants come in a significantly lower number than the
    customers resulting in more aggregation in the order counts and thus a
    better pattern recognition.
Second, from an operational point of view, forecasts for the pickups are more
    valuable because of the waiting times due to meal preparation.
We choose pixel sizes of $0.5~\text{km}^2$, $1~\text{km}^2$, $2~\text{km}^2$,
    and $4~\text{km}^2$, and time steps covering 60, 90, and 120 minute windows
    resulting in $H_{60}=12$, $H_{90}=9$, and $H_{120}=6$ time steps per day
    with the platform operating between 11 a.m. and 11 p.m. and corresponding
    frequencies $k_{60}=7*12=84$, $k_{90}=7*9=63$, and $k_{120}=7*6=42$ for the
    vertical time series.
Smaller pixels and shorter time steps yield no recognizable patterns, yet would
    have been more beneficial for tactical routing.
90 and 120 minute time steps are most likely not desirable for routing; however,
    we keep them for comparison and note that a UDP may employ such forecasts
    to activate more couriers at short notice if a (too) high demand is
    forecasted in an hour from now.
This could, for example, be implemented by paying couriers a premium if they
    show up for work at short notice.
Discrete lengths of 3, 4, 5, 6, 7, and 8 weeks are chosen as training
    horizons.
We do so as the structure within the pixels (i.e., number and kind of
    restaurants) is not stable for more than two months in a row in the
    covered horizon.
That is confirmed by the empirical finding that forecasting accuracy
    improves with longer training horizon but this effect starts to
    level off after about six to seven weeks.
So, the demand patterns of more than two months ago do not resemble more
    recent ones.

In total, 100,000s of distinct time series are forecast in the study.
