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- move tables to avoid half blank pages
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Alexander Hess 2020-10-25 19:31:17 +01:00
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@ -13,36 +13,6 @@ We labeled them "no", "low", "medium", and "high" demand pixels with
increasing ADD, and present the average MASE per cluster.
The $n$ do not vary significantly across the training horizons, which confirms
that the platform did not grow area-wise and is indeed in a steady-state.
We use this table to answer \textbf{Q1} regarding the overall best methods
under different ADDs.
All result tables in the main text report MASEs calculated with all time
steps of a day.
In contrast, \ref{peak_results} shows the same tables with MASEs calculated
with time steps within peak times only (i.e., lunch from 12 pm to 2 pm and
dinner from 6 pm to 8 pm).
The differences lie mainly in the decimals of the individual MASE
averages while the ranks of the forecasting methods do not change except
in rare cases.
That shows that the presented accuracies are driven by the forecasting methods'
accuracies at peak times.
Intuitively, they all correctly predict zero demand for non-peak times.
Unsurprisingly, the best model for pixels without demand (i.e.,
$0 < \text{ADD} < 2.5$) is \textit{trivial}.
Whereas \textit{hsma} also adapts well, its performance is worse.
None of the more sophisticated models reaches a similar accuracy.
The intuition behind is that \textit{trivial} is the least distorted by the
relatively large proportion of noise given the low-count nature of the
time series.
For low demand (i.e., $2.5 < \text{ADD} < 10$), there is also a clear
best-performing model, namely \textit{hsma}.
As the non-seasonal \textit{hses} reaches a similar accuracy as its
potentially seasonal generalization, the \textit{hets}, we conclude that
the seasonal pattern from weekdays is not yet strong enough to be
recognized in low demand pixels.
So, in the absence of seasonality, models that only model a trend part are
the least susceptible to the noise.
\begin{center}
\captionof{table}{Top-3 models by training weeks and average demand
@ -198,6 +168,38 @@ So, in the absence of seasonality, models that only model a trend part are
\hline
\end{tabular}
\end{center}
\
We use this table to answer \textbf{Q1} regarding the overall best methods
under different ADDs.
All result tables in the main text report MASEs calculated with all time
steps of a day.
In contrast, \ref{peak_results} shows the same tables with MASEs calculated
with time steps within peak times only (i.e., lunch from 12 pm to 2 pm and
dinner from 6 pm to 8 pm).
The differences lie mainly in the decimals of the individual MASE
averages while the ranks of the forecasting methods do not change except
in rare cases.
That shows that the presented accuracies are driven by the forecasting methods'
accuracies at peak times.
Intuitively, they all correctly predict zero demand for non-peak times.
Unsurprisingly, the best model for pixels without demand (i.e.,
$0 < \text{ADD} < 2.5$) is \textit{trivial}.
Whereas \textit{hsma} also adapts well, its performance is worse.
None of the more sophisticated models reaches a similar accuracy.
The intuition behind is that \textit{trivial} is the least distorted by the
relatively large proportion of noise given the low-count nature of the
time series.
For low demand (i.e., $2.5 < \text{ADD} < 10$), there is also a clear
best-performing model, namely \textit{hsma}.
As the non-seasonal \textit{hses} reaches a similar accuracy as its
potentially seasonal generalization, the \textit{hets}, we conclude that
the seasonal pattern from weekdays is not yet strong enough to be
recognized in low demand pixels.
So, in the absence of seasonality, models that only model a trend part are
the least susceptible to the noise.
For medium demand (i.e., $10 < \text{ADD} < 25$) and training horizons up to
six weeks, the best-performing models are the same as for low demand.