diff --git a/paper.pdf b/paper.pdf index 6eeca44..4bdce7d 100644 Binary files a/paper.pdf and b/paper.pdf differ diff --git a/tex/4_stu/4_overall.tex b/tex/4_stu/4_overall.tex index 4d11718..c36c876 100644 --- a/tex/4_stu/4_overall.tex +++ b/tex/4_stu/4_overall.tex @@ -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.