42 lines
2 KiB
TeX
42 lines
2 KiB
TeX
\subsubsection{Horizontal and Whole-day-ahead Forecasts.}
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\label{hori}
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The upper-left in Figure \ref{f:inputs} illustrates the simplest way to
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generate forecasts for a test day before it has started:
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For each time of the day, the corresponding horizontal slice becomes the input
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for a model.
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With whole days being the unified time interval, each model is trained $H$
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times, providing a one-step-ahead forecast.
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While it is possible to have models of a different type be selected per time
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step, that did not improve the accuracy in the empirical study.
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As the models in this family do not include the test day's demand data in
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their training sets, we see them as benchmarks to answer \textbf{Q4},
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checking if a UDP can take advantage of real-time information.
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The models in this family are as follows; we use prefixes, such as "h" here,
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when methods are applied in other families as well:
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\begin{enumerate}
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\item \textit{\gls{naive}}:
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Observation from the same time step one week prior
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\item \textit{\gls{trivial}}:
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Predict $0$ for all time steps
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\item \textit{\gls{hcroston}}:
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Intermittent demand method introduced by \cite{croston1972}
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\item \textit{\gls{hholt}},
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\textit{\gls{hhwinters}},
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\textit{\gls{hses}},
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\textit{\gls{hsma}}, and
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\textit{\gls{htheta}}:
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Exponential smoothing without calibration
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\item \textit{\gls{hets}}:
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ETS calibrated as described by \cite{hyndman2008b}
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\item \textit{\gls{harima}}:
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ARIMA calibrated as described by \cite{hyndman2008a}
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\end{enumerate}
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\textit{naive} and \textit{trivial} provide an absolute benchmark for the
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actual forecasting methods.
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\textit{hcroston} is often mentioned in the context of intermittent demand;
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however, the method did not perform well at all.
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Besides \textit{hhwinters} that always fits a seasonal component, the
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calibration heuristics behind \textit{hets} and \textit{harima} may do so
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as well.
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With $k=7$, an STL decomposition is unnecessary here.
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