39 lines
1.8 KiB
TeX
39 lines
1.8 KiB
TeX
\subsubsection{Vertical and Whole-day-ahead Forecasts without Retraining}
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\label{vert}
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The upper-right in Figure \ref{f:inputs} shows an alternative way to
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generate forecasts for a test day before it has started:
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First, a seasonally-adjusted time series $a_t$ is obtained from a vertical
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time series by STL decomposition.
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Then, the actual forecasting model, trained on $a_t$, makes an $H$-step-ahead
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prediction.
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Lastly, we add the $H$ seasonal na\"{i}ve forecasts for the seasonal component
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$s_t$ to them to obtain the actual predictions for the test day.
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Thus, only one training is required per model type, and no real-time data is
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used.
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By decomposing the raw time series, all long-term patterns are assumed to be
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in the seasonal component $s_t$, and $a_t$ only contains the level with
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a potential trend and auto-correlations.
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The models in this family are:
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\begin{enumerate}
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\item \textit{fnaive},
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\textit{pnaive}:
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Sum of STL's trend and seasonal components' na\"{i}ve forecasts
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\item \textit{vholt},
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\textit{vses}, and
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\textit{vtheta}:
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Exponential smoothing without calibration and seasonal
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fit
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\item \textit{vets}:
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ETS calibrated as described by \cite{hyndman2008b}
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\item \textit{varima}:
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ARIMA calibrated as described by \cite{hyndman2008a}
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\end{enumerate}
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As mentioned in Sub-section \ref{unified_cv}, we include the sum of the
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(seasonal) na\"{i}ve forecasts of the STL's trend and seasonal components
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as forecasts on their own:
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For \textit{fnaive}, we tune the "flexible" $ns$ parameter, and for
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\textit{pnaive}, we set it to a "periodic" value.
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Thus, we implicitly assume that there is no signal in the remainder $r_t$, and
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predict $0$ for it.
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\textit{fnaive} and \textit{pnaive} are two more simple benchmarks.
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