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Finally, the prediction values of the original water temperature datasets are calculated by the sum of the forecasting values of every sub-series.
The following figures compare the forecasting values with the true values, including weekly price forecasting values and urgency forecasting values.
This paper uses the ratios of mean square error (denoted by MSE θ ) and mean absolute error (denoted by MAE θ ) to the mean price to measure the error of the forecasting values of weekly price changes.
According to Eq. (9), the parallel combination of ARIMA and MLP is produced by Eq. (14): {widehat{y}}_t={w}_1{widehat{L}}_t+{w}_2{widehat{N}}_t (14 where, ( {widehat{y}}_t ), ( {widehat{L}}_t ) and ( {widehat{N}}_t ) are the forecasting values which are obtained by hybrid, MLP and ARIMA models at time t respectively and w i (i = 1, 2) is the weights allocated to each individual model.
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θ i (1) (t) is the forecasting value of ARIMA model of market i. θ i (2) (t) is the forecasting value of PLA regression model of market i.
Finally we get the forecasting value θ i (2) (t) of space model by the regression relations.
Considering the asynchronism of price changes and the accumulating of exogenous variables, this paper is conservative with the forecasting value of urgency.
We finally obtain two groups of values from the model: the forecasting value of the weekly price change θ i ' (t) and the daily adjusted price warning urgency value U i ' (t) in the market i at day t.
Let e t denote the residual of the ARIMA model at time t: {e}_t={y}_t-{widehat{L}}_t (6 where ( {widehat{L}}_t ) is the forecasting value for time t from the ARIMA model based on original data.
Then, {e}_t^{prime }={y}_t-{widehat{N}}_t (9 where ( {widehat{N}}_t ) is the forecasting value for time t in the MLP model based on the original data.
The levels of each process parameter for these five DMUs are shown in Table 7, where the forecasting value of a quality index is its value derived from the corresponding regression equations and the real value of a quality index means its value by re-running Moldflow on this combination of process parameters.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com