Three types of model inputs (as summarized in Table 1) were used in this study for the two case studies to investigate the effectiveness of input selection and wavelet transformation on the autoregressive forecasting. The first type of input is called ‘Original inputs' and these are created by selecting all probable inputs for forecasting. These Original inputs are not subjected to either of the 2 input preprocessing techniques. As shown in Table 1, for Data #1, a set of 15 time lagged inputs (i.e., *Y _{t}*

Table 1

Type of model inputs . | Description . | Data #1 . | Data #2 . |
---|---|---|---|

Original inputs | All probable inputs to forecast the current value Y _{t} | Y (15 inputs) _{t−1}, Y_{t−2},…, Y_{t−15} | Y_{t−7}, Y_{t−8},…, Y_{t−13} X_{(1)t−7}, X_{(1)t−8},…, X_{(1)t−13}_{;}X_{(2)t−7}, X_{(2)t−8},…, X_{(2)t−13…}_{;}X (63 inputs) _{(8)t−7}, X_{(8)t−8},…, X_{(8)t−13} |

PLC-selected inputs | Inputs selected by PLC technique from the Original inputs | Y (4 inputs) _{t−1}, Y_{t−11}, Y_{t−13,} Y_{t−15} | Y (3 inputs) _{t−7}, Y_{t−8}, Y_{t−13} |

PLC-Wavelet inputs | Inputs created by which wavelet transformation is applied on PLC inputs | D1_{t}_{−1,}D1_{t}_{−11}, D1_{t}_{−13}, D1_{t}_{−15}; D2_{t}_{−1,}D2_{t}_{−11}, D2_{t}_{−13}, D2_{t}_{−15}; D3_{t}_{−1,}D3_{t}_{−11}, D3_{t}_{−13}, D3_{t}_{−15}; A3_{t}_{−1,}A3_{t}_{−11}, A3_{t}_{−13}, A3_{t}_{−15}; (16 wavelet inputs) | D1_{t}_{−7,}D1_{t}_{−8}, D1_{t}_{−13}; D2_{t}_{−7,}D2_{t}_{−8}, D2_{t}_{−13}; D3_{t}_{−7,}D3_{t}_{−8}, D3_{t}_{−13}; A3_{t}_{−7,}A3_{t}_{−8}, A3_{t}_{−13}; (12 wavelet inputs) |

Type of model inputs . | Description . | Data #1 . | Data #2 . |
---|---|---|---|

Original inputs | All probable inputs to forecast the current value Y _{t} | Y (15 inputs) _{t−1}, Y_{t−2},…, Y_{t−15} | Y_{t−7}, Y_{t−8},…, Y_{t−13} X_{(1)t−7}, X_{(1)t−8},…, X_{(1)t−13}_{;}X_{(2)t−7}, X_{(2)t−8},…, X_{(2)t−13…}_{;}X (63 inputs) _{(8)t−7}, X_{(8)t−8},…, X_{(8)t−13} |

PLC-selected inputs | Inputs selected by PLC technique from the Original inputs | Y (4 inputs) _{t−1}, Y_{t−11}, Y_{t−13,} Y_{t−15} | Y (3 inputs) _{t−7}, Y_{t−8}, Y_{t−13} |

PLC-Wavelet inputs | Inputs created by which wavelet transformation is applied on PLC inputs | D1_{t}_{−1,}D1_{t}_{−11}, D1_{t}_{−13}, D1_{t}_{−15}; D2_{t}_{−1,}D2_{t}_{−11}, D2_{t}_{−13}, D2_{t}_{−15}; D3_{t}_{−1,}D3_{t}_{−11}, D3_{t}_{−13}, D3_{t}_{−15}; A3_{t}_{−1,}A3_{t}_{−11}, A3_{t}_{−13}, A3_{t}_{−15}; (16 wavelet inputs) | D1_{t}_{−7,}D1_{t}_{−8}, D1_{t}_{−13}; D2_{t}_{−7,}D2_{t}_{−8}, D2_{t}_{−13}; D3_{t}_{−7,}D3_{t}_{−8}, D3_{t}_{−13}; A3_{t}_{−7,}A3_{t}_{−8}, A3_{t}_{−13}; (12 wavelet inputs) |

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