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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., Yt−1 to Yt−15) is used to forecast the current value, Yt. For Data #2, nine variables are used as input, which include the eight variables presented earlier along with chlorophyll itself. For each of these nine variables, a time lag of 7–13 days is used (giving a total of 63 inputs) for the 7-day ahead forecasting of chlorophyll concentrations.

Table 1

Types of model inputs applied to the two datasets

Type of model inputsDescriptionData #1Data #2
Original inputs All probable inputs to forecast the current value Yt Yt−1, Yt−2,…, Yt−15 (15 inputs) Yt−7, Yt−8,…, Yt−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(8)t−7, X(8)t−8,…, X(8)t−13 (63 inputs) 
PLC-selected inputs Inputs selected by PLC technique from the Original inputs Yt−1, Yt−11, Yt−13, Yt−15 (4 inputs) Yt−7, Yt−8, Yt−13 (3 inputs) 
PLC-Wavelet inputs Inputs created by which wavelet transformation is applied on PLC inputs D1t−1,D1t−11, D1t−13, D1t−15; D2t−1,D2t−11, D2t−13, D2t−15; D3t−1,D3t−11, D3t−13, D3t−15; A3t−1,A3t−11, A3t−13, A3t−15; (16 wavelet inputs) D1t−7,D1t−8, D1t−13; D2t−7,D2t−8, D2t−13; D3t−7,D3t−8, D3t−13; A3t−7,A3t−8, A3t−13; (12 wavelet inputs) 
Type of model inputsDescriptionData #1Data #2
Original inputs All probable inputs to forecast the current value Yt Yt−1, Yt−2,…, Yt−15 (15 inputs) Yt−7, Yt−8,…, Yt−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(8)t−7, X(8)t−8,…, X(8)t−13 (63 inputs) 
PLC-selected inputs Inputs selected by PLC technique from the Original inputs Yt−1, Yt−11, Yt−13, Yt−15 (4 inputs) Yt−7, Yt−8, Yt−13 (3 inputs) 
PLC-Wavelet inputs Inputs created by which wavelet transformation is applied on PLC inputs D1t−1,D1t−11, D1t−13, D1t−15; D2t−1,D2t−11, D2t−13, D2t−15; D3t−1,D3t−11, D3t−13, D3t−15; A3t−1,A3t−11, A3t−13, A3t−15; (16 wavelet inputs) D1t−7,D1t−8, D1t−13; D2t−7,D2t−8, D2t−13; D3t−7,D3t−8, D3t−13; A3t−7,A3t−8, A3t−13; (12 wavelet inputs) 

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