Algorithm 1. The algorithm used for developing the stacked model

Input: training data $A={\{{\mathit{x}}_{\mathit{i}}, {\mathit{y}}_{\mathit{i}}\}}_{\mathit{i}={\displaystyle 1}}^{\mathit{m}}$ Output: a stacking regressor ${\mathit{M}}_{\mathit{f}}$ 1: Step 1: perform the training of the base-level regressors 2: for t = 1 to T do 3: Train ${\mathit{h}}_{\mathit{t}}$ based on database of A 4: end for 5: Step 2: design new database of predictions 6: for i = 1 to m do 7: ${\mathit{A}}_{\mathit{h}}=\left\{{\mathit{x}}_{\mathit{i}}{}^{\prime }, {\mathit{y}}_{\mathit{i}}\right\}$, where ${\mathit{x}}_{\mathit{i}}{}^{\prime }=\left\{{\mathit{h}}_{{\displaystyle 1}}\left({\mathit{x}}_{\mathit{i}}\right),\dots \dots ,{\mathit{h}}_{\mathit{T}}\left({\mathit{x}}_{\mathit{i}}\right)\right\}$ 8: end for 9: Step 3: perform the training of the meta-regressor 10: perform the training of ${\mathit{M}}_{\mathit{f}}$ based on ${\mathit{A}}_{\mathit{h}}$ 11: return ${\mathit{M}}_{\mathit{f}}$