Algorithm 1 Proposed OS-PELM

Input: A training set ${\{(x_t,y_t)\}}_{i=1}^N$, activation function h(x), g(x), f(x), two hidden layer node number Z1, Z2, thresholds CHth, CLth. Output: The actual predicted value YT. 1: Initialize: Randomly generate weights ρ, φ, ω, biases b1t, b2t. 2: Calculate the initial output weight matrix ${\beta }^{\left(0\right)}$ by using Equations (9)–(13). 3: Calculate the output $Y_T^0$ and corresponding standard deviation with YT. 4: Online adjust: Newly arrived samples should be inputted into the prediction model, relevant parameters would be regulated by using Equations (14)–(16). 5: Compute the contribution degree for all hidden layer nodes with Equations (17) and (18). 6: if one neuron needs to be divided then 7:   Calculate new neurons’ parameters by Equations (19)–(21); 8: else if one neuron needs to be merged 9:   Calculate new neuron’ output weight by Equation (22); 10: end if 11: Predict: Adjustment has been completed. Actual prediction should be carried on with the next data during the same month. However, when a new time point comes, the algorithm needs to be recycled from line 5. 12: END