Algorithm 1. Adjusted TOP method based on pruning and path segmentation algorithm

Pruning and Path Segmentation algorithm

Construct local distance matrix ε(t1,i,t2,j), for i, j = 0,1,2,…,n; Use formula (15) to determine the average thermal optimal path $\langle x\left(t\right)\rangle$, when the maximum value of independent variable i of g(i,t − i) used in (15) to compute $\langle x\left(t\right)\rangle$ is less than n*. Use formula (A12) in Appendix to determine the average thermal optimal path $\langle x\left(t\right)\rangle$,when the maximum value of independent variable i of g(i,t − i) used in (15) to compute $x\left(t\right)$ is between n* and n* + n1 − β. Use formula (A14) in Appendix to determine the average thermal optimal path $x\left(t\right)$,when the maximum value of independent variable i of g(i,t − i) used in (15) to compute $x\left(t\right)$ is between n* + n1 − β and n.

Note: the concrete definition and description of n*, n1 in Algorithm 1 can be funded in Appendix. In the following empirical study, n = 1249 (time-series data size) and we set n1 = 420 (a partition coefficient), n* = 510 (a threshold), and β = 30 (the possible maximum lag). Furthermore, the adjusted TOP method and existing TOP are the same for the case of small data (small time-series data size).