Algorithm 1 for data decomposition

1: procedure $x_t$.

2:    for $1\le l\le NE$ do

3:       $y_t^l\leftarrow x_t+{\epsilon }^l$, $y_{i=0,t}^l\leftarrow y_t^l$

4:       $Max\_local\leftarrow \mathrm{local}\mathrm{maxima}{y}_{i,t}^l$, $Min\_local\leftarrow \mathrm{local}\mathrm{minima}{y}_{i,t}^l$

5:       ${\overline{y}}_{i,t}^l\leftarrow$ apply endpoint condition method to $y_{i,t}^l$

6:       ${\overline{h}}_{max,i,t}^l\leftarrow$ upper envelop of ${\overline{y}}_{i,t}^l$; ${\overline{h}}_{max,i,t}^l\leftarrow$ lower envelop of ${\overline{y}}_{i,t}^l$

7:       ${\overline{m}}_{i,t}^l\leftarrow \frac{{\overline{h}}_{max,i,t}^l+{\overline{h}}_{min,i,t}^l}{2}$, ${\overline{r}}_{i,t}^l\leftarrow {\overline{y}}_{i,t}^l-{\overline{m}}_{i,t}^l$

8:       while ${\overline{y}}_{i,t}^l$ is a constant or trend do

9:       if ${\overline{r}}_{i,t}^l$ satisfies the two conditions of IMFs, do

10:          ${\overline{r}}_{i,t}^l$ is the i-th $IM{F}_{i,t}^{\ast }$

11:          $i\leftarrow i+1$

12:          ${\overline{y}}_{i,t}^l={\overline{y}}_{i-1,t}^l-{\overline{r}}_{i-1,t}^l$

13:       else

14:          ${\overline{y}}_{i,t}^l={\overline{r}}_{i,t}^l$

15:       end if

16:       $Max\_local\leftarrow \mathrm{local}\mathrm{maxima}{y}_{i,t}^l$, $Min\_local\leftarrow \mathrm{local}\mathrm{minima}{y}_{i,t}^l$

17:       ${\overline{h}}_{max,i,t}^l\leftarrow$ upper envelop of ${\overline{y}}_{i,t}^l$; ${\overline{h}}_{max,i,t}^l\leftarrow$ lower envelop of ${\overline{y}}_{i,t}^l$

18:       ${\overline{m}}_{i,t}^l\leftarrow \frac{{\overline{h}}_{max,i,t}^l+{\overline{h}}_{min,i,t}^l}{2}$

19:    end while

20: end for

21: end procedure $IM{F}_{i,t}^{\ast }$ and ${\overline{r}}_{i,t}$