# Table 3 CMG algorithm description

Algorithm: CMG (TS, winSize, n)

Input: Time series——TS,

Granulating window width——winSize,

A number of days to be predicted——n.

Output: Qualitative predicted feature sequence of cloud model $${\widehat{E}}_{\mathrm{xi}},{\widehat{E}}_{\mathrm{ni}},{\widehat{H}}_{\mathrm{ei}}\left(i=1,2,\dots, n\right).$$

Algorithm steps:

A. Granulating the TS by cloud model, the digital feature sequence E x , E n , H e of TS is generated.

a-1. Firstly, the original data series is converted into the granular unit data series according to the window width.

a-2. Second, for each granular unit, the sample mean of each granular unit is calculated $$\overrightarrow{X}=\frac{1}{n}\sum \limits_{i=1}^n{x}_i$$,which is the estimated value of expectation E X .

a-3. Then, it calculates the sample variance $${S}^2=\frac{1}{n-1}\sum \limits_{i=1}^n{\left({x}_i-\overline{X}\right)}^2$$ and first order sample absolute center moments $$\frac{1}{n}\sum \limits_{i=1}^n\left|{x}_i-\overline{X}\right|$$ of each granular;

a-4. Finally, it calculates the entropy $${E}_n=\sqrt{\frac{\pi }{2}}\times \frac{1}{n}\sum \limits_{i=1}^n\left|{x}_i-{E}_X\right|$$ and hyper entropy $$He=\sqrt{S^2-{E_n}^2}$$.

B. Regression prediction of E x by SVR.

b-1. First of all, it uses the grid search method to find the best kernel parameters for E X .

b-2. Then, it established the regression prediction model of E X by the above-selected parameter.

b-3. Finally, it used this model to predict the expectation Ex.

C. Regression prediction of E n by SVR.

c-1. First, this algorithm uses grid search method to find the best kernel parameters for E n .

c-2. Then, it established the regression prediction model of E n by the above-selected parameter.

c-3. Finally, it used this model to predict the entropy E n .

D. Regression prediction of He by SVR.

d-1. First, it uses the grid search method to find the best kernel parameters for He.

d-2. Then, it established the regression prediction model of He by above best parameter.

d-3. Finally, using the model d-2 to predict He. 