2.2.2 Transition matrix

Assuming that there are n states denoting as E1, E2, …, En, the transition probability amounts to frequency approximately in general, namely, Pij <sup>¼</sup> <sup>M</sup>ð Þ<sup>l</sup> ij Mi . Then, we can get the <sup>l</sup>th step transition matrix P lðÞ¼ <sup>P</sup>ð Þ<sup>l</sup> ij n�n . Mð Þ<sup>l</sup> ij is the data of raw series transferring l step from the state Qi to the state Qj .

### 2.2.3 The forecasting value

The eventual forecast is in the center of the Gray zone, which is denoted as Y0 ð Þ¼ <sup>k</sup> <sup>1</sup> <sup>2</sup> <sup>Q</sup>1<sup>i</sup> <sup>þ</sup> <sup>Q</sup>2<sup>i</sup> ð Þ¼ Y k ^ð Þ¼ <sup>1</sup> <sup>2</sup> ð Þ E1<sup>i</sup> þ E2<sup>i</sup> . Eventually, the forecasting sequence is obtained as Y<sup>0</sup> ð Þ¼ k Y<sup>0</sup> ð Þ1 ; Y<sup>0</sup> ð Þ2 ; …; Y<sup>0</sup> f g ð Þ m .
