Acknowledgements

integrate the changes from all the rules to determine the rules for the STI. The transition rules are derived from Table 1. For example, Fð Þ! 201501 Fð Þ 201502 is

Step 7. We calculate each rule by determining all the rules of the STI, and the calculation results can be used to forecast future values. Table 1 shows the fore-

Year Actual ln(Actual) Fuzzified The forecast value 201805 63.759 4.155 A3 4.221 201806 62.712 4.139 A3 4.221

Step 8. The calculated STI rules can define the intervals of the STI data; using these intervals, we can determine the variation in future long-term intervals. The long-term predictive value interval for the STI is given as (3.726, 4.913). Thus, the long-term predictive interval for the STI is given as (41.506, 136.022). Therefore, the current long-term S STI is bounded by this interval. According to Step 8, the fuzzy STI of 201501 shown in Table 1 is A5, and from Table 2, we can see that the rules are the fuzzy logical relationships in Rule 8 of Table 2, in which the current state of fuzzy logical relationships is A3. Thus, the 201806 STI predictive

Step 9. Letting defuzzified S be ΔS, the STI 201806 forecast value based on our investigation is 68.090, and its trading range is between 41.506 and 136.002. Thus, the new triangular fuzzy numbers by S = (41.506, 68.090, 136.002). Thus, the

The result shows that based on the long-term significance level, the STI is currently oversold. This result and the risk–reward ratio are both related within the

d tð Þ = 68.090. ΔS is called a long-

A<sup>5</sup> ! A5. Table 2 shows all transition rules obtained from Table 1.

casting results from 201001 to 201806.

defuzzified S is ΔS = 74.981, and ΔS = 74.981 > ^

value is 41.506.

32

Table 1.

Table 2.

Figure 3.

Forecast STI and actual STI.

Fuzzy historical STI data and the forecasted results.

Time Series Analysis - Data, Methods, and Applications

r<sup>1</sup> : A<sup>3</sup> ! A<sup>3</sup> r<sup>5</sup> : A<sup>5</sup> ! A<sup>4</sup> r<sup>2</sup> : A<sup>3</sup> ! A<sup>4</sup> r<sup>6</sup> : A<sup>5</sup> ! A<sup>5</sup> r<sup>3</sup> : A<sup>4</sup> ! A<sup>4</sup> r<sup>7</sup> : A<sup>5</sup> ! A<sup>6</sup> r<sup>4</sup> : A<sup>4</sup> ! A<sup>3</sup> r<sup>8</sup> : A<sup>6</sup> ! A<sup>5</sup>

Fuzzy transitions derived from Table 1.

term significance level up.

This chapter is extended and revised the article "An improved fuzzy time series theory with applications in the Shanghai containerized freight index".

Time Series Analysis - Data, Methods, and Applications

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