Elliott Wave Theory has the advantages of universality and accuracy. It accurately depicts the way the stock market works and has become an important tool in securities market modeling. Elliott Wave Theory includes five rising waves and three descending waves, which have important quantitative features related to the Fibonacci series and the golden ratio. At the same time, China’s Shanghai Composite Index reflects the systemic risk of the stock market to a certain extent. If China’s Shanghai Composite Index could be accurately predicted, we could take the necessary precautions to prevent risk in the system. Therefore, this paper uses gray model features, which are highly adaptable and can handle parameter changes. The cross-sectional data of the inflection points of the Elliott wave line are selected as the original data to fit the small sample number required for gray modeling. According to the special mapping relationship between Elliott Wave Theory and the Fibonacci sequence, by combining the important properties of the Fibonacci sequence and the golden ratio, the background value of the gray GM (1, 1) model is optimized, the new models F1 - GM and F2 - GM are presented, and the important properties of the new models are studied. Finally, the Elliott wave line is drawn using the Chinese Shanghai Composite Index, and the inflection point data for the whole wave, rising waves and falling waves of the wave line are used as empirical data. The results show that the new model can choose an optimal model according to the data characteristics and is more effective. The new model can also provide new information for the forecasting of stock price indexes and provide help and reference for stock price index forecasts.
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