大數據分析和人工智慧已是當前的科技主流，然而從研究方法角度解析「累加性數字」的方法較少被提及，因此，本研究提供了一種利用異質變異數估計的數學方法，以達到為複雜金融數據建立更精確的數學模型之目的。透過特定或多種數學模型的建構，由AI判斷最佳的模型，包含 (1.)運用AI，針對特定線性或非線性模型，進行資料數量的決策（AI多線段法），以及 (2.) 運用AI，從多種數學模型當中抉擇出最佳模式。後者須同時考量期望值模型和變異數異質性模型，並能合併二者以達到研究人員所能做到之最佳數學模式。同時，以新冠肺炎前後期間，台灣股價指數期貨日收益率為例。研究發現人工智慧可建構更為符合數據之數學模型，並以數學式提供良好訊號，做決策依據使用。若使用AI多線段法，則可對應上該期間市場發生的事件。若使用AI判斷多種數學模型，則可在無人為干預或設定下，符合人工智慧特性，甚至做到人類無法計算的精確數學模型結果。即使是黑天鵝的新冠肺炎事件，在本研究之分析方法上，亦得到非常良好的結果。

Big data analysis and artificial intelligence are the current mainstream of science and technology, but the method of analyzing additive numbers from the perspective of research methods is rarely mentioned. Therefore, this study provides a method of building a more accurate mathematical model for complex financial data by using heterogeneous variance estimation. This research uses the daily yields of Taiwan Stock Index Futures as the source of raw data and focuses on analyzing three distinct time frames: before COVID-19, during COVID-19, and the entire time period. There are two methods used, and both involve AI: an AI multi-line segment method followed up with mathematical models selected by AI. AI multi-line segment method uses either a specific linear or nonlinear model fitted with optimal data quantity determined by AI. Followed up by a mathematical model selection method where AI screens for the best model from a variety of mathematical models. The latter must consider both the expected value model and the variance heterogeneity model and combine the two to achieve the goal of a more accurate mathematical model. When the AI multi-line method is used, trends and turning points coincidentally corresponds to previous events of significant impact. On the flip side, having AI decide on the two mathematical models used, out of a pool of prospects, meet the characteristics of artificial intelligence without human intervention or setting. It is found that artificial intelligence is capable of selecting more suitable mathematical models based on the characteristics of the inputted raw data. As the results are derived from a mathematical formula, it is free of manipulation and advantageous for decision-making. In addition, the result also shows higher accuracy that cannot be calculated by humans. Even during a black swan event such as the COVID-19 pandemic, this method has achieved highly accurate results.

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