本篇論文之主旨係針對臺美經濟活動與關係進行指標設計與討論，將貿易、投資、金融方面量化活動加以變數處理分析後，進行主成分分析與加權，並用迴歸自向量模型和Granger因果檢定，檢視三大方面共13個變數強度因果關係分析。
資料涵蓋2015年1月至2024年12月。透過單根檢定確保變數平穩性後，運用主成分分析法（PCA）提取第一主成分並計算加權權重，建立臺美經濟關係加權綜合指標。進一步將指標轉換為景氣燈號，以視覺化方式呈現經濟互動強度。為驗證因果關係，採用向量自迴歸（VAR）模型下之 Granger 因果檢定評估各變數對指標之領先效果，並以 ARIMA 模型進行短期預測能力測試。
實證結果顯示，對美進出口額、貿易對GDP占比及雙邊直接投資等為指標中最具權重之關鍵變數，凸顯以貿易為主、投資為輔的為臺美關係的核心支柱。景氣燈號分析亦指出，自2021年起臺美經濟互動熱度明顯升溫，紅燈頻現。Granger因果檢定中，實質貿易類變數最具顯著領先性，具備預測經濟變動能力。Autoregressive Integrated Moving Average (ARIMA) 模型預測顯示，該指標可穩定預測六個月內趨勢。

This thesis constructs a composite index to measure Taiwan–U.S. economic relations by quantifying trade, investment, and financial activities into 13 representative variables. Using data from January 2015 to December 2024, the study applies unit root tests to ensure data stationarity, followed by principal component analysis (PCA) to extract the first principal component and assign weights. The resulting index is then transformed into a five-level signal system to visually represent the strength of bilateral economic interaction.
Granger causality tests under a vector autoregressive (VAR) model are conducted to identify variables with leading effects, and an Autoregressive Integrated Moving Average (ARIMA) model is used to evaluate short-term forecast accuracy. Empirical findings show that variables such as import and export value, and trade-to-GDP ratio, U.S carry the highest weights, highlighting the dominant role of trade and financial ties. The index indicates a significant rise in Taiwan–U.S. engagement after 2021. Moreover, trade-related variables show strong leading effects, and ARIMA forecasting confirms the index’s ability to capture six-month economic trends with stability and accuracy.

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