銅價波動可能影響企業的原物料採購成本與規劃安排。本研究旨在比較納入外生變數前後的銅價預測模型表現，探討其差異是否隨預測期間而有所不同，並說明其於採購規劃中的參考意義。本研究以 2023 年 1 月至 2025 年 12 月之 COMEX 銅期貨價格為分析對象，納入 XLI 與 DXIF.TO 作為外生變數，建立 ARIMA 與兩種 ARIMAX 模型，並比較其於一個月、三個月、六個月、與一年預測期間下的表現。 研究結果顯示，一個月預測中，納入 XLI 的外生變數模型平均誤差較低，但雙外生變數模型未呈現一致改善；三個月預測中，ARIMA 模型的平均 MAPE 較低，顯示外生變數於短期預測中仍未穩定降低誤差。六個月預測中，雙外生變數模型開始呈現較低平均誤差；一年預測中，納入 XLI 與 DXIF.TO 的雙外生變數模型表現較佳。 模型參考價值可能隨預測期間而異。ARIMAX 分析係在測試期間外部市場資訊已知條件下，比較外生變數納入前後的預測誤差差異。因此，研究結果可作為企業價格監控、採購規劃與價格風險評估的參考資訊，但不代表企業於預測起點即可直接取得未來外生變數資訊，亦不表示實際採購成本必然降低。;Copper price fluctuations may affect raw material procurement costs and planning. This study compares ARIMA and ARIMAX models for copper price forecasting and examines whether the effect of exogenous variables differs across forecasting horizons. Using COMEX copper futures prices from January 2023 to December 2025， this study incorporates XLI and DXIF.TO as exogenous variables and evaluates model performance over one-month， three-month， six-month， and one-year horizons. The results show that the effect of exogenous variables differs across forecasting horizons. For the one-month horizon， the ARIMAX model with XLI shows lower average errors， while the two-exogenous-variable model does not consistently improve performance. For the three-month horizon， ARIMA shows lower average MAPE. For the six-month and one-year horizons， the ARIMAX model with both XLI and DXIF.TO presents lower average forecast errors. These findings suggest that the reference value of forecasting models varies by forecasting horizon. Since the ARIMAX analysis uses observed exogenous-variable data during the test periods， the results should be interpreted as conditional model comparisons rather than fully ex ante forecasts. The findings may support price monitoring， procurement planning， and price risk assessment， but they do not imply that actual procurement costs will necessarily decrease.
