機率分配預測（density forecasting）可完整呈現預測不確定性，已廣泛應用於經濟預測、風險管理及政策評估等領域。基於其實務重要性，許多中央銀行，如英格蘭銀行與挪威銀行，已將 GDP、通膨等重要總體經濟變數的機率分配預測或預測區間納入貨幣政策溝通。然而，建構準確的機率分配預測仍面臨兩項主要挑戰：其一，如何有效整合高頻資訊，以提升低頻變數的預測表現；其二，如何處理依賴單一預測模型所衍生的模型不確定性。

本研究提出一套新的機率分配預測合併方法（density-forecast model averaging, DFMA），建立一個兼顧混合頻率資訊與模型不確定性的機率分配預測架構。具體而言，首先利用混合資料抽樣分量迴歸（mixed-data sampling quantile regression, MIDAS-QR）估計低頻目標變數的條件分量；其次，將估計之條件分量與參數化的偏態 t 分配進行配適，以建構各候選 MIDAS 模型的機率分配預測；最後，以歷史對數評分（logarithmic score）作為 Kullback–Leibler 資訊量準則（Kullback–Leibler information criterion, KLIC）的經驗近似，估計各候選機率分配預測的組合權重，進而建構合併後的機率分配預測。

本研究透過蒙地卡羅模擬及美國實質 GDP 季成長率即時預測應用，評估所提 DFMA 方法的預測績效。模擬結果顯示，DFMA 所產生之預測區間的涵蓋率最接近名目水準，且依標準密度評分指標衡量，其整體表現優於其他競爭方法。實證分析則利用非農就業人數、工業生產、產能利用率、芝加哥聯邦準備銀行全國經濟活動指數，以及芝加哥聯邦準備銀行全國金融情勢指數等五項高頻經濟指標，設定實質 GDP 季成長率的候選 MIDAS 預測模型，並據以得到相應的機率分配預測。實證結果顯示，DFMA 所建構的合併機率分配及預測區間具有良好的預測表現；尤其當候選模型建立於具經濟意涵且精簡的實質景氣指標（如產能利用率）時，其預測績效尤為突出。

Density forecasts are widely used to quantify forecast uncertainty and support economic forecasting, risk management, and policy evaluation. Reflecting their practical importance, several central banks routinely publish density forecasts for key macroeconomic aggregates. Constructing accurate predictive densities, however, remains challenging because it requires effectively incorporating high-frequency information into low-frequency forecasts while accounting for model uncertainty.

This thesis proposes a novel density-forecast model averaging (DFMA) procedure that provides a unified framework for mixed-frequency density forecasting under model uncertainty. The procedure integrates mixed-frequency conditional quantile forecasting, quantile-to-density construction, and density forecast combination. Specifically, MIDAS quantile regression is used to estimate conditional quantiles from mixed-frequency data; the resulting quantile estimates are transformed into candidate predictive densities using a four-parameter skewed-t distribution; and the candidate densities are combined using weights estimated from the historical logarithmic score, an empirical approximation to the Kullback–Leibler information criterion.

The proposed method is evaluated through Monte Carlo simulations and a real-time forecasting application to U.S. quarterly GDP growth. Simulation results show that DFMA produces forecast intervals with empirical coverage probabilities closest to the nominal levels while generally outperforming competing methods under standard density scoring rules. The empirical application further demonstrates that DFMA performs well, particularly when the candidate model set is constructed from parsimonious and economically coherent real-activity indicators. Overall, the proposed framework provides a practical and unified approach to mixed-frequency density forecasting under model uncertainty.

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