本文以台灣股價加權指數，使用 AR(3)-GJR-GRACH(1,1) 模型，白噪音假設為 Normal 、 Skew-Normal 、 Student t 、 skew-t 、 EPD 、 SEPD 、與 AEPD 等七種分配。著重於兩個部份，(一) Student t 分配一族與 EPD 分配一族在模型配適與風險值估計的比較；(二) 預測風險值區分為低震盪與高震盪兩個區間，比較不同分配在兩區間預測風險值的差異。

實證分析顯示， t 分配一族與 EPD 分配一族配適的結果，無論是只考慮峰態 ( t 分配與 EPD 分配) ，或者加入影響偏態的參數 ( skew-t 分配與 SEPD 分配) ， t 分配一族的配適程度都較 EPD 分配一族為佳。更進一步考慮分配兩尾厚度不同的 AEPD 分配，配適結果為七種分配中最佳。

風險值的估計在低震盪的區間，常態分配與其他厚尾分配皆能通過回溯測試，採用厚尾分配效果不大；在高震盪的區間，左尾風險值回溯測試結果，常態分配與其他厚尾分配皆無法全數通過，但仍以 AEPD 分配為最佳。最後比較損失函數，左尾風險值估計以 AEPD 分配為最佳，右尾風險值則無一致的結果。因此我們認為 AEPD 分配可作為風險管理有用的工具。

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