針對以上四個合適的模型與風險矩陣在風險值估計中顯示當相同的顯著水 準 α 下 TAR-GARCH 模型所產生的最大損失是最小的。圖三至圖七顯示在 99%
的信賴水準下保留值與風險值的穿透率和捕捉波動的情況，結果顯示此四個模型 在99%的信賴水準下皆無資料超出風險值故穿透率為 0%，而風險矩陣為有 1 筆 資料超過風險值，由表五風險值評估標準當穿透筆數在0-4 筆時屬於綠色安全範 圍，5-9 筆屬於黃色需注意範圍，10 以上則為紅色警戒範圍；而此五個模型穿透
率在99%信賴水準下皆在綠色安全範圍內，故此五個模型皆為適合。而圖八至圖 十二顯示在95%的信賴水準下保留值與風險值的穿透率和捕捉波動的情況，圖八 GARCH 和圖九 EGARCH 模型中有 4 筆資料超過風險值，穿透率為 1.6%；在圖 十 GJR-GARCH 和圖十一 TAR-GARCH 模型中有 2 筆資料超過風險值，穿透率 為0.8%；圖十二風險矩陣模型中有 13 筆資料超過風險值，穿透率為 5.2%，表示 此四個模式在95%信賴水準下是適合的而風險矩陣較不合適。我們可以在所有的 風險值時間序列圖看出其能有效的捕捉到波動的情形，而在表六為分別在信賴水 準 99%和 95%時各模型的穿透率比較，在 99%時除了風險矩陣的穿透筆數為 1 筆之外，其餘穿透筆數皆為0 筆，故由表五可以看出，所有模型的穿透情況皆屬 於綠色安全範圍，而在 95%時，GARCH 與 EGARCH 模型穿透筆數為 4 筆，
GJR-GARCH 與 TAR-GARCH 穿透筆數為 2 筆，風險矩陣穿透筆數為 13 筆，顯 示模型在已給定顯著水準 α 越高的情況下，越不穩定，其穿透率的情況也越嚴 重。綜合以上結果我們發現 GJR-GARCH 和 TAR-GARCH 模型較佳，表示非對 稱模型較對稱模型來的更為適合。
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表附錄.
表一. 敘述統計量表.
Statistics N Mean (%)
Taiwan 1566 -0.0028 1.7512 -0.0120 2.1705 307.2305 P-value (0.9489) (0.8462) (0.0000) (0.0000)
LM為Lagrange multiplier test統計量，P-value < 0.01，
拒絕虛無假設，則資料屬於變異數異質性。
表三. 各模型之參數估計值
Variable GARCH EGARCH GJR-GARCH TAR-GARCH RiskMetrics Coeff P-value Coeff P-value Coeff P-value Coeff P-value Coeff P-value φ0 0.0731 0.0589 - - - - - - - -
Model GARCH EGARCH GJR-GARCH TAR-GARCH RiskMetrics
Ststistics Q P-value Q P-value Q P-value Q P-value Q P-value
Q(5) 6.5648 0.2551 17.2096 0.0041 8.1198 0.1497 13.3555 0.0203 9.7903 0.0814 Q(10) 9.0681 0.5256 21.1438 0.0201 11.0290 0.3552 16.4482 0.0875 12.4484 0.2561 Q(15) 13.5546 0.5595 25.5867 0.0426 17.7105 0.2782 23.0659 0.0827 16.4371 0.3536 Q(20) 15.4968 0.7473 27.5852 0.1196 19.1251 0.5137 24.4963 0.2214 19.1829 0.5099 Q2(5) 9.2692 0.0988 0.1289 0.9997 5.8779 0.3183 4.2992 0.1993 11.3843 0.0443 Q2(10) 20.0053 0.0292 0.6383 0.9999 13.4289 0.2007 17.9443 0.0559 21.2459 0.0195 Q2(15) 20.7262 0.1458 2.6949 0.9997 15.3475 0.4994 20.2863 0.1612 22.4516 0.0965 Q2(20) 29.7899 0.1145 3.0942 0.9999 18.0757 0.5824 24.0226 0.2414 27.9469 0.1106
|Q( 5)| 13.4834 0.0192 4.0072 0.5484 10.7849 0.0558 13.0007 0.0234 13.3676 0.0201
|Q(10)| 22.1118 0.0145 11.8672 0.2940 17.7684 0.0590 21.5836 0.0174 20.9439 0.0215
|Q(15)| 16.2707 0.0811 16.2707 0.3643 19.1919 0.2052 24.9526 0.0506 21.6737 0.1166
|Q(20)| 27.9649 0.1102 19.7486 0.4738 21.9091 0.3455 28.1429 0.1060 26.3833 0.1535 Notes: Q-stat of standardized residuals is Q(‧), squared standardized residuals is Q2( ) and absolute‧ standardized residuals
is |Q( )| . “ ”is‧ ‧ the numbers of lags.
表五. VaR 99% 評估標準
Basel Accord Penalty Zones
Zone Number of Violations Increase in k Green 0 to 4 0.00
Yellow 5 0.40
6 0.50 7 0.65 8 0.75 9 0.85 Red 10+ 1.00 Note: The number of violations is calculated on the basis of 250 business days.
表六. 各模型穿透情況
注: 回顧觀察天數為 250 天，在 99%時除了風險矩陣的穿透筆數為 1 筆之外，其餘穿透筆數皆為 0 筆，
故由表五可以看出，所有模型的穿透清況皆屬於綠色安全範圍；而在95%時，GARCH 與 EGARCH
模型穿透筆數為4 筆，GJR-GARCH 與 TAR-GARCH 穿透筆數為 2 筆，風險矩陣穿透筆數為 13 筆，
表示非對稱模型較其他模型更為適合。
GARCH EGARCH GJR-GARCH TAR-GARCH RiskMetrics
穿透筆數 0 0 0 0 1
99% 穿透率 0% 0% 0% 0% 0.4%
穿透筆數 4 4 2 2 13
95% 穿透率 1.6% 1.6% 0.8% 0.8% 5.2%
GARCH model
Taiw am stock index time series
200 400 600 800 1000 1200 1400
3000
200 400 600 800 1000 1200 1400
-10.0
EGARCH model
25 50 75 100 125 150 175 200 225 250
-3.6 -2.4 -1.2 0.0 1.2 2.4
圖四. EGARCH 模型.
在EGARCH 模型中有 0 筆資料超過風險值，穿透率為 0%，表示此模式適合。
圖五. GJR-GARCH 模型.
在GJR-GARCH 模型中有 0 筆資料超過風險值，穿透率為 0%，表示此模式適合。
圖六. TAR-GARCH 模型.
在TAR-GARCH 模型中有 0 筆資料超過風險值，穿透率為 0%，表示此模式適合。
GJR-GARCH model
25 50 75 100 125 150 175 200 225 250
-5.0 -2.5 0.0 2.5
TAR-GARCH model
25 50 75 100 125 150 175 200 225 250
-4 -3 -2 -1 0 1 2 3
RiskMetrics
25 50 75 100 125 150 175 200 225 250
-5.0 -2.5 0.0 2.5
圖七. 風險矩陣.
在風險矩陣中有1 筆資料超過風險值，穿透率為 0.4%，表示此模式適合。
95% 保留值與 VaR 時間序列圖 圖八. GARCH 模型.
在GARCH 模型中有 4 筆資料超過風險值，穿透率為 1.6%，表示此模式適合。
圖九. EGARCH 模型.
在EGARCH 模型中有 4 筆資料超過風險值，穿透率為 1.6%，表示此模式適合。
GARCH model
25 50 75 100 125 150 175 200 225
-3 -2 -1 0 1 2 3
EGARCH model
120 140 160 180 200 220 240 260 280 300 320 340 360
-3 -2 -1 0 1 2 3
Riskmetrics