Table 8 Summary of the backtesting results for each probability level for the stock indices. Number of test rejections for the four indexes
Model | τ = 0.01 | τ = 0.05 | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
UC | IND | CC | DQ | Mean (M-Loss) | UC | IND | CC | DQ | Mean (M-Loss) | |
Hist | 1 | 1 | 1 | 4 | 0.4504 | 1 | 0 | 1 | 1 | 0.8882 |
Normal | 2 | 1 | 1 | 4 | 0.6490 | 1 | 0 | 1 | 2 | 0.9201 |
CAViaR-SAV | 0 | 0 | 0 | 4 | 0.3144 | 0 | 0 | 0 | 1 | 0.7912 |
CAViaR-AS | 0 | 0 | 0 | 3 | 0.2044 | 0 | 0 | 0 | 0 | 0.6677 |
CAViaR-IGARCH | 0 | 0 | 0 | 3 | 0.2678 | 0 | 0 | 0 | 1 | 0.7088 |
CAViaR-Adaptive | 0 | 0 | 0 | 4 | 0.2904 | 0 | 0 | 0 | 1 | 0.9012 |
QRNN | 1 | 0 | 1 | 2 | 0.1990 | 2 | 0 | 2 | 3 | 0.7970 |
LASSO-QR | 3 | 0 | 3 | 4 | 0.6661 | 1 | 0 | 0 | 2 | 0.8867 |
QR-RF | 2 | 0 | 0 | 2 | 0.1949 | 0 | 0 | 0 | 0 | 0.4057 |
QR-GBDT | 3 | 0 | 2 | 4 | 0.2164 | 0 | 0 | 0 | 1 | 0.4592 |
QR-SVM | 0 | 1 | 0 | 4 | 0.3907 | 1 | 0 | 1 | 1 | 0.8367 |
QR-CNN | 0 | 0 | 0 | 3 | 0.3032 | 0 | 0 | 0 | 2 | 0.6485 |
QR-LSTM | 0 | 0 | 0 | 4 | 0.2891 | 2 | 0 | 2 | 2 | 0.7939 |
QR-GRU | 0 | 0 | 0 | 4 | 0.2655 | 1 | 0 | 0 | 1 | 0.6533 |
Proposed Model | 0 | 0 | 0 | 1 | 0.1379 | 0 | 0 | 0 | 0 | 0.3370 |