Research Article
A Comparative Study of VaR Estimation for Structured Products
Table 5
Backtesting method of selected time series models for alternative notes during various periods.
| | Time series model | The whole period | The low oil period | The high oil period | | Total number | Exception | LR | Total number | Exception | LR | Total number | Exception | LR |
| | Panel A: RUD notes |
| | AR()-ARCH(5) | 997 | 44 | 63.7726 | 326 | 5 | 0.8065 | 671 | 29 | 41.0709 | | AR()-GARCH(1,1) | 997 | 72 | 164.6229 | 326 | 5 | 0.8065 | 671 | 56 | 142.8076 | | AR()-GARCH(1,4) | 997 | 64 | 132.9438 | 326 | 14 | 19.6867 | 671 | 56 | 142.8076 | | AR()-EGARCH(1,1) | 997 | 79 | 193.9234 | 326 | 11 | 11.4628 | 671 | 64 | 179.1857* |
| | Panel B: SPO notes |
| | AR()-ARCH(5) | 997 | 1 | 13.42211 | 326 | 2 | 0.5706 | 671 | 5 | 0.4828 | | AR()-GARCH(1,1) | 997 | 1 | 13.42211 | 326 | 0 | 6.5528 | 671 | 1 | 7.6617 | | AR()-GARCH(2,5) | 997 | 5 | 3.0636 | 326 | 0 | 6.5528 | 671 | 7 | 0.0125 | | AR()-EGARCH(1,1) | 997 | 2 | 9.5784 | 326 | 0 | 6.5528 | 671 | 2 | 4.6115* |
| | Panel C: DJQ notes |
| | AR()-ARCH(5) | 997 | 27 | 20.0334 | 326 | 13 | 16.7807 | 671 | 20 | 17.3730 | | AR()-GARCH(2,1) | 997 | 10 | 0.0001 | 326 | 13 | 16.7807 | 671 | 11 | 2.3223 | | AR()-GARCH(2,5) | 997 | 12 | 0.3920 | 326 | 17 | 29.2640 | 671 | 13 | 4.6749 | | AR()-EGARCH(2,1) | 997 | 12 | 0.3920 | 326 | 14 | 19.6867 | 671 | 8 | 0.2360 | | AR()-EGARCH(2,2) | 997 | 9 | 0.0985 | 326 | 11 | 11.4628 | 671 | 8 | 0.2360 |
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Note that the symbol denotes a 5% critical value of 3.84. LR demonstrates an unconditional coverage.
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