A Research Based On POT-CAViaR Model of Extreme Risk Measure
Publié en ligne: 20 août 2020
Pages: 461 - 472
Reçu: 25 nov. 2019
Accepté: 01 févr. 2020
© 2020 Baoshuai Zhang et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.
Fig. 1
Sequence diagram of the rate of return of the sampleFig. 2
QQ diagram of sample sequenceFig. 3
POT model diagnosis diagram of HS300 extreme residual sequenceExtreme quantile 1% VaR posteriori test results
| | Out-Sample(n = 500) |
---|
|
---|
| | POT-SAV | POT-AS | POT-IGARCH | GARCH-POT | POT |
---|
HS300 | Failure N | 9 | 8 | 7 | 9 | 10 |
LR Statistics | 2.61 | 1.54 | 0.72 | 2.61 | 3.91 |
P | 0.106 | 0.2149 | 0.3966 | 0.106 | 0.0479 |
HSI | Failure N | 7 | 8 | 4 | 8 | 9 |
LR Statistics | 0.72 | 1.54 | 0.22 | 1.54 | 2.61 |
P | 0.3966 | 0.2149 | 0.6414 | 0.2149 | 0.106 |
N225 | Failure N | 6 | 7 | 3 | 8 | 9 |
LR Statistics | 0.19 | 0.72 | 0.94 | 1.54 | 2.61 |
P | 0.6630 | 0.3966 | 0.3314 | 0.2149 | 0.106 |
Quantile parameter estimation results of CAViaR class model
| | | β1 | β2 | β3 | β4 |
---|
SAV | HS300 | 1% | 0.0729**(0.0338) | 0.9440*(0.0381) | 0.2393*(0.0905) | - |
5% | 0.0155*£0.0033¤ | 0.9774*£0.0087¤ | 0.0614*£0.0155¤ | - |
HSI | 1% | 0.1393**(0.0667) | 0.8291*(0.0629) | 0.3124**£0.1374¤ | - |
5% | 0.0659*£0.0659¤ | 0.9124*£0.0251¤ | 0.1840*£0.0218¤ | - |
N225 | 1% | 0.1833*(0.0215) | 0.8612*(0.0128) | 0.2871*£0.0159¤ | - |
5% | 0.0722*£0.0072¤ | 0.9103*£0.0115¤ | 0.1899*£0.0222¤ | - |
AS | HS300 | 1% | 0.0115***£0.0585¤ | 0.9464*£0.0791¤ | 0.209£0.2476¤ | 0.1537***£0.1513¤ |
5% | 0.0011***£0.0029¤ | 0.9782*£0.0083¤ | 0.0472***£0.0172¤ | 0.0514*£0.0195¤ |
HSI | 1% | 0.0916***£0.0582¤ | 0.8513*£0.0665¤ | 0.1649£0.1547¤ | 0.4753*£0.1078¤ |
5% | 0.0271*£0.0104¤ | 0.9067*£0.0252¤ | 0.0550***£0.0323¤ | 0.2449*£0.0722¤ |
N225 | 1% | 0.1109**£0.0385¤ | 0.8012*£0.0922¤ | 0.2555£0.2640¤ | 0.6211***£0.3828¤ |
5% | 0.0314*£0.0070¤ | 0.8939*£0.0152¤ | 0.0466***£0.0314¤ | 0.2814*£0.0391¤ |
IGARCH | HS300 | 1% | 0.0026***£0.0294¤ | 0.9309*£0.0150¤ | 0.5488£1.7734¤ | - |
5% | 0.0033***£0.0030¤ | 0.9811*£0.0031¤ | 0.0583£0.6437¤ | - |
HSI | 1% | 0.1635***£0.1237¤ | 0.7802*£0.0653¤ | 1.1863£0.4317¤ | - |
5% | 0.0128***£0.0089¤ | 0.9207*£0.0141¤ | 0.1795**£0.9726¤ | - |
N225 | 1% | 0.2110*£0.0616¤ | 0.7647*£0.0133¤ | 1.0777£0.9034¤ | - |
5% | 0.0196**£0.0094¤ | 0.9120*£0.0052¤ | 0.1970***£0.3962¤ | - |
The result of the posterior test based on the CAViaR class model
Out-Sample (n = 500) |
---|
|
---|
| | SAV | AS | IGARCH |
---|
|
---|
| 1% | 5% | 1% | 5% | 1% | 5% |
---|
HS300 | Failure N | 15 | 29 | 19 | 31 | 14 | 30 |
LR Statistics | 13.16 | 0.64 | 23.13 | 1.41 | 10.99 | 0.3192 |
P | 0.0001 | 0.4229 | 0.0000 | 0.2346 | 0.0009 | 0.4229 |
HSI | Failure N | 16 | 26 | 17 | 28 | 15 | 26 |
LR Statistics | 15.48 | 0.0416 | 17.90 | 0.37 | 13.16 | 0.0416 |
P | 0.0000 | 0.8384 | 0.0002 | 0.5455 | 0.0003 | 0.8384 |
N225 | Failure N | 16 | 26 | 18 | 28 | 13 | 27 |
LR Statistics | 15.48 | 0.0416 | 20.46 | 0.37 | 8.97 | 0.16 |
P | 0.0000 | 0.8384 | 0.0000 | 0.5455 | 0.0027 | 0.6852 |
Descriptive statistics of samples
Sample | Mean | Max | Min | SD | Skewness | Kurtosis | J-B |
---|
HS300 | 0.0200 | 3.8786 | −4.4987 | 0.8460 | −0.4424 | 6.4561 | 1419* |
HSI | 0.0093 | 5.8225 | −8.3011 | 0.7212 | −0.3047 | 18.5013 | 26833* |
N225 | 0.0081 | 5.7478 | −11.1353 | 0.7359 | −1.6032 | 27.9836 | 70742* |
POT estimation of the extreme standard residual sequence
| | SAV | AS | IGARCH |
---|
HS300 | μ | 0.916 | 0.851 | 0.926 |
ξ | 0.342 | 0.222 | 0.276 |
σ | 0.333 | 0.450 | 0.441 |
HSI | μ | 0.731 | 0.704 | 0.671 |
ξ | 0.180 | 0.231 | 0.172 |
σ | 0.473 | 0.451 | 0.341 |
N225 | μ | 0.767 | 0.712 | 0.681 |
ξ | 0.172 | 0.213 | 0.351 |
σ | 0.365 | 0.461 | 0.672 |