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Financial Innovation

Table 4 Out-of-sample VaR forecast evaluation of FTSE100

From: Forecasting VaR and ES by using deep quantile regression, GANs-based scenario generation, and heterogeneous market hypothesis

 

HR

LRUC

LRIND

LRCC

DQ

M-Loss

FTSE100 (\(\tau = 0.01\))

 Hist

0.0119

0.1451 (0.7033)

0.1205 (0.7285)

0.2656 (0.8757)

21.6577 (0.0014)

0.5430

 Normal

0.0238

5.8313 (0.0157)

0.4879 (0.4849)

6.3192 (0.0424)

16.8946 (0.0097)

0.6574

 CAViaR-SAV

0.0143

0.6879 (0.4069)

0.1739 (0.6767)

0.8618 (0.6499)

17.3118 (0.0082)

0.4599

 CAViaR-AS

0.0119

0.1451 (0.7033)

0.1205 (0.7285)

0.2656 (0.8757)

21.4963 (0.0015)

0.3109

 CAViaR-IGARCH

0.0119

0.1451 (0.7033)

0.1205 (0.7285)

0.2656 (0.8757)

20.5383 (0.0022)

0.4081

 CAViaR-Adaptive

0.0119

0.1451 (0.7033)

0.1205 (0.7285)

0.2656 (0.8757)

21.9149 (0.0013)

0.3567

 QRNN

0.0190

2.7446 (0.0976)

0.3107 (0.5773)

3.0553 (0.2171)

12.5440 (0.0509)

0.2695

 LASSO-QR

0.0285

9.7430 (0.0018)

0.9032 (0.3419)

10.6462 (0.0049)

63.6024 (0.0000)

0.6429

 QR-RF

0.0190

2.7629 (0.0964)

0.3114 (0.5767)

3.0744 (0.2149)

7.0202 (0.3189)

0.1465

 QR-GBDT

0.0237

5.8313 (0.0157)

0.4878 (0.4848)

6.3191 (0.0424)

20.1541 (0.0026)

0.2352

 QR-SVM

0.0047

1.4438 (0.2295)

0.0191 (0.8899)

1.4630 (0.4811)

67.9498 (0.0000)

0.3003

 QR-CNN

0.0142

0.6879 (0.4068)

0.1739 (0.6766)

0.8618 (0.6499)

16.2832 (0.0123)

0.4346

 QR-LSTM

0.0095

0.0097 (0.9212)

0.0769 (0.7815)

0.0866 (0.9575)

25.6281 (0.0002)

0.3166

 QR-GRU

0.0095

0.0097 (0.9212)

0.0769 (0.7815)

0.0866 (0.9575)

25.6967 (0.0002)

0.2739

 Proposed model

0.0095

0.0098 (0.9212)

0.0769 (0.7815)

0.0867 (0.9576)

1.5349 (0.9571)

0.0752

FTSE100 (\(\tau = 0.05\))

 Hist

0.0190

10.9777 (0.0009)

0.3107 (0.5773)

11.2884 (0.0035)

12.2992 (0.0556)

0.6499

 Normal

0.0238

7.4618 (0.0063)

0.4879 (0.4849)

7.9496 (0.0188)

9.3648 (0.1541)

0.6789

 CAViaR-SAV

0.0689

2.8823 (0.0896)

0.5078 (0.4761)

3.3901 (0.1836)

19.4318 (0.0035)

0.8580

 CAViaR-AS

0.0523

0.0494 (0.8241)

0.0234 (0.8785)

0.0728 (0.9643)

5.6001 (0.4694)

0.7585

 CAViaR-IGARCH

0.0618

1.1688 (0.2797)

0.1009 (0.7508)

1.2696 (0.5300)

11.9362 (0.0634)

0.7417

 CAViaR-Adaptive

0.0523

0.0494 (0.8241)

-0.0486 (1.0000)

0.0008 (0.9996)

11.6363 (0.0706)

0.7584

 QRNN

0.0808

7.1932 (0.0073)

0.0788 (0.7790)

7.2720 (0.0264)

20.2884 (0.0025)

0.6577

 LASSO-QR

0.0404

0.8555 (0.3550)

0.1361 (0.7122)

0.9916 (0.6091)

21.8211 (0.0013)

0.8343

 QR-RF

0.0667

2.2692 (0.1319)

0.0099 (0.9203)

2.2792 (0.3199)

7.9304 (0.2432)

0.4509

 QR-GBDT

0.0689

2.8823 (0.0896)

0.0000 (0.9986)

2.8823 (0.2367)

13.4368 (0.0366)

0.5641

 QR-SVM

0.0190

10.9777 (0.0009)

0.3106 (0.5772)

11.2884 (0.0035)

10.9918 (0.0886)

0.6224

 QR-CNN

0.0617

1.1687 (0.2796)

0.2983 (0.5848)

1.4671 (0.4801)

13.6996 (0.0331)

0.5077

 QR-LSTM

0.0237

7.4617 (0.0063)

0.4962 (0.4811)

7.9580 (0.0187)

9.0742 (0.1694)

0.5667

 QR-GRU

0.0380

1.3605 (0.2434)

1.2676 (0.2602)

2.6281 (0.2687)

10.1684 (0.1177)

0.6394

 Proposed model

0.0475

0.0509 (0.8215)

-0.0335 (1.0000)

0.0174 (0.9914)

9.8586 (0.1307)

0.2592

  1. In brackets are the p values corresponding to the statistics. HR = N1/(N1 + N0), N1 and N0 are respectively the numbers of times that the VaR estimate is and is not exceeded. Bold values mean that the null hypothesis is not rejected
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