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Financial Innovation

Table 5 Out-of-sample VaR forecast evaluation of N225

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

0.0143

0.6879 (0.4069)

0.1739 (0.6767)

0.8618 (0.6499)

17.7829 (0.0068)

0.2771

 Normal

0.0190

2.7446 (0.0976)

0.3107 (0.5773)

3.0553 (0.2171)

28.1403 (0.0001)

0.4588

 CAViaR-SAV

0.0143

0.6879 (0.4069)

0.1739 (0.6767)

0.8618 (0.6499)

17.2207 (0.0085)

0.2356

 CAViaR-AS

0.0166

1.5705 (0.2101)

0.2373 (0.6262)

1.8078 (0.4050)

24.1412 (0.0005)

0.0776

 CAViaR-IGARCH

0.0166

1.5705 (0.2101)

0.2373 (0.6262)

1.8078 (0.4050)

27.8503 (0.0001)

0.2287

 CAViaR-Adaptive

0.0166

1.5705 (0.2101)

0.2373 (0.6262)

1.8078 (0.4050)

29.3186 (0.0001)

0.3251

 QRNN

0.0238

5.8313 (0.0157)

0.4879 (0.4849)

6.3192 (0.0424)

22.9050 (0.0008)

0.2766

 LASSO-QR

0.0309

11.9641 (0.0005)

0.6840 (0.4082)

12.6481 (0.0018)

65.5847 (0.0000)

0.5607

 QR-RF

0.0214

4.1974 (0.0404)

0.4252 (0.5143)

4.6227 (0.0991)

20.5688 (0.0021)

0.0059

 QR-GBDT

0.0190

2.7629 (0.0964)

0.3666 (0.5448)

3.1295 (0.2091)

21.2311 (0.0016)

0.0140

 QR-SVM

0.0190

2.7629 (0.0964)

0.3114 (0.5767)

3.0744 (0.2149)

24.1986 (0.0004)

0.3314

 QR-CNN

0.0095

0.0097 (0.9212)

0.0769 (0.7815)

0.0866 (0.9575)

26.6151 (0.0001)

0.1799

 QR-LSTM

0.0166

1.5704 (0.2101)

0.2372 (0.6261)

1.8077 (0.4049)

24.4211 (0.0004)

0.1601

 QR-GRU

0.0095

0.0097 (0.9212)

0.0769 (0.7815)

0.0866 (0.9575)

26.6151 (0.0002)

0.1164

 Proposed Model

0.0071

0.3846 (0.5351)

0.0432 (0.8354)

0.4278 (0.8074)

7.6041 (0.2686)

0.0539

FTSE100 (\(\tau = 0.05\))

 Hist

0.0475

0.0509 (0.8215)

0.0026 (0.9594)

0.0535 (0.9736)

9.2246 (0.1613)

0.7780

 Normal

0.0499

0.0000 (1.0000)

0.0027 (0.9587)

0.0027 (0.9987)

14.8019 (0.0219)

0.8230

 CAViaR-SAV

0.0475

0.0509 (0.8215)

2.0008 (0.1572)

2.0517 (0.3585)

6.3994 (0.3800)

0.7570

 CAViaR-AS

0.0570

0.4321 (0.5110)

2.9109 (0.0880)

3.3430 (0.1880)

6.6924 (0.3502)

0.5730

 CAViaR-IGARCH

0.0428

0.4731 (0.4916)

1.6125 (0.2041)

2.0856 (0.3525)

9.5196 (0.1464)

0.7122

 CAViaR-Adaptive

0.0475

0.0509 (0.8215)

2.0008 (0.1572)

2.0517 (0.3585)

12.3425 (0.0548)

0.9100

 QRNN

0.0784

6.1956 (0.0128)

1.4514 (0.2283)

7.6470 (0.0219)

11.1709 (0.0832)

1.2096

 LASSO-QR

0.0475

0.0509 (0.8215)

0.0026 (0.9594)

0.0535 (0.9736)

9.5989 (0.1426)

0.7427

 QR-RF

0.0500

0.0001 (0.9910)

2.0569 (0.1515)

2.0570 (0.3575)

6.1982 (0.4013)

0.1075

 QR-GBDT

0.0571

0.4473 (0.5035)

2.7198 (0.0991)

3.1672 (0.2052)

4.7453 (0.5768)

0.3773

 QR-SVM

0.0523

0.0545 (0.8153)

-0.0482 (1.0000)

0.0062 (0.9968)

11.0896 (0.0856)

0.7758

 QR-CNN

0.0522

0.0493 (0.8241)

2.4334 (0.1187)

2.4827 (0.2889)

7.3555 (0.2892)

0.6974

 QR-LSTM

0.0617

1.1687 (0.2796)

3.4339 (0.0638)

4.6027 (0.1001)

6.8096 (0.3388)

0.7412

 QR-GRU

0.0427

0.4730 (0.4915)

1.6124 (0.2041)

2.0855 (0.3524)

10.9791 (0.0890)

0.5282

 Proposed model

0.0333

2.7691 (0.0961)

0.9657 (0.3258)

3.7348 (0.1545)

9.6196 (0.1416)

0.2862

  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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