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Financial Innovation

Table 6 Out-of-sample VaR forecast evaluation of SPX500

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

0.0214

4.1742 (0.0411)

6.5479 (0.0105)

10.7221 (0.0047)

57.3800 (0.0001)

0.3337

 Normal

0.0285

9.7430 (0.0018)

4.2422 (0.0394)

13.9852 (0.0009)

110.5046 (0.0000)

0.6047

 CAViaR-SAV

0.0166

1.5705 (0.2101)

0.2373 (0.6262)

1.8078 (0.4050)

14.0880 (0.0287)

0.1270

 CAViaR-AS

0.0166

1.5705 (0.2101)

0.2373 (0.6262)

1.8078 (0.4050)

3.6195 (0.7280)

0.1107

 CAViaR-IGARCH

0.0143

0.6879 (0.4069)

0.1739 (0.6767)

0.8618 (0.6499)

1.9139 (0.9274)

0.1211

 CAViaR-Adaptive

0.0166

1.5705 (0.2101)

2.7692 (0.0961)

4.3397 (0.1142)

34.3068 (0.0000)

0.1808

 QRNN

0.0190

2.7446 (0.0976)

0.3107 (0.5773)

3.0553 (0.2171)

18.8983 (0.0043)

0.1487

 LASSO-QR

0.0238

5.8313 (0.0157)

1.4700 (0.2254)

7.3013 (0.0260)

39.3872 (0.0000)

0.6639

 QR-RF

0.0167

1.5840 (0.2081)

0.2378 (0.6257)

1.8218 (0.4021)

3.3463 (0.7642)

0.0055

 QR-GBDT

0.0285

9.7809 (0.0017)

0.8998 (0.3428)

10.6808 (0.0047)

31.8562 (0.0000)

0.0106

 QR-SVM

0.0095

0.0088 (0.9251)

5.1193 (0.0236)

5.1282 (0.0769)

57.6851 (0.0000)

0.3503

 QR-CNN

0.0095

1.5704 (0.2101)

0.2372 (0.6261)

1.8077 (0.4049)

2.9629 (0.8134)

0.1223

 QR-LSTM

0.0166

1.5704 (0.2101)

2.7692 (0.0960)

4.3396 (0.1141)

35.2707 (0.0000)

0.2261

 QR-GRU

0.0095

0.0097 (0.9212)

0.0769 (0.7815)

0.0866 (0.9575)

23.6436 (0.0006)

0.1555

 Proposed model

0.0166

1.5705 (0.2101)

0.2373 (0.6262)

1.8078 (0.4050)

13.8936 (0.0309)

0.2413

FTSE100 (\(\tau = 0.05\))

      

 Hist

0.0475

0.0509 (0.8215)

0.9928 (0.3191)

1.0437 (0.5934)

25.9359 (0.0002)

0.8358

 Normal

0.0499

0.0000 (1.0000)

0.7718 (0.3797)

0.7718 (0.6799)

23.7367 (0.0006)

0.9056

 CAViaR-SAV

0.0475

0.0509 (0.8215)

0.9928 (0.3191)

1.0437 (0.5934)

4.1866 (0.6515)

0.5249

 CAViaR-AS

0.0546

0.1947 (0.6590)

0.4212 (0.5164)

0.6159 (0.7349)

4.2419 (0.6440)

0.4051

 CAViaR-IGARCH

0.0499

0.0000 (1.0000)

0.7718 (0.3797)

0.7718 (0.6799)

11.5924 (0.0717)

0.4300

 CAViaR-Adaptive

0.0570

0.4321 (0.5110)

0.2883 (0.5913)

0.7205 (0.6975)

16.5270 (0.0112)

0.6931

 QRNN

0.0594

0.7579 (0.3840)

3.1667 (0.0752)

3.9246 (0.1405)

18.1966 (0.0058)

0.5948

 LASSO-QR

0.0451

0.2068 (0.6493)

1.2470 (0.2641)

1.4539 (0.4834)

21.3708 (0.0016)

0.8884

 QR-RF

0.0619

1.1941 (0.2744)

3.4427 (0.0635)

4.6368 (0.0984)

4.9043 (0.5561)

0.0732

 QR-GBDT

0.0642

1.6921 (0.1933)

0.4165 (0.5186)

2.1086 (0.3484)

6.9544 (0.3250)

0.0397

 QR-SVM

0.0452

0.1969 (0.6571)

1.2410 (0.2652)

1.4380 (0.4872)

20.8298 (0.0019)

0.7870

 QR-CNN

0.0403

0.8554 (0.3550)

1.8654 (0.1719)

2.7209 (0.2565)

14.6888 (0.0228)

0.5434

 QR-LSTM

0.0427

0.4730 (0.4915)

1.5369 (0.2150)

2.0100 (0.3660)

13.7159 (0.0329)

0.7124

 QR-GRU

0.0427

0.4730 (0.4915)

1.5369 (0.2150)

2.0100 (0.3660)

13.2865 (0.0387)

0.6553

 Proposed model

0.0475

0.0509 (0.8215)

3.2571 (0.0711)

3.3080 (0.1913)

11.7756 (0.0672)

0.4115

  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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