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

Wang, Jianzhou; Wang, Shuai; Lv, Mengzheng; Jiang, He

doi:10.1186/s40854-023-00564-5

Financial Innovation

Table 7 Out-of-sample VaR forecast evaluation of DAX

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

	HR	LR_UC	LR_IND	LR_CC	DQ	M-Loss
FTSE100 (\(\tau = 0.01\))
Hist	0.0143	0.6879 (0.4069)	0.1739 (0.6767)	0.8618 (0.6499)	17.2559 (0.0084)	0.6477
Normal	0.0166	1.5705 (0.2101)	0.2373 (0.6261)	1.8078 (0.4050)	15.7729 (0.0150)	0.8753
CAViaR-SAV	0.0166	1.5705 (0.2101)	0.2373 (0.6261)	1.8078 (0.4050)	14.5064 (0.0245)	0.4353
CAViaR-AS	0.0119	0.1451 (0.7033)	0.1205 (0.7285)	0.2656 (0.8757)	20.5229 (0.0022)	0.3184
CAViaR-IGARCH	0.0119	0.1451 (0.7033)	0.1205 (0.7285)	0.2656 (0.8757)	19.5541 (0.0033)	0.3134
CAViaR-Adaptive	0.0190	2.7446 (0.0976)	0.3107 (0.5773)	3.0553 (0.2171)	19.3534 (0.0036)	0.2989
QRNN	0.0071	0.3846 (0.5351)	0.0432 (0.8354)	0.4278 (0.8074)	1.2566 (0.9740)	0.1013
LASSO-QR	0.0143	0.6879 (0.4069)	0.1739 (0.6767)	0.8618 (0.6499)	26.1722 (0.0002)	0.7968
QR-RF	0.0214	4.1974 (0.0404)	0.3951 (0.5296)	4.5925 (0.1006)	24.2296 (0.0005)	0.6218
QR-GBDT	0.0214	4.1742 (0.0411)	0.3942 (0.5301)	4.5683 (0.1019)	20.0751 (0.0027)	0.6056
QR-SVM	0.0142	0.6879 (0.4068)	0.1739 (0.6766)	0.8618 (0.6499)	16.4757 (0.0114)	0.5806
QR-CNN	0.0166	1.5704 (0.2101)	0.2372 (0.6261)	1.8077 (0.4049)	14.8120 (0.0217)	0.4762
QR-LSTM	0.0142	0.6879 (0.4068)	0.1739 (0.6766)	0.8618 (0.6499)	16.3423 (0.0120)	0.4536
QR-GRU	0.0190	2.7445 (0.0975)	0.3106 (0.5772)	3.0552 (0.2170)	14.2153 (0.0273)	0.5161
Proposed model	0.0071	0.3846 (0.5351)	0.0432 (0.8354)	0.4278 (0.8074)	1.7891 (0.9380)	0.1812
FTSE100 (\(\tau = 0.05\))
Hist	0.0546	0.1947 (0.6590)	0.0639 (0.8004)	0.2587 (0.8787)	3.3210 (0.7676)	1.2893
Normal	0.0546	0.1947 (0.6590)	0.0639 (0.8004)	0.2587 (0.8787)	4.2481 (0.6431)	1.2728
CAViaR-SAV	0.0475	0.0509 (0.8215)	0.0026 (0.9594)	0.0535 (0.9736)	3.4985 (0.7442)	1.0248
CAViaR-AS	0.0499	0.0000 (1.0000)	0.0027 (0.9587)	0.0027 (0.9987)	0.5658 (0.9969)	0.9339
CAViaR-IGARCH	0.0546	0.1947 (0.6590)	0.4212 (0.5164)	0.6159 (0.7349)	4.4775 (0.6124)	0.9515
CAViaR-Adaptive	0.0475	0.0509 (0.8215)	0.0026 (0.9594)	0.0535 (0.9736)	8.2815 (0.2182)	1.2434
QRNN	0.0736	4.3996 (0.0360)	1.0393 (0.3080)	5.4388 (0.0659)	17.8002 (0.0068)	0.7259
LASSO-QR	0.0285	4.7707 (0.0290)	0.7060 (0.4008)	5.4767 (0.0647)	6.3422 (0.3860)	1.0813
QR-RF	0.0593	0.7579 (0.3839)	0.2019 (0.6531)	0.9598 (0.6188)	3.9701 (0.6807)	0.9914
QR-GBDT	0.0475	0.0509 (0.8215)	2.0008 (0.1572)	2.0517 (0.3585)	3.1034 (0.7958)	0.8558
QR-SVM	0.0427	0.4730 (0.4915)	0.0681 (0.7941)	0.5411 (0.7629)	1.1158 (0.9808)	1.1616
QR-CNN	0.0570	0.4321 (0.5109)	0.2883 (0.5912)	0.7204 (0.6975)	3.2423 (0.7778)	0.8453
QR-LSTM	0.0783	6.1955 (0.0128)	0.0010 (0.9744)	6.1966 (0.0451)	12.6532 (0.0488)	1.1551
QR-GRU	0.0285	4.7707 (0.0289)	0.7059 (0.4007)	5.4767 (0.0646)	5.9811 (0.4253)	0.7904
Proposed model	0.0333	2.7691 (0.0961)	0.9657 (0.3258)	3.7348 (0.1545)	4.9745 (0.5471)	0.3911

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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