A comparative VaR analysis between low-frequency and high-frequency conditional EVT models during COVID-19 crisis

Figures & data

Table 1. Summary statistics of daily log-returns, $r_t.$

Statistics	DJIA	FTSE100	BVSP	MERVAL
Mean	0.0003	0.0001	0.0004	0.0014
Standard Deviation	0.0113	0.0103	0.1302	0.0262
Skewness	−1.055	−0.8968	−0.9807	−3.3124
Kurtosis	25.27	13.35	13.54	56.31
Min	−0.1384	−0.1151	−0.1599	−0.4769
Max	0.1076	0.0867	0.0165	0.0977
Jarque–Bera	56023	15919	15996	270840
	**	**	**	**

The * and ** represent the significant value of p at 5% and 1% level, respectively.

Table 2. Summary statistics of intraday returns, ${\mathrm{\text{log}}\hspace{0.17em}\mathit{\text{RV}}}_t.$

Statistics	DJIA	FTSE100	BVSP	MERVAL
Mean	−5.09	−4.446	−4.654	−3.913
Standard Deviation	6.95E-01	0.35228	0.31955	0.34047
Skewness	1.3135	1.1183	0.36919	0.72201
Kurtosis	6.5186	3.522	2.4186	2.3665
Min	−6.8668	−5.3509	−5.8959	−4.7731
Max	1.2606	−2.1967	−2.6653	−1.2614
Jarque–Bera	4330.2	1521.7	544.37	612.28
	**	**	**	**

The * and ** represent the significant value of p at 5% and 1% level, respectively.

Figure 1. Q-Q Plot of daily returns, $r_t\mathrm{ }$ and intraday returns, ${\mathrm{\text{log}}\hspace{0.17em}\mathit{\text{RV}}}_t.$

Table 3. The heteroskedasticity and serial correlation test during the non-crisis period.

Stock Index	Model	ARCH-LM	Q	Q^2
DJIA	GARCH	0.137 [0.891]	6.899 [ 0.735]	9.89 [0.45]
	EGARCH	0.090 [0.928]	6.271 [0.792]	6.99 [0.73]
	FIEGARCH	0.087 [0.951]	6.130 [0.799]	6.00 [0.75]
	RV- G	0.109 [0.913]	36.511 [0.00]**	0.13 [1.00]
	RV-EG	0.125 [0.901]	28.365 [0.00]**	0.103 [1.00]
	RV-FIE	0.132 [0.882]	29.213 [0.00]**	0.11 [1.00]
	HAR	0.036 [0.972]	8.595 [0.571]	23.4 [0.01]**
	HAR-G	1.277 [0.208]	7.671 [0.661]	17.98 [0.06]
	HAR-EG	0.085 [0.933]	8.362 [0.594]	10.793 [0.37]
	HAR-FIE	0.078 [0.987]	8.024 [0.678]	9.85 [0.47]
FTSE100	GARCH	0.868 [0.386]	8.049 [0.624]	6.037 [0.812]
	EGARCH	0.424 [0.671]	10.374 [0.408]	1.847 [0.997]
	FIEGARCH	0.575 [0.502]	9.582 [0.495]	3.257 [0.7521]
	RV-G	0.453 [0.651]	289.83 [0.00]**	21.47 [0.02]*
	RV-EG	0.298 [0.766]	283.31 [0.00]**	21.34 [0.02]*
	RV-FIE	0.127 [0.785]	2793.2 [0.00]**	21.21 [0.00]*
	HAR	1.166 [0.249]	17.676 [0.061]	2.901 [0.984]
	HAR-G	1.860 [0.069]	20.597 [0.024]*	7.965 [0.632]
	HAR-EG	0.286 [0.776]	25.947 [0.00]**	4.416 [0.927]
	HAR-FIE	0.252 [0.786]	24.154 [0.00]**	3.566 [0.982]
BVSP	GARCH	0.666 [0.506]	3.403 [0.970]	3.983 [0.948]
	EGARCH	0.671 [0.502]	4.274 [0.934]	4.273 [0.934]
	FIEGARCH	0.684 [0.522]	4.551 [0.956]	4.524 [0.954]
	RV- G	1.563 [0.146]	12.226 [0.270]	13.88 [0.179]
	RV-EG	1.562 [0.146]	12.199 [0.272]	13.885 [0.178]
	RV-FIE	1.552 [0.141]	12.058 [0.275]	13.888 [0.177]
	HAR	1.223 [0.299]	7.113 [0.715]	16.31 [0.091]
	HAR-G	1.298 [0.257]	7.150 [0.711]	17.45 [0.065]
	HAR-EG	1.183 [0.325]	6.965 [0.729]	15.154 [0.127]
	HAR-FIE	1.152 [0.381]	6.825 [0.735]	15.112 [0.129]
MERVAL	GARCH	0.996 [0.319]	10.887 [0.366]	6.022 [0.813]
	EGARCH	0.873 [0.383]	10.642 [0.386]	8.931 [0.539]
	FIEGARCH	0.789 [0.254]	10.588 [0.389]	8.526 [0.556]
	RV-G	1.018 [0.309]	212.5 [0.00]**	17.225 [0.070]
	RV-EG	0.876 [0.382]	202.4 [0.00]**	15.937 [0.101]
	RV-FIE	0.855 [0.389]	201.2 [0.00]**	15.248 [0.125]
	HAR	1.614 [0.112]	11.09 [0.35]	21.02 [0.021]*
	HAR-G	0.545 [0.589]	12.30 [0.27]	18.45 [0.048]*
	HAR-EG	1.067 [0.291]	12.44 [0.26]	3.9127 [0.951]
	HAR-FIE	1.099 [0.282]	12.687 [0.26]	3.8251 [0.988]

Table 4. The heteroskedasticity and serial correlation test during the crisis period.

Model	Stock Index	ARCH-LM	Q	Q^2	Stock Index	ARCH-LM	Q	Q^2
GARCH	DJIA	1.190 [0.235]	13.328 [0.206]	3.627 [0.963]	BVSP	0.615 [0.539]	14.580 [0.148]	6.107 [0.806]
EGARCH		0.233 [0.816]	12.853 [0.232]	3.869 [0.953]		0.844 [0.399]	12.164 [0.274]	7.796 [0.649]
FIEGARCH		0.263 [0.805]	12.921 [0.204]	3.799 [0.968]		0.754 [0.421]	11.258 [0.280]	6.847 [0.795]
RV- G		1.515 [0.131]	69.817 [0.00]**	41.6 [0.00]**		0.188 [0.851]	21.415 [0.018]*	19.36 [0.04]*
RV-EG		1.529 [0.127]	46.851 [0.00]**	30.4 [0.00]**		0.238 [0.812]	21.984 [0.015]*	17.77 [0.059]
RV-FIE		1.623 [0.118]	45.267 [0.00]**	29.3 [0.00]**		0.197 [0.857]	20.256 [0.014]*	17.22 [0.051]
HAR		0.773 [0.452]	28.387 [0.00]**	16.2 [0.093]		0.413 [0.685]	12.223 [0.270]	9.252 [0.508]
HAR-G		0.400 [0.701]	26.597 [0.00]**	16.84 [0.078]		0.072 [0.944]	26.177 [0.00]**	6.107 [0.806]
HAR-EG		0.093 [0.929]	30.008 [0.00]**	10.62 [0.388]		0.102 [0.921]	14.982 [0.133]	6.632 [0.760]
HAR-FIE		0.088 [0.935]	29.877 [0.00]**	9.985 [0.392]		0.098 [0.935]	12.257 [0.087]	6.524 [0.779]
GARCH	FTSE100	0.542 [0.588]	19.503 [0.03]*	29.7 [0.00]**	MERVAL	0.345 [0.730]	6.014 [0.814]	15.88 [0.103]
EGARCH		1.293 [0.197]	18.888 [0.042]*	12.64 [0.245]		0.322 [0.747]	5.397 [0.863]	13.81 [0.182]
FIEGARCH		1.358 [0.188]	17.584 [0.052]	11.78 [0.251]		0.304 [0.758]	5.186 [0.875]	13.01 [0.199]
RV- G		4.07 [0.00]**	62.88 [0.00]**	34.0 [0.00]**		4.07 [0.00]**	62.88 [0.000]**	34.0 [0.00]**
RV-EG		1.982 [0.05]*	52.972 [0.00]**	31.28 [0.0]**		1.98 [0.05]*	52.97 [0.00]**	31.3 [0.00]**
RV-FIE		1.855 [0.05]*	48.741 [0.00]**	30.6 [0.00]**		1.788 [0.051]	48.7 [0.00]**	30.6 [0.00]**
HAR		0.218 [0.830]	34.892 [0.00]**	26.5 [0.00]**		0.948 [0.359]	7.1032 [0.716]	8.923 [0.539]
HAR-G		1.278 [0.237]	36.751 [0.00]**	26.3 [0.00]**		1.019 [0.342]	6.925 [0.732]	8.232 [0.606]
HAR-EG		0.268 [0.795]	37.168 [0.00]**	9.420 [0.493]		0.228 [0.826]	9.782 [0.460]	4.214 [0.937]
HAR-FIE		0.324 [0.705]	36.547 [0.00]**	8.579 [0.521]		0.197 [0.855]	8.547 [0.528]	3.887 [0.948]

The * and ** represent the significant value of p at 5% and 1% level, respectively.

Table 5. The GPD parameter estimates during non-crisis period (2014–2019).

Risk Model	Index	ξ	ψ	VaR		ES		Index	ξ	ψ	VaR		ES
				0.95	0.99	0.95	0.99				0.95	0.99	0.95	0.99
GARCH	DJIA	0.232**	0.004**	0.012	0.019	0.017	0.026	BVSP	0.139**	0.210**	0.44	0.809	0.677	1.105
EGARCH		0.212*	0.004**	0.012	0.019	0.017	0.026		0.141*	0.209*	0.44	0.808	0.677	1.105
FIEGARCH		0.212*	0.004**	0.012	0.019	0.017	0.026		0.117**	0.219**	0.431	0.81	0.674	1.103
RV- G		0.846**	0.078**	0.467	0.689	0.886	2.325		0.139**	0.210**	0.44	0.809	0.677	1.105
RV-EG		0.902*	0.071**	0.465	0.676	1.061	3.221		0.141**	0.209**	0.44	0.808	0.677	1.105
RV-FIE		0.916*	0.070**	0.464	0.673	1.139	3.62		0.117*	0.219**	0.431	0.81	0.674	1.103
HAR		−0.665*	0.368**	0.347	0.41	0.385	0.423		−0.573*	0.270*	0.438	0.595	0.533	0.633
HAR-G		−0.70**	0.382**	0.371	0.429	0.407	0.441		−0.758*	0.346*	0.475	0.622	0.565	0.648
HAR-EG		−0.94**	0.513**	0.379	0.416	0.402	0.421		−0.489*	0.254**	0.448	0.611	0.546	0.655
HAR-FIE		−0.66**	0.362**	0.31	0.372	0.348	0.386		−0.67**	0.307**	0.456	0.597	0.542	0.626
GARCH	FTSE	−0.230*	0.007**	0.014	0.024	0.02	0.028	MERVAL	−0.087*	0.013**	0.036	0.056	0.048	0.066
EGARCH		−0.276*	0.008**	0.014	0.024	0.02	0.029		−0.077*	0.013**	0.037	0.056	0.049	0.067
FIEGARCH		−0.250*	0.007**	0.014	0.024	0.02	0.028		−0.057*	0.012**	0.037	0.056	0.048	0.066
RV- G		0.197**	0.166**	0.53	0.831	0.728	1.103		−0.096*	0.261*	0.594	0.988	0.835	1.194
RV-EG		0.218*	0.159*	0.532	0.825	0.726	1.1		−0.136*	0.280*	0.588	1	0.839	1.202
RV-FIE		0.219**	0.159*	0.53	0.821	0.723	1.096		−0.121*	0.274*	0.582	0.99	0.831	1.195
HAR		−1.551*	0.086*	0.441	0.483	0.469	0.485		−0.785*	0.432*	0.693	0.866	0.799	0.896
HAR-G		0.095*	0.019*	0.485	0.527	0.511	0.558		−0.600*	0.355**	0.736	0.92	0.848	0.963
HAR-EG		−2.279*	0.326**	0.495	0.539	0.526	0.539		−0.57**	0.351**	0.612	0.816	0.735	0.866
HAR-FIE		−1.217*	0.253**	0.398	0.45	0.431	0.454		−0.78**	0.431**	0.664	0.838	0.771	0.869

The * and ** represent the significant value of p at 5% and 1% level, respectively.

Table 6. The GPD parameter estimates during crisis period (2020–2022).

Risk Model	Index	ξ	ψ	VaR		ES		Index	ξ	ψ	VaR		ES
				0.95	0.99	0.95	0.99				0.95	0.99	0.95	0.99
GARCH	DJIA	0.394**	0.008**	0.023	0.051	0.044	0.09	BVSP	0.256*	0.010**	0.029	0.056	0.047	0.084
EGARCH		0.366*	0.008**	0.024	0.051	0.044	0.087		0.300**	0.009*	0.029	0.056	0.048	0.087
FIEGARCH		0.366*	0.008**	0.024	0.051	0.044	0.087		0.326**	0.009**	0.029	0.056	0.048	0.089
RV- G		−0.128**	0.556**	1.071	1.683	1.444	1.986		−0.072*	0.152*	0.447	0.659	0.578	0.775
RV-EG		−0.074*	0.528**	1.093	1.772	1.51	2.142		−0.071*	0.152**	0.447	0.66	0.578	0.777
RV-FIE		−0.094*	0.547**	1.093	1.772	1.51	2.142		−0.058*	0.147**	0.439	0.651	0.57	0.77
HAR		−0.492*	0.992**	0.921	1.178	1.076	1.248		−1.072*	0.249**	0.31	0.34	0.329	0.344
HAR-G		−0.667*	1.312**	0.951	1.131	1.06	1.168		−2.231*	0.358**	0.317	0.327	0.324	0.327
HAR-EG		−0.74**	1.301**	0.95	1.088	1.035	1.114		−2.126*	0.344**	0.291	0.302	0.299	0.302
HAR-FIE		−0.43**	0.916**	0.996	1.286	1.171	1.373		−2.696*	0.479**	0.335	0.342	0.34	0.342
GARCH	FTSE	0.240**	0.007*	0.024	0.042	0.036	0.059	MERVAL	−0.081*	0.021*	0.047	0.076	0.064	0.091
EGARCH		0.216**	0.007*	0.022	0.04	0.034	0.056		−0.140*	0.023**	0.048	0.077	0.065	0.09
FIEGARCH		0.168**	0.008*	0.022	0.04	0.034	0.055		−0.11**	0.022**	0.049	0.077	0.066	0.092
RV- G		−0.147*	0.576*	0.952	1.654	1.379	1.99		−0.152*	0.267*	0.575	0.888	0.765	1.036
RV-EG		−0.096*	0.515**	0.903	1.592	1.324	1.954		−0.145*	0.266**	0.571	0.886	0.762	1.038
RV-FIE		−0.092*	0.506**	0.899	1.582	1.317	1.943		−0.13**	0.260**	0.586	0.905	0.781	1.062
HAR		−0.037*	0.300**	0.645	1.082	0.914	1.336		−0.197*	0.226*	0.424	0.635	0.552	0.728
HAR-G		0.811**	0.109**	0.671	2.547	3.668	13.604		0.189*	0.141**	0.407	0.797	0.663	1.144
HAR-EG		−0.045*	0.305**	0.713	1.147	0.98	1.395		0.046**	0.169**	0.497	0.807	0.691	1.016
HAR-FIE		−0.039*	0.302**	0.713	1.15	0.983	1.404		−0.213*	0.232**	0.445	0.653	0.571	0.742

The * and ** represent the significant value of p at 5% and 1% level, respectively.

Table 7. The VaR violation ratios of the Conditional-EVT Model.

Stock Index	Low-frequency	Normal	Crisis	High-frequency	Normal	Crisis
DJIA	G-EVT	10.45	9.63	RV-G-EVT	9.88	11.11
	EG-EVT	10.86	11.03	RV-EG-EVT	9.79	9.55
	FIEGARCH	10.53		RV-FIEG-EVT	9.71	9.55
				HAR-EVT	1.51	1.05
				HAR-G-EVT	2.26	2.00
				HAR-EG-EVT	1.89	4.00
				HAR-FIEG-EVT	8.00	2.00
FTSE	G-EVT	10.95	10.56	RV-G-EVT	9.68	11.59
	EG-EVT	10.48	10.87	RV-EG-EVT	10.00	10.56
	FIEGARCH	10.48	11.67	RV-FIEG-EVT	10.00	10.00
				HAR-EVT	1.13	2.00
				HAR-G-EVT	0.97	4.00
				HAR-EG-EVT	1.61	6.00
				HAR-FIEG-EVT	9.43	2.00
BVSP	G-EVT	0.74	0.66	RV-G-EVT	12.43	9.22
	EG-EVT	10.54	10.37	RV-EG-EVT	10.70	10.78
	FIEGARCH	10.78	11.11	RV-FIEG-EVT	10.70	11.77
				HAR-EVT	1.13	0.69
				HAR-G-EVT	0.76	5.52
				HAR-EG-EVT	1.51	6.00
				HAR-FIEG-EVT	0.38	6.00
MERVAL	G-EVT	10.08	10.62	RV-G-EVT	9.60	11.61
	EG-EVT	10.08	9.88	RV-EG-EVT	9.68	11.28
	FIEGARCH	10.24	10.53	RV-FIEG-EVT	3.17	11.08
				HAR-EVT	0.38	2.00
				HAR-G-EVT	0.76	1.43
				HAR-EG-EVT	0.38	2.14
				HAR-FIEG-EVT	1.51	2.14

The bold figure represents the performance is acceptable and good.

Table 8. The UC and CC test statistics of the Conditional-EVT Model during normal period.

Index	Low-freq	LRUC		LRCC		High-freq	LRUC		LRCC
		Stat	p	Stat	p		Stat	p	Stat	p
DJIA	G-EVT	436.45	0	438.03	0	RV-G-EVT	394.76	0	394.77	0
	EG-EVT	467.21	0	468.71	0	RV-EG-EVT	388.94	0	388.94	0
	FIEG-EVT	442.53	0	450.23	0	RV-FIEG-EVT	383.15	0	383.19	0
						HAR-EVT	0.63	0.43	0.63	.73
						HAR-G-EVT	3.33	0.07	3.33	.19
						HAR-EG-EVT	1.76	0.19	1.76	.42
						HAR-FIE-EVT	79.36	0	79.39	0
FTSE	G-EVT	460.51	0	461.21	0	RV-G-EVT	395.2	0	395.2	0
	EG-EVT	454.41	0	454.42	0	RV-EG-EVT	418.5	0	422.58	0
	FIEG-EVT	448.35	0	450.57	0	RV-FIEG-EVT	400.98	0	402.02	0
						HAR-EVT	0.05	0.83	0.05	.98
						HAR-G-EVT	0	0.95	0	1
						HAR-EG-EVT	1.04	0.31	1.83	0.4
						HAR-FIE-EVT	2.011	0.156	2.017	.365
BVSP	G-EVT	442.53	0	442.55	0	RV-G-EVT	591.75	0	592.59	0
	EG-EVT	460.99	0	469.58	0	RV-EG-EVT	454.8	0	464.89	0
	FIEG-EVT	454.8	0	459.47	0	RV-FIEG-EVT	454.8	0	459.47	0
						HAR-EVT	0.05	0.83	0.05	.98
						HAR-G-EVT	0.18	0.67	0.18	.91
						HAR-EG-EVT	0.63	0.43	2.18	.34
						HAR-FIE-EVT	1.404	0.24	1.41	.494
MERV	G-EVT	424.41	0	468.68	0	RV-G-EVT	389.46	0	421.49	0
	EG-EVT	424.41	0	424.41	0	RV-EG-EVT	395.2	0	427.67	0
	FIEG-EVT	436.31	0	481.48	0	RV-FIEG-EVT	40.88	0	46.15	0
						HAR-EVT	1.4	0.24	1.41	0.49
						HAR-G-EVT	0.18	0.67	0.18	.91
						HAR-EG-EVT	1.4	0.24	1.41	.49
						HAR-FIE-EVT	1.404	0.24	1.41	.494

The bold figures mean the null hypothesis is accepted based on p-value above 5% and critical values less than 3.841 which implies that the corresponding VaR model has adequate forecasting ability.

Table 9. The UC and CC test statistics of the Conditional-EVT Model during crisis period.

Index	Low-freq	LRUC		LRCC		High-freq	LRUC		LRCC
		Stat	p	Stat	p		Stat	p	Stat	p
DJIA	G-EVT	377.39	0	379.82	0	RV-G-EVT	486.06	0	487.2	0
	EG-EVT	479.75	0	484.65	0	RV-EG-EVT	371.67	0	372.73	0
	FIEG-EVT	442.53	0	447.125	0	RV-FIEG-EVT	371.667	0	372.223	0
						HAR-EVT	0	0.96	0.02	.99
						HAR-G-EVT	0.41	0.52	0.46	.8
						HAR-EG-EVT	2.8	0.1	2.81	.25
						HAR-FIE-EVT	0.413	0.52	0.456	.796
FTSE	G-EVT	460.51	0	463.94	0	RV-G-EVT	542.66	0	544.34	0
	EG-EVT	485.21	0	485.48	0	RV-EG-EVT	460.51	0	460.85	0
	FIEG-EVT	549.2	0	551.479	0	RV-FIEG-EVT	418.504	0	419.791	0
						HAR-EVT	0.41	0.52	0.46	.8
						HAR-G-EVT	2.8	0.1	2.81	.25
						HAR-EG-EVT	6.48	0.01	6.5	.04
						HAR-FIE-EVT	0.413	0.52	0.456	.796
BVSP	G-EVT	430.39	0	432.31	0	RV-G-EVT	349.1	0	373.45	0
	EG-EVT	424.37	0	426.29	0	RV-EG-EVT	460.99	0	466.66	0
	FIEG-EVT	486.06	0	486.932	0	RV-FIEG-EVT	537.818	0	541.88	0
						HAR-EVT	0.16	0.69	0.18	.92
						HAR-G-EVT	15.92	0	18.55	0
						HAR-EG-EVT	6.48	0.01	6.48	.04
						HAR-FIE-EVT	29.26	0	29.26	0
MERV	G-EVT	448.65	0	448.79	0	RV-G-EVT	524.68	0	524.73	0
	EG-EVT	394.76	0	398.2	0	RV-EG-EVT	498.8	0	503.46	0
	FIEG-EVT	442.53	0	448.275	0	RV-FIEG-EVT	459.951	0	460.297	0
						HAR-EVT	0.04	0.84	0.46	.8
						HAR-G-EVT	0.24	0.62	0.24	.89
						HAR-EG-EVT	1.47	0.23	1.47	.48
						HAR-FIE-EVT	1.471	0.225	1.471	.479

The bold figure means the null hypothesis is accepted based on p-value above 5% and critical values of 3.841 which implies that the corresponding VaR model has adequate forecasting ability.

Table 10. The RLF and FLF values.

Stock Index	Models	Non-crisis		Crisis
		RLF	FLF	RLF	FLF
DJIA	HAR-EVT	0.0706	0.1740	0.1900	0.3460
	HAR-G-EVT	0.0002	0.2550	0.1630	0.3340
	HAR-EG-EVT	0.0087	0.2300	0.1530	0.3130
	HAR-FIEG-EVT	0.0797	0.1920	0.0796	0.0782
FTSE	HAR-EVT	0.0906	0.1750	0.0334	0.0320
	HAR-G-EVT	0.0901	0.1780	0.0314	0.0300
	HAR-EG-EVT	0.0962	0.1830	0.0285	0.0270
	HAR-FIEG-EVT	0.1140	0.2020	0.6010	0.5990
BVSP	HAR-EVT	0.0011	0.0000	0.2970	0.3470
	HAR-G-EVT	0.0011	0.2350	0.1560	0.2240
	HAR-EG-EVT	0.0000	0.0000	0.0557	0.0549
	HAR-FIEG-EVT	0.0016	0.2270	0.1460	0.2070
MERVAL	HAR-EVT	0.0503	0.1530	0.0431	0.1050
	HAR-G-EVT	0.0543	0.1510	0.0391	0.1000
	HAR-EG-EVT	0.0006	0.0046	0.0400	0.1020
	HAR-FIEG-EVT	0.0596	0.1760	0.0823	0.1640

Table 11. The backtesting procedure of expected shortfall.

Stock Index	Risk Model	Non-crisis			Crisis
		GB	z	p	GB	z	p
DJIA	G-EVT	43.37	95.47	0	8.31	0.47	.64
	EG-EVT	43.37	95.47	0	8.31	0.48	.63
	FIEG-EVT	43.37	95.47	0	8.31	0.47	.64
	RV-G-EVT	2	−231.14	0	0	−64.55	0
	RV-EG-EVT	2	−231.14	0	0	−64.55	0
	RV-FIEG-EVT	2	−231.14	0	0	−64.55	0
	HAR-EVT	1.84	0.29	.77	0	−5.53	0
	HAR-G-EVT	1.84	0.29	.77	0	−5.53	0
	HAR-E-EVT	1.84	0.29	.77	0	−5.53	0
	HAR-F-EVT	1.95	1.21	.23	0	−5.53	0
FTSE	G-EVT	27	−36.53	0	7.71	−5.22	0
	EG-EVT	23.08	−67.47	0	11.28	22.95	0
	FIEG-EVT	23.88	−61.19	0	10.74	18.65	0
	RV-G-EVT	4.62	−211.83	0	0	−65.73	0
	RV-EG-EVT	4.62	−211.84	0	0	−65.73	0
	RV-FIEG-EVT	4.62	−211.86	0	0	−65.73	0
	HAR-EVT	1.83	0.45	.63	0	−5.72	0
	HAR-G-EVT	1.84	0.46	.64	0	−5.72	0
	HAR-E-EVT	1.83	0.46	.64	0	−5.72	0
	HAR-F-EVT	1.83	0.46	.64	0	−5.72	0
BVSP	G-EVT	6.8	−188.27	0	9.58	11.07	0
	EG-EVT	6.81	−188.26	0	9.17	7.87	0
	FIEG-EVT	7.73	−180.95	0	9.17	7.84	0
	RV-G-EVT	1.99	−226.31	0	0.99	−56.33	0
	RV-EG-EVT	1.99	−226.31	0	0.99	−56.33	0
	RV-FIE-EVT	1.99	−226.31	0	0.99	−56.33	0
	HAR-EVT	0.99	−6.18	0	0	−5.72	0
	HAR-G-EVT	0.99	−6.17	0	0	−5.72	0
	HAR-E-EVT	1	−6.15	0	−0.81	−12.09	0
	HAR-F-EVT	0.99	−6.16	0	0	−5.72	0

The significance level used in this analysis is 5% significance level. The bold figures show that the ES models are accurate.

Table 12. The best performance models based on the VaR forecast.

Total		Non-crisis	Crisis
	HAR-EVT	2	0
	HAR-G-EVT	2	2
	HAR-EG-EVT	4	4
	HAR-FIEG-EVT	0	1

The bold figure represents the best performing model.