Table 3.

VaR and ES forecasts at the 99% level of confidence for individual returns following AR(1)-GJR-GARCH(1,1) models with a normal or Student’s $t$ innovation.

		Estimative VaR		Improved VaR		Estimative ES		Improved ES
		VaR	CCP	VaR	CCP	ES	$Z_{\mathrm{MF}}$ ($p$-value)	ES	$Z_{\mathrm{MF}}$ ($p$-value)
Before COVID-19
OIL	$N$	3.504	99.492%	3.224	99.163%	4.019	−0.074 (0.628)	3.767	−0.509 (0.979)
	$t$	3.820	99.495%	3.344	99.183%	4.894	−0.054 (0.490)	4.365	0.293 (0.220)
BTC	$N$	8.573	99.451%	7.957	99.134%	9.807	−0.197 (0.858)	9.253	−0.045 (0.488)
	$t$	8.202	99.372%	7.120	99.102%	12.322	1.078 (0.119)	10.797	0.870 (0.169)
USDT	$N$	1.012	99.784%	0.886	99.508%	1.156	0.000 (0.358)	1.044	−0.301 (0.829)
	$t$	1.076	99.649%	0.867	99.377%	1.488	0.000 (0.267)	1.223	−0.660 (0.719)
USD	$N$	0.591	99.329%	0.559	99.065%	0.678	−0.164 (0.824)	0.650	−0.259 (0.866)
	$t$	0.597	99.312%	0.565	99.061%	0.691	0.000 (0.314)	0.661	−0.155 (0.665)
During COVID-19
OIL	$N$	9.985	96.697%	13.712	99.599%	11.447	0.000 (0.378)	14.877	0.000 (0.055)
	$t$	10.634	98.170%	13.456	99.244%	14.982	0.005 (0.312)	18.620	0.634 (0.098)
BTC	$N$	9.813	99.494%	9.012	99.156%	11.278	−0.047 (0.598)	10.558	−0.243 (0.840)
	$t$	12.646	99.088%	12.219	99.003%	19.734	−0.422 (0.578)	19.111	−0.297 (0.525)
USDT	$N$	0.089	99.472%	0.081	99.162%	0.103	0.192 (0.144)	0.096	0.491 (0.051)
	$t$	0.058	99.673%	0.047	99.449%	0.082	−1.400 (0.980)	0.068	0.215 (0.305)
USD	$N$	0.995	98.859%	1.018	99.003%	1.142	0.393 (0.050)	1.162	0.297 (0.065)
	$t$	1.011	98.975%	1.019	99.019%	1.167	−0.303 (0.946)	1.174	−0.343 (0.968)

Note: CCP refers to the conditional coverage probability of the VaR forecast computed using the simulation method of Kabaila and Syuhada (2008). The test statistic $Z_{\mathrm{MF}}$ of McNeil and Frey (2000) was utilized for ES backtesting we carried out through bootstrapping. The resulting $p$-value in italics indicates that the corresponding null hypothesis fails to be rejected at the 5% level of significance.