Table 11.

Back-testing for the VaR.

	Student-t distribution				Normal distribution
Segment A: January 04, 2010, to November 30, 2019
Confidence level	Expected Exceed	Actual Exceed	LRuc	LRcc	Expected Exceed	Actual Exceed	LRuc	LRcc
GOLD
95%	124	132	0.4541905	0.6191286	124	114	0.9758747	0.9859311
99%	124	31	104.603**	105.304**	124	45	70.1861**	71.4780**
Wheat
95%	124	113	1.171848	1.175275	124	99	5.9380**	5.9392**
99%	124	21	136.88**	137.24**	124	31	104.60**	105.38**
WTI
95%	124	64	37.461**	47.989**	124	52	56.522**	64.591**
99%	124	8	194.92**	194.97**	124	16	156.42**	156.63**
Beverages
95%	124	32	101.77**	108.96**	124	25	123.02**	133.04**
99%	124	6	206.64**	206.67**	124	6	206.64**	206.67**
Brent OIL
95%	124	79	20.078**	23.898**	124	73	26.257**	29.263**
99%	124	9	189.45**	189.51**	124	20	140.57**	142.63**
Segment B: December 1, 2019, to May 10, 2020
GOLD
95%	5	11	4.0277**	4.032149	5	10	2.735223	5.9914**
99%	5	7	0.268301	0.9218936	5	9	3.841459	1.787974
Wheat
95%	5	12	5.5215**	5.52153**	5	11	4.0277**	4.032149
99%	5	6	3.841459	0.6782979	5	7	0.268301	0.9218936
Beverages
95%	5	6	0.0112879	0.6782979	5	5	3.841459	0.5663942
99%	5	2	3.40306	3.474492	5	2	3.40306	3.474492

Notes: ** denotes significance at 5% level. These are the results of the Kupiec test, Christferson test, and hit process given in Eqs. (16), (17), (18), (19)).