On the volatility of daily stock returns of Total Nigeria Plc: evidence from GARCH models, value-at-risk and backtesting

Financial Innovation

Table 9 Implements the VaR Duration Test of Christoffersen and Pelletier on Total Nigeria Plc Returns

H₀: “Duration Between Exceedances have no memory (Weibull b = 1 = Exponential)”
Model	VaR alpha	B	uLL	rLL	LRp	Decision
eGARCH(1,1) with normal	1%	0.9113	−411.8762	− 412.687	0.2029	Accept
	5%	1.0604	− 843.6371	− 844.3382	0.2363	Accept
	10%	1.0353	− 1176.545	− 1176.938	0.3758	Accept
NGARCH(1,1) With std	1%	0.8837	− 407.4371	− 408.826	0.0956	Accept
	5%	1.0022	− 814.8295	−814.8304	0.9660	Accept
	10%	0.9996	− 1126.9	−1126.9	0.9926	Accept

Note: b: the estimated Weibull parameter that, when restricted to the value of 1, results in exponential distribution; uLL: the unrestricted log-likelihood value; rLL: the restricted log-likelihood value; LRp: the likelihood-ratio test statistic