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

Financial Innovation

Table 10 Implements the VaR Duration Test of Christoffersen and Pelletier on Cleansed Total Nigeria Plc returns

H₀: “Duration Between Exceedances have no memory (Weibull b = 1 = Exponential)”
Model	VaR alpha	b	uLL	rLL	LRp	Decision
sGARCH(1,1) with normal	1%	0.9277	−419.8567	− 420.374	0.3091	Accept
	5%	1.0387	− 805.6184	−805.884	0.4661	Accept
	10%	1.0063	− 1124.353	−1124.366	0.8754	Accept
NGARCH(1,1) With std	1%	0.9974	− 2332.186	−2332.194	0.9030	Accept
	5%	0.9941	− 2347.843	−2347.882	0.7806	Accept
	10%	0.9936	− 2352.093	−2352.139	0.7620	Accept

Note: b: the estimated Weibull parameter, which 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