Estimating Risk of Natural Gas Portfolios by Using GARCH-EVT-Copula Model

Table 2

Estimated parameters of agricultural commodity returns for marginal model.

	TTFFD	TTFFM	TTFFQ	TTFFS	TTFFY
	−0.0002; (0.0004)	−0.0007^**; (0.0003)	−0.0008; (0.0003)	−0.0005^*; (0.0002)	−0.0003; (0.0002)
	−0.1350^**; (0.0234)	0.0363; (0.0206)	0.0206; (0.0190)	0.0668^**; (0.0218)	0.0588^**; (0.0223)
	0.0000^**; (0.0000)	0.0000; (0.0000)	0.0000^**; (0.0000)	0.0000^**; (0.0000)	0.0000^**; (0.0000)
	0.2045^**; (0.0263)	0.0560^**; (0.0169)	0.0120^**; (0.0035)	0.1865^**; (0.0341)	0.1661^**; (0.0243)
	0.7945^**; (0.0238)	0.9430^**; (0.0170)	0.9848^**; (0.0030)	0.8125^**; (0.0305)	0.8329^**; (0.0213)
	4.3963^**; (0.3857)	3.2386^**; (0.2172)	2.8659^**; (0.1965)	3.1684^**; (0.1866)	3.6138^**; (0.2616)
LL	3910.0000	4943.7790	5154.1850	5409.1680	5794.5190
AIC	−4.0372	−5.1063	−5.3239	−5.5876	−5.9861
ARCH(10)	0.7074	0.8258	0.9988	1.0000	0.9996

Note. The table shows the estimates and the standard errors of the parameters for the marginal distribution model defined in (3) and (4). ** and * denote rejection of the null hypothesis at the 1% and 5% significance levels, respectively. ARCH(10) is the P value of Engle’s LM test for the ARCH effect in the residuals up to the 10th order.