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.