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Table 3 Parameter estimate of fat-tail asymmetric GARCH

From: Asymmetric GARCH type models for asymmetric volatility characteristics analysis and wind power forecasting

 δCAR(1)AR(4)MA(1)MA(5)Ωα1β1φγδvk
GJR -M1-t−0.020440.14460.77810.06369−0.5473−0.056600.068320.15390.9014−0.111010.67
 (0.01101)(0.1309)(0.05725)(0.02893)(0.06796)(0.02630)(0.02625)(0.02112)(0.01234)(0.02329)(2.172)
GJR -M2-t−0.14920.27600.77730.06403−0.5468−0.056870.070620.15260.9021−0.111910.62
 (0.06686)(0.1378)(0.05722)(0.02886)(0.06789)(0.02622)(0.02624)(0.02089)(0.01223)(0.02312)(2.152)
GJR -M3-t−0.19030.19390.77400.06443−0.5441− 0.056680.070430.15170.9042−0.115110.60
 (0.07945)(0.1305)(0.05742)(0.02872)(0.06810)(0.02619)(0.02582)(0.02063)(0.01199)(0.02278)(2.144)
GJR-M1-GED−0.01770.13370.77540.06374−0.5489− 0.053390.060290.15520.9031−0.11421.563
 (0.01078)(0.1274)(0.05768)(0.02889)(0.06821)(0.02607)(0.02475)(0.02138)(0.01211)(0.02358)(0.0626)
GJR-M2-GED−0.124970.23630.77330.06477−0.5469− 0.054300.062380.15380.9037−0.11471.565
 (0.06520)(0.1336)(0.05771)(0.02879)(0.06824)(0.02602)(0.02471)(0.02111)(0.01201)(0.02333)(0.0625)
GJR-M3-GED−0.154850.1628940.76950.06559−0.54368−0.054560.062400.15290.9054− 0.11711.568
 (0.07659)0.125744(0.05796)(0.02866)(0.06853)(0.02601)(0.02432)(0.02084)(0.01179)(0.02297)(0.0626)
APARCH-M1-t−0.032880.15820.78600.05783−0.5545− 0.056760.044120.10580.9042− 0.39361.10310.33
 (0.01120)(0.1293)(0.05693)(0.02913)(0.06773)(0.02630)(0.01444)(0.01410)(0.01241)(0.09959)(0.1987)(2.060)
APARCH-M2-t−0.18050.33860.76790.06169−0.5330−0.055750.033920.078160.9278−0.60821.06610.48
 (0.06391)(0.1334)(0.05630)(0.02800)(0.06695)(0.02622)(0.01150)(0.01148)(0.01021)(0.1306)(0.1850)(2.132)
APARCH-M3-t−0.18820.22910.75940.06475−0.5256−0.055310.034130.077850.9276−0.59991.14210.46
 (0.07244)(0.1254)(0.05679)(0.02788)(0.06749)(0.02623)(0.01246)(0.01203)(0.01041)(0.1326)(0.1964)(2.123)
APARCH-M1-GED−0.028250.15750.76330.06057−0.5307−0.053670.028790.071610.9348− 0.69991.0231.575
 (0.01124)(0.1213)(0.05676)(0.02783)(0.06749)(0.02614)(0.009713)(0.01016)(0.009282)(0.1373)(0.1732)(0.0647)
APARCH-M2-GED−0.15110.29540.75810.06320−0.5270−0.052610.029990.0736960.9322−0.65721.1041.575
 (0.06286)(0.1299)(0.05699)(0.02780)(0.06765)(0.02620)(0.01082)(0.01105)(0.009838)(0.1388)(0.1874)(0.0643)
APARCH-M3-GED−0.14950.19570.75060.06595−0.5192−0.052880.029990.075080.9306−0.62771.1791.575
 (0.07015)(0.1207)(0.05730)(0.02767)(0.06804)(0.02623)(0.01171)(0.01171)(0.01019)(0.1377)(0.1999)(0.0641)
EGARCH-M1-t−0.035400.16360.77700.05879−0.5424−0.05575− 0.089050.15040.98600.0915610.33
 (0.01151)(0.1254)(0.05592)(0.02823)(0.06641)(0.02620)(0.01568)(0.02055)(0.003915)(0.01428)(2.061)
EGARCH-M2-t−0.17510.33290.76880.06149−0.5355−0.05546− 0.095190.156810.98670.0901510.21
 (0.06069)(0.1270)(0.05653)(0.02810)(0.06713)(0.02623)(0.01652)(0.02183)(0.003842)(0.01459)(2.008)
EGARCH-M3-t−0.16550.21580.7628460.063439−0.53197−0.05560− 0.101160.163200.98740.0885110.17
 (0.06188)(0.1199)(0.05716)(0.02808)(0.06786)(0.02627)(0.01724)(0.02271)(0.003775)(0.01472)(1.991)
EGARCH-M1-GED−0.030100.15510.76260.06124−0.5297−0.05350− 0.08130.13460.98820.096631.569
 (0.01139)(0.1197)(0.05641)(0.02776)(0.06700)(0.02613)(0.01468)(0.01892)(0.003598)(0.01354)(0.0638)
EGARCH-M2-GED−0.14650.2906880.7566560.06352−0.5260−0.05208− 0.089040.14320.98880.094291.566
 (0.05970)(0.1238)(0.05691)(0.02774)(0.06746)(0.02620)(0.01539)(0.02021)(0.003462)(0.01391)(0.0635)
EGARCH-M3-GED−0.12190.19200.7489720.06536−0.5178−0.05329− 0.093450.14650.99000.093841.565
 (0.05999)(0.1156)(0.05738)(0.02754)(0.06803)(0.026269(0.01582)(0.020851)(0.003297)(0.01388)(0.0636)