Table 3 Parameter estimate of fat-tail asymmetric GARCH

GJR -M¹-t

−0.02044

0.1446

0.7781

0.06369

−0.5473

−0.05660

0.06832

0.1539

0.9014

–

−0.1110

–

–

10.67

(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

−0.1492

0.2760

0.7773

0.06403

−0.5468

−0.05687

0.07062

0.1526

0.9021

–

−0.1119

–

–

10.62

(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

−0.1903

0.1939

0.7740

0.06443

−0.5441

− 0.05668

0.07043

0.1517

0.9042

–

−0.1151

–

–

10.60

(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

−0.0177

0.1337

0.7754

0.06374

−0.5489

− 0.05339

0.06029

0.1552

0.9031

–

−0.1142

–

1.563

–

(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

−0.12497

0.2363

0.7733

0.06477

−0.5469

− 0.05430

0.06238

0.1538

0.9037

–

−0.1147

–

1.565

–

(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

−0.15485

0.162894

0.7695

0.06559

−0.54368

−0.05456

0.06240

0.1529

0.9054

–

− 0.1171

–

1.568

–

(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

−0.03288

0.1582

0.7860

0.05783

−0.5545

− 0.05676

0.04412

0.1058

0.9042

–

− 0.3936

1.103

–

10.33

(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

−0.1805

0.3386

0.7679

0.06169

−0.5330

−0.05575

0.03392

0.07816

0.9278

–

−0.6082

1.066

–

10.48

(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

−0.1882

0.2291

0.7594

0.06475

−0.5256

−0.05531

0.03413

0.07785

0.9276

–

−0.5999

1.142

–

10.46

(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

−0.02825

0.1575

0.7633

0.06057

−0.5307

−0.05367

0.02879

0.07161

0.9348

–

− 0.6999

1.023

1.575

–

(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

−0.1511

0.2954

0.7581

0.06320

−0.5270

−0.05261

0.02999

0.073696

0.9322

–

−0.6572

1.104

1.575

–

(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

−0.1495

0.1957

0.7506

0.06595

−0.5192

−0.05288

0.02999

0.07508

0.9306

–

−0.6277

1.179

1.575

–

(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

−0.03540

0.1636

0.7770

0.05879

−0.5424

−0.05575

− 0.08905

0.1504

0.9860

0.09156

–

–

–

10.33

(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

−0.1751

0.3329

0.7688

0.06149

−0.5355

−0.05546

− 0.09519

0.15681

0.9867

0.09015

–

–

–

10.21

(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

−0.1655

0.2158

0.762846

0.063439

−0.53197

−0.05560

− 0.10116

0.16320

0.9874

0.08851

–

–

–

10.17

(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

−0.03010

0.1551

0.7626

0.06124

−0.5297

−0.05350

− 0.0813

0.1346

0.9882

0.09663

–

–

1.569

–

(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

−0.1465

0.290688

0.756656

0.06352

−0.5260

−0.05208

− 0.08904

0.1432

0.9888

0.09429

–

–

1.566

–

(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

−0.1219

0.1920

0.748972

0.06536

−0.5178

−0.05329

− 0.09345

0.1465

0.9900

0.09384

–

–

1.565

–

(0.05999)

(0.1156)

(0.05738)

(0.02754)

(0.06803)

(0.026269

(0.01582)

(0.020851)

(0.003297)

(0.01388)

–

–

(0.0636)

–