Model

Parameter

Estimate

s.e

t-ratio

p-value

Information Criteria

AIC

BIC

HQIC

ARIMA (1,1,0)-GARCH (1,0)-norm

$\mu$

0.0181

2.0e⁻⁶

7416.5857

0.0000

9.5841

9.5929

9.5873

${\phi }_1$

−0.1188

4.1e⁻⁵

−2892.9449

0.0000

$\omega$

0.0000

0.0000

4.8845

0.0000

${\alpha }_1$

0.9755

0.0004

2331.4143

0.0000

ARIMA (1,1,0)-GARCH (1,0)-std

$\mu$

−8.0e⁻⁴

0.0004

−1.9660

0.0493

−4.4395

−4.4286

−4.4356

${\phi }_1$

−0.0671

0.0241

−2.7856

0.0053

$\omega$

4.0e⁻⁴

2.3e⁻⁵

18.2910

0.0000

${\alpha }_1$

0.6093

0.0739

8.2413

0.0000

ARIMA (1,1,0)-GARCH (1,1)-norm

$\mu$

−5.0e⁻⁴

9.0e⁻⁵

−56.1884

0.0000

−4.5492

−4.5382

−4.5452

${\phi }_1$

−0.0339

0.0225

−1.5108

0.1308

$\omega$

5.0e⁻⁶

0.0000

67.9874

0.0000

${\alpha }_1$

0.1528

0.0105

14.5331

0.0000

${\beta }_1$

0.8462

0.0088

95.5935

0.0000

ARIMA (1,1,0)-EGARCH (1,1)-norm

$\mu$

0.0000

2.0e⁻⁵

−0.0004

0.9997

−4.5912

−4.5781

−4.5865

${\phi }_1$

−0.0363

0.0231

1.5721

0.1159

$\omega$

−0.6564

0.0065

−101.1563

0.0000

${\alpha }_1$

0.0155

0.0164

0.9474

0.3434

${\beta }_1$

0.9063

0.0007

1341.0781

0.0000

${\gamma }_1$

0.4184

0.0107

38.9643

0.0000

ARIMA (1,1,0)-EGARCH (1,1)-std

$\mu$

−4.0e⁻⁶

0.0000

−41.393

0.0000

−5.1507

−5.1354

−5.1452

${\phi }_1$

−0.1572

0.0029

−56.078

0.0000

$\omega$

0.0141

0.0003

49.642

0.0000

${\alpha }_1$

1.1589

0.0001

12452.741

0.0000

${\beta }_1$

1.0000

1.0e⁻⁵

84465.444

0.0000

${\gamma }_1$

1.1730

0.0001

11481.44

0.0000