Model

Parameter

Estimate

s.e

t-ratio

p-value

Information Criteria

AIC

BIC

HQIC

ARIMA (2,1,1)- GARCH (1,0)-std

$\mu$

−9.93e⁻⁴

3.81e⁻⁴

−2.6037

0.0092

−4.3202

−4.3049

−4.3147

${\phi }_1$

0.6479

0.1134

5.7155

0.0000

${\phi }_2$

0.0115

0.0246

0.4676

0.6401

${\theta }_1$

−0.7192

0.1107

6.4961

0.0000

$\omega$

4.9e⁻⁴

2.6e⁻⁵

18.9763

0.0000

${\alpha }_1$

0.5380

0.0581

9.2597

0.0000

ARIMA (2,1,1)- GARCH (2,0)-std

$\mu$

0.0000

0.0000

−0.0179

0.9857

−5.0430

−5.0255

−5.0367

${\phi }_1$

−0.2748

0.1017

−2.7030

0.0069

${\phi }_2$

0.1899

0.0250

7.5938

0.0000

${\theta }_1$

0.2976

0.0988

3.0112

0.0026

$\omega$

0.0000

0.0000

0.0000

1.0000

${\alpha }_1$

0.5085

0.0215

23.6094

0.0000

${\alpha }_2$

0.4899

0.0216

22.6980

0.0000

ARIMA (2,1,1)- GARCH (1,1)-norm

$\mu$

−1.89e⁻⁴

4.6e⁻⁵

−4.1466

0.00003

−4.3997

−4.3843

4.3941

${\phi }_1$

0.7177

0.1399

5.1280

0.0000

${\phi }_2$

0.0116

0.0248

0.4695

0.6387

${\theta }_1$

−0.7663

0.1386

−5.5302

0.0000

$\omega$

5.0e⁻⁶

0.0000

21.4307

0.0000

${\alpha }_1$

0.1499

0.0084

17.9265

0.0000

${\beta }_1$

0.8491

0.0065

131.3783

0.0000

ARIMA (2,1,1)- EGARCH (1,1)-norm

$\mu$

−1.325e⁻³

4.67e⁻⁴

−2.8394

0.0045

−4.3056

−4.2881

−4.2993

${\phi }_1$

−0.6678

0.0235

−28.3624

0.0000

${\phi }_2$

−0.0247

0.0222

−1.1137

0.2654

${\theta }_1$

0.6243

0.0237

26.3269

0.0000

$\omega$

−1.8914

0.3467

−5.4553

0.0000

${\alpha }_1$

−0.0003

0.0199

−0.0137

0.9891

${\beta }_1$

0.7326

0.0488

15.0204

0.0000

${\gamma }_1$

0.3446

0.0484

7.12488

0.0000

ARIMA (2,1,1)- EGARCH (1,1)-std

$\mu$

0.0000

7.0e⁻⁶

−0.0005

0.9995

−4.4228

−4.4031

−4.4157

${\phi }_1$

−0.2876

0.0271

−10.6033

0.0000

${\phi }_2$

0.0023

0.0203

0.1135

0.9096

${\theta }_1$

0.2356

0.0275

8.5685

0.0000

$\omega$

−0.8316

0.0198

−41.9417

0.0000

${\alpha }_1$

−0.0537

0.0284

−1.8871

0.0000

${\beta }_1$

0.8820

0.0011

773.2336

0.0000

${\gamma }_1$

0.9400

0.0378

24.8684

0.0000