Table 6 Fitting results of GARCH models for the AR and CS estimators, and statistics of residual tests

(a) AR estimator

AIC

9451.6

9948.2

10,083.4

9928.0

10,052.9

10,382.4

µ

3.32 (0.08)

4.36 (0.06)

1.67 (0.04)

7.78 (0.14)

4.06 (0.03)

− 1.53 (4.35)

ω

0.05 (1E−4)

0.04 (1E−4)

0.015 (4E−5)

0.12 (3E−5)

0.04 (5E−5)

0.96 (5.39)

α

− 0.02 (6E−4)

− 0.01 (5E−4)

− 0.0183 (0.0002)

− 0.02 (6E−4)

− 0.02 (6E−4)

0.05 (0.02)

β

0.99 (3E−6)

1.00 (1E−6)

0.998 (6E−8)

0.99 (9E−7)

0.99 (1E−7)

0.95 (0.06)

γ

0.21 (6E−3)

0.17 (1E−3)

0.136 (0.005)

0.27 (4E−3)

0.15 (2E−3)

− 1.00 (0.01)

δ

–

–

–

–

–

1.2 (1.0)

η

2.44 (0.06)

2.59 (0.03)

2.35 (0.03)

2.41 (0.02)

3.45 (0.05)

3.1 (0.5)

λ

0.77 (0.07)

0.78 (0.02)

0.68 (0.03)

0.75 (0.02)

0.68 (0.02)

0.59 (0.10)

Q(10)

6.63

6.62

9.99

9.27

7.39

6.94

Q²(10)

3.06

5.87

45.83***

4.49

13.93

0.24

ARCH(10)

4.68

10.11

51.09***

5.50

17.40*

0.24

ADF

− 31.18***

− 15.59***

− 20.52***

− 17.46***

− 21.08***

− 31.02***

KPSS

0.06

0.07

0.10

0.06

0.09

0.05

(b) CS estimator

AIC

8237.2

8849.5

8905.1

8815.3

8811.5

9229.1

µ

− 0.07 (0.50)

0.74 (0.40)

− 0.64 (0.003)

− 0.56 (0.85)

− 0.12 (0.78)

− 0.63 (0.95)

ω

0.22 (0.08)

0.12 (0.13)

0.26 (0.14)

0.12 (0.32)

0.15(0.57)

0.47(0.69)

α

0.09 (0.01)

0.05 (0.02)

0.27 (0.09)

0.11 (0.26)

0.03(0.02)

0.05(0.01)

β

0.95 (0.01)

0.95 (0.06)

0.97 (0.02)

0.98 (0.04)

0.97(0.01)

0.95(0.02)

γ

− 0.09(0.01)

− 0.98(0.18)

0.07 (0.03)

0.09 (0.02)

− 1.00 (4E−4)

− 1.00 (5E−3)

δ

–

0.51(0.57)

–

–

1.20 (0.74)

1.1 (0.25)

η

4.6 (0.5)

5.51 (0.96)

3.4 (0.4)

3.6 (0.4)

4.3 (0.50)

3.5 (0.39)

λ

0.61 (0.03)

0.55 (0.04)

0.51 (0.03)

0.49 (0.12)

0.64 (0.07)

0.51 (0.05)

Q(10)

4.03

5.34

6.80

6.50

6.00

4.97

Q²(10)

9.89

15.62

6.69

14.89

2.19

0.57

ARCH(10)

10.23

15.39

6.97

15.14

2.09

0.55

ADF

− 31.03***

− 31.68***

− 32.80***

− 21.25***

− 21.07***

− 29.75***

KPSS

0.05

0.07

0.05

0.10

0.08

0.05