Table 5 Fitting results of GARCH models for the log returns and log Amihud ratio and statistics of residual tests

(a) Log return

AIC

9894.1

10,504.7

10,530.3

10,383.3

10,557.2

10,663.5

µ

1.41 (0.86)

2.40 (1.28)

0.03 (1.02)

2.44 (1.08)

1.80 (1.22)

− 1.15 (0.91)

ω

0.87 (0.80)

0.78 (0.32)

0.45 (0.14)

157 (58)

89 (61)

427 (293)

α

0.07 (0.02)

0.22 (0.05)

0.38 (0.07)

0.16 (0.04)

0.16 (0.04)

0.39 (0.11)

β

0.93 (0.03)

0.90 (0.04)

0.95 (0.02)

0.80 (0.05)

0.88 (0.04)

0.61 (0.16)

γ

− 0.0007 (0.03)

− 0.08 (0.06)

0.004 (0.03)

–

− 0.10 (0.04)

–

δ

–

–

–

–

–

–

η

3.3 (0.3)

4.3 (0.6)

2.8 (0.3)

3.7 (0.5)

3.7 (0.4)

2.8 (0.2)

λ

–

–

–

–

–

–

Q(10)

10.33

11.28

7.34

12.01

9.84

6.38

Q²(10)

3.94

3.35

3.76

3.28

8.03

0.34

ARCH(10)

12.37

4.23

4.37

3.27

8.72

0.33

ADF

− 30.22***

− 16.15***

− 31.24***

− 17.74***

− 16.14***

− 32.15***

KPSS

0.62**

0.45*

0.24

0.39

0.21

0.23

(b) Log Amihud ratio

AIC

1504.3

1332.3

1444.9

1460.5

1432.7

1598.2

µ

− 0.02 (0.02)

− 0.02 (0.02)

− 0.01 (0.05)

− 0.01 (0.02)

− 0.03 (0.04)

− 0.03 (0.02)

ω

0.06 (0.01)

0.07 (0.01)

0.10 (0.15)

0.04 (0.04)

0.09 (0.03)

0.11 (0.05)

α

0.09 (0.04)

0.05 (0.03)

0.00 (0.24)

0.05 (0.04)

0.09 (0.06)

0.04 (0.05)

β

0.76 (0.04)

0.65 (0.06)

0.64 (0.75)

0.44 (0.11)

0.63 (0.10)

0.60 (0.20)

γ

− 0.09 (0.04)

–

–

− 0.39 (0.10)

− 0.07 (0.06)

–

δ

–

–

–

4.0 (1.6)

–

–

η

8.1 (1.7)

8.9 (2.3)

9.0 (5.7)

5.8 (0.9)

6.2(1.1)

7.3(1.6)

λ

− 0.41 (0.04)

− 0.42 (0.04)

− 0.37 (0.05)

− 0.51 (0.04)

− 0.43 (0.04)

− 0.30 (0.04)

Q(10)

2.78

4.09

2.05

2.15

6.81

6.23

Q²(10)

6.39

3.77

8.22

3.38

4.09

11.05

ARCH(10)

7.06

3.93

8.35

4.16

4.37

14.39

ADF

− 32.00***

− 31.89***

− 31.97***

− 31.41***

− 21.37***

− 32.07***

KPSS

0.31

0.47**

0.22

0.23

0.26

0.30