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Financial Innovation

Table 4 Fitting results of the ARIMA model and statistics of residual tests

From: Relationships among return and liquidity of cryptocurrencies

 

(p, d, q)

AIC

Q(10)

Q2(10)

ARCH(10)

ADF

KPSS

(a) Log return

BTC

(0, 0, 4)

10,211.5

8.73

14.94

76.30***

− 31.59***

0.49*

ETH

(2, 0, 6)

10,767.2

6.85

20.93**

43.80***

− 31.77***

0.36*

XRP

(0, 0, 0)

11,173.7

7.74

64.89***

56.58***

− 32.77***

0.12

BNB

(2, 0, 2)

10,933.0

15.67

98.08***

123.77***

− 8.98***

0.28

LTC

(1, 0, 4)

10,845.8

4.35

45.76***

49.56***

− 31.60***

0.15

DOGE

(3, 0, 3)

11,857.4

2.92

13.17

11.99

− 31.60***

0.25

(b) Log Amihud ratio

BTC

(4, 1, 5)

1648.2

12.41

0.78

7.77

− 40.68***

0.43*

ETH

(0, 1, 1)

1446.4

5.12

0.35

5.36

− 38.72***

0.58**

XRP

(2, 1, 5)

1533.3

3.60

0.16

8.54

− 39.03***

0.35*

BNB

(0, 1, 1)

1632.7

3.32

0.16

4.46

− 37.32***

0.32

LTC

(0, 1, 1)

1597.2

5.96

0.21

6.25

− 23.70***

0.93***

DOGE

(2, 1, 1)

1668.6

9.15

0.37

10.52

− 38.19***

0.36*

(c) AR estimator

BTC

(5, 1, 7)

10,207.8

4.07

4.15

12.46

− 31.34***

0.08

ETH

(2, 1, 3)

10,705.7

3.18

12.17

33.00***

− 15.37***

0.12

XRP

(3, 1, 9)

11,175.8

2.47

27.28***

32.05***

− 31.40***

0.09

BNB

(3, 1, 3)

10,928.4

7.32

37.72***

60.25***

− 30.89***

0.04

LTC

(6, 1, 3)

10,745.7

2.15

26.98***

34.71***

− 31.55***

0.09

DOGE

(7, 1, 8)

12,023.8

3.07

0.74

0.72

− 31.87***

0.04

(d) CS estimator

BTC

(1, 1, 1)

8765.0

6.50

63.36***

62.72***

− 31.61***

0.05

ETH

(0, 1, 2)

9239.1

6.85

143.15***

145.29***

− 31.43***

0.04

XRP

(0, 1, 9)

9724.8

1.37

146.89***

97.22***

− 31.38***

0.08

BNB

(6, 1, 4)

9705.3

6.75

310.38***

299.31***

− 31.68***

0.07

LTC

(1, 1, 1)

9424.4

7.75

15.63

11.68

− 31.61***

0.06

DOGE

(7, 1, 8)

10,848.8

4.58

0.97

0.94

− 31.43***

0.05

  1. *Indicate rejection of the respective null hypotheses at the 10% significance level
  2. **Indicate rejection of the respective null hypotheses at the 5% significance level
  3. ***Indicate rejection of the respective null hypotheses at the 1% significance level
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