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Table 9 Full estimation results of the R-vine copula for G7 basket

From: The linkage between Bitcoin and foreign exchanges in developed and emerging markets

Tree

Edge

Copula

Copula parameters

Kendall’s \(\tau\)

Tail dependence

\(\theta\) (\(\rho\) for t or \({\mathcal {N}}\))

\(\delta\) (\(\nu\) for t)

\(\lambda _U\)

\(\lambda _L\)

\(T_1\)

2,1

\({\mathcal {F}}\)

0.29 (0.10)***

0.03

0

0

2,4

t

0.15 (0.02)***

3.72 (0.30)***

0.10

0.12

0.12

3,2

t

0.45 (0.02)***

2.09 (0.10)***

0.30

0.36

0.36

5,3

t

0.46 (0.02)***

2.03 (0.09)***

0.30

0.37

0.37

\(T_2\)

4,1 | 2

t

0.04 (0.02)**

20.9 (7.11)***

0.03

0.00

0.00

3,4 | 2

t

0.09 (0.02)***

7.36 (1.03)***

0.06

0.03

0.03

5,2 | 3

t

− 0.04 (0.02)**

2.68 (0.15)***

− 0.03

0.12

0.12

\(T_3\)

3,1 | 4,2

\({\mathcal {J}}^{180}\)

1.02 (0.01)***

0.01

0

0.03

5,4 | 3,2

t

− 0.01 (0.02)

13.4 (2.91)***

− 0.01

0.00

0.00

\(T_4\)

5,1 | 3,4,2

t

− 0.01 (0.02)

27.8 (10.1)***

− 0.01

0

0

  1. This table reports the full estimation results of the R-vine decomposition for Bitcoin and the developed G7 exchange rates. The best structure is a regular (R) vine. Standard errors of the estimated parameters are in parentheses. The edges are 1 \(\leftrightarrow\) BTC, 2 \(\leftrightarrow\) CAD, 3 \(\leftrightarrow\) EUR, 4 \(\leftrightarrow\) GBP, and 5 \(\leftrightarrow\) JPY. The employed copulas are Independent (\({\mathcal {I}}\)), Gaussian (\({\mathcal {N}}\)), t, Clayton (\({\mathcal {C}}\)), Gumbel (\({\mathcal {G}}\)), Frank (\({\mathcal {F}}\)), Joe (\({\mathcal {J}}\)), BB1, BB6, BB7, BB8, Tawn 1 (\({\mathcal {T}}_1\)), and Tawn 2 (\({\mathcal {T}}_2\)). Rotation degrees are indicated as superscripts. The log-likelihood of this structure is 1578.91, the AIC: \(-\)3121.82, and the BIC: \(-\)3011.35
  2. *** Statistically significant at the 1% level
  3. ** Statistically significant at the 5% level