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Table 10 Full estimation results of the R-vine copula for BRICS basket

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

Tree

Edge

Family

Copula parameters

Kendall’s \(\tau\)

Tail dependence

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

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

\(\lambda _U\)

\(\lambda _L\)

\(T_1\)

3,1

t

0.05 (0.02)**

18.0 (5.72)***

0.03

0.00

0.00

2,4

t

0.25 (0.02)***

2.69 (0.16)***

0.16

0.22

0.22

3,2

t

0.05 (0.02)**

6.33 (0.84)***

0.03

0.04

0.04

3,5

t

0.31 (0.02)***

3.15 (0.19)***

0.20

0.21

0.21

6,3

t

0.44 (0.02)***

2.35 (0.12)***

0.29

0.33

0.33

\(T_2\)

5,1 | 3

BB7180

1.01 (0.01)***

0.05 (0.02)**

0.03

0.00

0.02

3,4 | 2

t

0.02 (0.02)

9.55 (1.59)***

0.02

0.01

0.01

5,2 | 3

t

0.03 (0.02)

8.43 (1.26)***

0.02

0.01

0.01

6,5 | 3

t

0.24 (0.02)***

3.31 (0.22)***

0.15

0.17

0.17

\(T_3\)

2,1 | 5,3

t

0.02 (0.02)

17.8 (5.60)***

0.01

0.00

0.00

5,4 | 3,2

t

0.02 (0.02)

24.4 (8.87)***

0.01

0.00

0.00

6,2 | 5,3

t

− 0.04 (0.02)**

19.9 (6.65)***

− 0.03

0.00

0.00

\(T_4\)

4,1 | 2,5,3

t

0.02 (0.02)

23.5 (8.32)***

0.01

0.00

0.00

6,4 | 5,3,2

t

-0.06 (0.02)***

19.7 (5.88)***

− 0.04

0.00

0.00

\(T_5\)

6,1 | 4,2,5,3

\({\mathcal {I}}\)

0.00

0

0

  1. This table reports the full estimation results of the R-vine decomposition for Bitcoin and the emerging BRICS 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 \(\leftrightarrow\) BRL, 3 \(\leftrightarrow\) RUB, 4 \(\leftrightarrow\) INR, 5 \(\leftrightarrow\) CNH, and 6 \(\leftrightarrow\) ZAR. 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 1382.93, the AIC: \(-\)2709.86, and the BIC: \(-\)2538.02
  2. *** Statistically significant at the 1% level
  3. ** Statistically significant at the 5% level