Table 4 Estimation results: DCC-GARCH models

Panel A: DCC-GJR-GARCH (1,1) model for ATE

Estimated parameters—mean equation AR(1)

AR(1)

− 0.020

− 0.051^***

0.117^***

0.131^***

− 0.033^**

− 0.022

0.012

− 0.017

(0.014)

(0.015)

(0.016)

(0.016)

(0.015)

(0.016)

(0.013)

(0.014)

Estimated parameters—variance equation

ARCH (α)

0.010

− 0.015^**

0.005

0.0048

0.019^**

0.034^***

0.01^***

0.039^***

(0.007)

(0.007)

(0.010)

(0.0083)

(0.007)

(0.008)

(0.004)

(0.008)

GARCH (β)

0.911^***

0.899^***

0.902^***

0.9018^***

0.950^***

0.963^***

0.972^***

0.960^***

(0.011)

(0.011)

(0.014)

(0.0127)

(0.008)

(0.009)

(0.003)

(0.008)

Gamma (γ)

0.125^***

0.189^***

0.152^***

0.1529^***

0.050^***

− 0.008

0.013^**

− 0.007

(0.017)

(0.021)

(0.020)

(0.0195)

(0.010)

(0.011)

(0.005)

(0.007)

ρ with ATE

0.900^***

0.820^***

0.6171^***

0.1762^**

− 0.011

0.027

− 0.311^***

Panel B: DCC-GJR-GARCH (1,1) model for MIT

Estimated parameters—mean equation AR(1)

AR(1)

0.073^***

− 0.051^***

0.117^***

0.131^***

− 0.033^**

− 0.022

0.012

− 0.017

(0.014)

(0.015)

(0.016)

(0.016)

(0.015)

(0.016)

(0.013)

(0.014)

Estimated parameters—variance equation

ARCH (α)

0.016^*

− 0.015^**

0.005

0.004

0.019^**

0.034^***

0.010^***

0.039^***

(0.008)

(0.007)

(0.010)

(0.008)

(0.007)

(0.008)

(0.004)

(0.008)

GARCH (β)

0.905^***

0.899^***

0.902^***

0.901^***

0.950^***

0.963^***

0.972^***

0.960^***

(0.013)

(0.011)

(0.014)

(0.012)

(0.008)

(0.009)

(0.003)

(0.008)

Gamma (γ)

0.122^***

0.189^***

0.152^***

0.152^***

0.050^***

− 0.008

0.013^**

− 0.007

(0.018)

(0.021)

(0.020)

(0.019)

(0.010)

(0.011)

(0.005)

(0.007)

ρ with MIT

0.863^***

0.841^***

0.643^***

0.190^***

0.028

0.067

− 0.289^***

Panel C: DCC-GJR-GARCH (1,1) model for ABI

Estimated parameters—mean equation AR(1)

AR(1)

− 0.003

− 0.051^***

0.117^***

0.131^***

− 0.033^**

− 0.022

0.012

− 0.017

(0.015)

(0.015)

(0.016)

(0.016)

(0.015)

(0.016)

(0.013)

(0.014)

Estimated parameters—variance equation

ARCH (α)

0.031^***

− 0.015^**

0.005

0.004

0.019^**

0.034^***

0.010^***

0.039^***

(0.009)

(0.007)

(0.010)

(0.008)

(0.007)

(0.008)

(0.004)

(0.008)

GARCH (β)

0.927^***

0.899^***

0.902^***

0.901^***

0.950^***

0.963^***

0.972^***

0.960^***

(0.012)

(0.011)

(0.014)

(0.012)

(0.008)

(0.009)

(0.003)

(0.008)

Gamma (γ)

0.059

0.189^***

0.152^***

0.152^***

0.050^***

− 0.008

0.013^**

− 0.007

(0.014)

(0.021)

(0.020)

(0.019)

(0.010)

(0.011)

(0.005)

(0.007)

ρ with ABI

0.662*^**

0.587^***

0.427^***

0.094*^*

− 0.011

0.013

− 0.213^***

Panel D: DCC− GARCH (1,1) model for SPC

Estimated parameters—mean equation ARMA (1,0)

AR(1)

0.157^***

− 0.056^***

0.119^***

0.123^***

− 0.034^**

− 0.015

0.006

− 0.029^*

(0.016)

(0.016)

(0.016)

(0.016)

(0.016)

(0.017)

(0.015)

(0.015)

Estimated parameters—variance equation

ARCH (α)

0.088^***

0.115^***

0.1097^***

0.105^***

0.053^***

0.035^***

0.029^***

0.032^***

(0.012)

(0.014)

(0.016)

(0.016)

(0.008)

(0.009)

(0.003)

(0.007)

GARCH (β)

0.902^***

0.861^***

0.878^***

0.878^***

0.941^***

0.959^***

0.969^***

0.963^***

(0.013)

(0.015)

(0.017)

(0.017)

(0.009)

(0.010)

(0.003)

(0.008)

ρ with SPC

0.088^***

0.049^***

0.017

0.033

0.005

− 0.007

− 0.002

Panel E: DCC-GARCH (1,1) model for FIN

Estimated parameters—mean equation AR(1)

AR(1)

0.000

− 0.053

0.073^*

0.101^***

− 0.032

− 0.026

0.062^*

− 0.049

(0.038)

(0.041)

(0.039)

(0.036)

(0.033)

(0.028)

(0.034)

(0.035)

Estimated parameters—variance equation

ARCH (α)

0.130^**

0.198^***

0.213^***

0.173^***

0.039^***

0.005

0.020

0.036

(0.054)

(0.049)

(0.059)

(0.048)

(0.0131)

(0.006)

(0.013)

(0.029)

GARCH (β)

0.830^***

0.763^***

0.742^***

0.686^***

0.937^***

0.975^***

0.978^***

0.941^***

(0.064)

(0.038)

(0.052)

(0.084)

(0.022)

(0.011)

(0.013)

(0.058)

ρ with FIN

0.734^***

0.729^***

0.531^***

0.128*^*

− 0.069

− 0.000

− 0.275^***

Panel F: DCC-GARCH (1,1) model for BTC

Estimated parameters—mean equation AR(1)

AR(1)

0.067^**

− 0.053^*

0.095^***

0.130^***

− 0.048^*

− 0.043^*

0.030

− 0.057^**

(0.033)

(0.031)

(0.031)

(0.029)

(0.028)

(0.024)

(0.028)

(0.028)

Estimated parameters—variance equation

ARCH (α)

0.134^***

0.211^***

0.212^***

0.138^***

0.058^***

0.012^***

0.018^***

0.020^**

(0.033)

(0.040)

(0.048)

(0.034)

(0.014)

(0.004)

(0.006)

(0.010)

GARCH (β)

0.818^***

0.742^***

0.749^***

0.838^***

0.922^***

0.984^***

0.981^***

0.974^***

(0.041)

(0.034)

(0.040)

(0.037)

(0.021)

(0.006)

(0.006)

(0.013)

ρ with BTC

− 0.017

0.0008

− 0.0072

− 0.0048

0.0380

0.0333

− 0.0087