Table II. The estimates of DCC-GARCH...

Table II.

The estimates of DCC-GARCH models for different dry bulk sectors

Mean equation	Capesize	Panamax	Supramax
d₁	−1.785^*** (−3.515)	−0.378 (−1.202)	0.218 (1.600)
d₂	−0.567^** (−2.011)	−0.353 (−1.126)	0.075 (0.719)
d₃	8.457^*** (6.551)	10.400^*** (5.692)	3.955^*** (5.971)
a₁	0.611^*** (11.540)	0.839^*** (25.004)	0.803^*** (24.392)
a₂	−0.179^*** (-5.852)	−0.105^*** (−3.469)	−0.075^*** (−2.897)
a₃	0.100 (1.155)	0.017 (0.261)	0.394^*** (2.822)
b₁	0.474^*** (6.639)	0.117^*** (4.417)	0.182^*** (5.681)
b₂	1.204^*** (27.086)	1.065^*** (43.107)	1.605^*** (38.483)
b₃	−0.241^** (−2.270)	0.113 (1.583)	−0.183^** (−1.468)
c₁	0.123^*** (4.222)	0.066^*** (3.195)	0.026^*** (2.985)
c₂	0.047^*** (2.922)	0.055^*** (2.678)	0.012^* (1.810)
c₃	0.512^*** (6.389)	0.249^* (1.894)	0.549^*** (9.926)
Variance equation
ω₁	0.000 (0.296)	0.004 (1.648)	0.002^*** (4.025)
α₁	0.011^*** (57.011)	0.329^** (2.202)	0.241^*** (3.007)
β₁	0.989^*** (105.582)	0.335 (1.041)	0.381^*** (3.322)
ω₂	0.000 (1.478)	0.002^** (2.519)	0.001^*** (2.801)
α₂	0.129^*** (2.930)	0.222^*** (3.355)	0.615^*** (5.748)
β₂	0.850^*** (16.814)	0.562^** (5.113)	0.239^*** (2.350)
ω₃	0.098^*** (3.372)	0.045^** (7.700)	0.003 (0.760)
α₃	0.277 (1.504)	0.325 (1.597)	0.050^* (1.737)
β₃	0.064 (0.482)	0.000^** (2.923)	0.928^*** (17.174)
θ₁	0.031^*** (67.534)	0.002 (0.100)	0.048 (1.644)
θ₂	0.831^*** (61.394)	0.980^*** (75.399)	0.759^*** (5.370)
Diagnostics
LogL	278.725	755.850	877.219
AIC	0.434	0.507	0.544
SC	0.427	0.487	0.514
ARCH(12) of ERN	0.253 (0.995)	0.314 (0.987)	0.262 (0.820)
ARCH(12) of SR	0.606 (0.837)	0.384 (0.969)	0.121 (0.998)
ARCH(12) of FIX	0.575 (0.862)	0.976 (0.861)	0.483 (0.924)

Mean equation	Capesize	Panamax	Supramax
d₁	−1.785^*** (−3.515)	−0.378 (−1.202)	0.218 (1.600)
d₂	−0.567^** (−2.011)	−0.353 (−1.126)	0.075 (0.719)
d₃	8.457^*** (6.551)	10.400^*** (5.692)	3.955^*** (5.971)
a₁	0.611^*** (11.540)	0.839^*** (25.004)	0.803^*** (24.392)
a₂	−0.179^*** (-5.852)	−0.105^*** (−3.469)	−0.075^*** (−2.897)
a₃	0.100 (1.155)	0.017 (0.261)	0.394^*** (2.822)
b₁	0.474^*** (6.639)	0.117^*** (4.417)	0.182^*** (5.681)
b₂	1.204^*** (27.086)	1.065^*** (43.107)	1.605^*** (38.483)
b₃	−0.241^** (−2.270)	0.113 (1.583)	−0.183^** (−1.468)
c₁	0.123^*** (4.222)	0.066^*** (3.195)	0.026^*** (2.985)
c₂	0.047^*** (2.922)	0.055^*** (2.678)	0.012^* (1.810)
c₃	0.512^*** (6.389)	0.249^* (1.894)	0.549^*** (9.926)
Variance equation
ω₁	0.000 (0.296)	0.004 (1.648)	0.002^*** (4.025)
α₁	0.011^*** (57.011)	0.329^** (2.202)	0.241^*** (3.007)
β₁	0.989^*** (105.582)	0.335 (1.041)	0.381^*** (3.322)
ω₂	0.000 (1.478)	0.002^** (2.519)	0.001^*** (2.801)
α₂	0.129^*** (2.930)	0.222^*** (3.355)	0.615^*** (5.748)
β₂	0.850^*** (16.814)	0.562^** (5.113)	0.239^*** (2.350)
ω₃	0.098^*** (3.372)	0.045^** (7.700)	0.003 (0.760)
α₃	0.277 (1.504)	0.325 (1.597)	0.050^* (1.737)
β₃	0.064 (0.482)	0.000^** (2.923)	0.928^*** (17.174)
θ₁	0.031^*** (67.534)	0.002 (0.100)	0.048 (1.644)
θ₂	0.831^*** (61.394)	0.980^*** (75.399)	0.759^*** (5.370)
Diagnostics
LogL	278.725	755.850	877.219
AIC	0.434	0.507	0.544
SC	0.427	0.487	0.514
ARCH(12) of ERN	0.253 (0.995)	0.314 (0.987)	0.262 (0.820)
ARCH(12) of SR	0.606 (0.837)	0.384 (0.969)	0.121 (0.998)
ARCH(12) of FIX	0.575 (0.862)	0.976 (0.861)	0.483 (0.924)

Notes:

***

and

mean statistically significant at 1%, 5% and 10%, respectively. The t-statistics is reported in the parenthesis. LogL is the log-likelihood. AIC is the Akaike information criterion. SC is the Schwarz information criterion. ARCH(12) is Engle’s F-test for ARCH effects. Figures in the brackets under the ARCH(12) estimates indicate the significance levels.

ln(ERN_t) = d₁ + a₁ln(ERN_t₋₁) + b₁ln(SR_t−1) + c₁ln(FIX_t−₁) + ε_1,t

ln(SR_t) = d₂ + a₂ln(ERN_t₋₁) + b₂ln(SR_t₋₁) + c₂ln(FIX_t₋₁) + ε_2,t

ln(FIX_t) = d₃ + a₃ln(ERN_t₋₁) + b₃ln(SR_t₋₁) + c₃ln(FIX_t₋₁) + ε_3,t

ε_t|Ω_t−1∼(0,Ht), H_t = D_tR_tD_t, $D_{t} = d i a g (h_{11, t}^{1 / 2}, h_{22, t}^{1 / 2}, h_{33, t}^{1 / 2})$ ⁠,

$h_{i i, t} = ω_{i} + α_{i} ε_{i, t - 1}^{2} + β_{i} h_{i, t - 1}, \forall i = 1, 2, 3$

$R_{t} = d i a g (q_{11, t}^{- 1 / 2}, q_{22, t}^{- 1 / 2}, q_{33, t}^{- 1 / 2}) Q_{t} d i a g (q_{11, t}^{- 1 / 2}, q_{22, t}^{- 1 / 2}, q_{33, t}^{- 1 / 2})$

$Q_{t} = (1 - θ_{1} - θ_{2}) \bar{Q} + θ_{1} z_{t - 1} z_{t - 1}^{'} + θ_{2} Q_{t - 1}$

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