Table AI. The estimates of the GARCH...

Table AI.

The estimates of the GARCH models to calculate the volatilities of the FFA returns for different dry bulk sectors

Capesize	Q1	Q2	Q3	Q4
C₀	−0.00463 (−1.053)	−0.0043 (−1.139)	−0.0037 (−1.004)	−0.010 (−1.556)
C₁	0.276^*** 3.990)	0.307^*** (4.768)	0.327^*** (4.857)	0.179^** (2.558)
ω	0.0009^*** (2.804)	0.0012^*** (4.343)	0.0005^*** (4.246)	0.0078^***(8.386)
α	0.184^*** (3.055)	0.654^*** (6.086)	0.191^*** (3.962)	0.324^*** (5.610)
β	0.668^*** (8.004)	0.368^*** (5.490)	0.692^*** (14.650)	−0.062 (−0.561)
Diagnostics
Adjusted R²	0.061	0.026	0.014	−0.038
Log-likelihood	389.53	378.10	406.262	296.04
DW Statistics	2.014	2.127	2.210	2.332
AIC	−2.457	−2.361	−2.572	−1.878
SC	−2.397	−2.302	−2.512	−1.817
ARCH(12)	0.512 (0.907)	0.499 (0.915)	0.409 (0.960)	0.072 (1.000)
Panamax
C₀	−0.0034 (−1.371)	−0.0031 (−1.006)	−0.0043 (−1.777)	0.003 (0.518)
C₁	0.185^*** (3.356)	0.102 (1.593)	0.230^*** (3.742)	0.044 (0.465)
ω	0.0002^** (2.081)	0.0001^* (1.885)	0.0001^** (2.516)	0.005^*** (14.225)
α	0.243^*** (3.716)	0.209^*** (5.027)	0.201^*** (4.257)	0.177^** (2.784)
β	0.701^*** (8.619)	0.806^*** (27.55)	0.751^*** (16.681)	−0.059 (−1.434)
Diagnostics
Adjusted R²	0.030	0.010	0.006	−0.032
Log-likelihood	512.508	485.79	511.05	401.53
DW Statistics	1.986	1.982	2.151	2.472
AIC	−3.243	−3.043	−3.244	−2.558
SC	−3.183	−2.984	−3.184	−2.498
ARCH(12)	1.572 (0.099)	0.221 (0.997)	0.266 (0.994)	1.099 (0.361)
Supramax
C₀	−0.0034 (−1.507)	−0.0051^** (−2.186)	−0.004^** (−1.916)	−0.003 (−1.625)
C₁	0.187^*** (2.974)	0.087 (1.206)	0.214^*** (3.252)	0.189 (26.440)
ω	0.000^*** (3.175)	0.000^*** (2.703)	0.0002^*** (3.03)	0.000 (5.433)
α	0.193^*** (4.212)	0.080^*** (3.904)	0.210^*** (3.434)	−0.039 (−9.863)
β	0.787^*** (20.13)	0.891^*** (37.543)	0.639^*** (7.358)	1.013 (124.376)
Diagnostics
Adjusted R²	0.014	−0.0068	0.017	−0.009
Log-likelihood	598.51	579.43	591.43	628.91
DW Statistics	2.050	2.092	1.89	2.141
AIC	−3.554	−3.450	−3.654	−3.736
SC	−3.497	−3.393	−3.595	−3.679
ARCH(12)	1.198 (0.284)	0.068 (1.000)	1.187 (0.291)	1.594 (0.092)

Capesize	Q1	Q2	Q3	Q4
C₀	−0.00463 (−1.053)	−0.0043 (−1.139)	−0.0037 (−1.004)	−0.010 (−1.556)
C₁	0.276^*** 3.990)	0.307^*** (4.768)	0.327^*** (4.857)	0.179^** (2.558)
ω	0.0009^*** (2.804)	0.0012^*** (4.343)	0.0005^*** (4.246)	0.0078^***(8.386)
α	0.184^*** (3.055)	0.654^*** (6.086)	0.191^*** (3.962)	0.324^*** (5.610)
β	0.668^*** (8.004)	0.368^*** (5.490)	0.692^*** (14.650)	−0.062 (−0.561)
Diagnostics
Adjusted R²	0.061	0.026	0.014	−0.038
Log-likelihood	389.53	378.10	406.262	296.04
DW Statistics	2.014	2.127	2.210	2.332
AIC	−2.457	−2.361	−2.572	−1.878
SC	−2.397	−2.302	−2.512	−1.817
ARCH(12)	0.512 (0.907)	0.499 (0.915)	0.409 (0.960)	0.072 (1.000)
Panamax
C₀	−0.0034 (−1.371)	−0.0031 (−1.006)	−0.0043 (−1.777)	0.003 (0.518)
C₁	0.185^*** (3.356)	0.102 (1.593)	0.230^*** (3.742)	0.044 (0.465)
ω	0.0002^** (2.081)	0.0001^* (1.885)	0.0001^** (2.516)	0.005^*** (14.225)
α	0.243^*** (3.716)	0.209^*** (5.027)	0.201^*** (4.257)	0.177^** (2.784)
β	0.701^*** (8.619)	0.806^*** (27.55)	0.751^*** (16.681)	−0.059 (−1.434)
Diagnostics
Adjusted R²	0.030	0.010	0.006	−0.032
Log-likelihood	512.508	485.79	511.05	401.53
DW Statistics	1.986	1.982	2.151	2.472
AIC	−3.243	−3.043	−3.244	−2.558
SC	−3.183	−2.984	−3.184	−2.498
ARCH(12)	1.572 (0.099)	0.221 (0.997)	0.266 (0.994)	1.099 (0.361)
Supramax
C₀	−0.0034 (−1.507)	−0.0051^** (−2.186)	−0.004^** (−1.916)	−0.003 (−1.625)
C₁	0.187^*** (2.974)	0.087 (1.206)	0.214^*** (3.252)	0.189 (26.440)
ω	0.000^*** (3.175)	0.000^*** (2.703)	0.0002^*** (3.03)	0.000 (5.433)
α	0.193^*** (4.212)	0.080^*** (3.904)	0.210^*** (3.434)	−0.039 (−9.863)
β	0.787^*** (20.13)	0.891^*** (37.543)	0.639^*** (7.358)	1.013 (124.376)
Diagnostics
Adjusted R²	0.014	−0.0068	0.017	−0.009
Log-likelihood	598.51	579.43	591.43	628.91
DW Statistics	2.050	2.092	1.89	2.141
AIC	−3.554	−3.450	−3.654	−3.736
SC	−3.497	−3.393	−3.595	−3.679
ARCH(12)	1.198 (0.284)	0.068 (1.000)	1.187 (0.291)	1.594 (0.092)

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 criterion. DW statistics is the Durbin–Watson statistics. ARCH(12) is Engle’s F-test for ARCH effects. Figures in the brackets under the ARCH(12) estimates indicate the significance levels.

RT_t = C₀ + C₁·RT_t₋₁ + ε_t, ε_t∼(0,h_t), $h_{t} = ω + α ε_{t - 1}^{2} + β h_{t - 1}$

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