. 2021 Feb 17;15(1):1. doi: 10.1186/s11782-021-00097-7

Table 8.

Asymmetric BEKK-GARCH model estimation results

	$R_{m, t}^{c}$	$R_{a, t}^{c}$	$R_{d, t}^{c}$
Mean equation
γ_{i, 11}	0.013 (0.655)	− 0.161*** (− 8.236)	2.487 × 10^− 3 (− 0.122)
γ_{i, 12}	0.287*** (14.047)	−0.038*** (− 2.855)	0.247*** (8.962)
γ_{i, 21}	−6.973 × 10^− 3 (− 0.466)	2.683 × 10^− 3 (0.167)	−3.091 × 10^− 3 (− 0.354)
γ_{i, 22}	−0.049** (− 2.110)	−0.045** (− 2.145)	−0.050** (− 2.283)
Variance equation
a_{i, 11}	0.170*** (8.341)	0.266*** (18.900)	0.228*** (12.724)
a_{i, 12}	−0.075** (− 2.735)	− 0.024 (− 1.252)	−0.044*** (− 3.003)
a_{i, 21}	0.025 (1.155)	0.015 (1.440)	−0.050 (− 1.490)
a_{i, 22}	0.053 (1.000)	− 0.025 (− 0.587)	0.019 (0.440)
b_{i, 11}	0.978*** (232.517)	0.962*** (269.475)	0.972*** (271.051)
b_{i, 12}	0.014** (2.240)	3.587 × 10^− 3 (0.737)	0.012*** (3.094)
b_{i, 21}	−0.029*** (− 4.055)	−0.011** (− 2.072)	−0.041*** (− 4.454)
b_{i, 22}	0.892*** (105.880)	0.897*** (127.187)	0.897*** (120.926)
d_{i, 11}	−0.117*** (− 2.846)	−0.038 (− 0.970)	−0.084** (− 2.369)
d_{i, 12}	−0.080*** (− 3.167)	−0.091*** (− 3.877)	−0.078*** (− 4.879)
d_{i, 21}	−0.077** (− 3.512)	−0.047*** (− 3.134)	−0.127*** (− 4.517)
d_{i, 22}	−0.506*** (− 19.320)	−0.509*** (− 21.449)	−0.489*** (− 19.543)

Notes. This table shows the estimation results of the asymmetric BEKK-GARCH model. The maximum likelihood estimation is applied, and the estimation method is Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. The results are converged within 100 iterations. The sample period spans from January 1, 2010, to March 31, 2020. $R_{m, t}^{c}$ , $R_{a, t}^{c}$ , and $R_{d, t}^{c}$ denote different $R_{i, t}^{c}$ in the mean equation of the asymmetric BEKK-GARCH model. The estimations of the constants in the mean and variance equations are omitted. The t-statistics of the coefficients are shown in parenthesis. One, two and three asterisks (*), respectively, indicate that the t-values are significant at the 0.1, 0.05, and 0.01 level