
\( {R}_{m,t}^c \)

\( {R}_{a,t}^c \)

\( {R}_{d,t}^c \)


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 BEKKGARCH model. The maximum likelihood estimation is applied, and the estimation method is BroydenFletcherGoldfarbShanno (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 BEKKGARCH model. The estimations of the constants in the mean and variance equations are omitted. The tstatistics of the coefficients are shown in parenthesis. One, two and three asterisks (*), respectively, indicate that the tvalues are significant at the 0.1, 0.05, and 0.01 level