Estimation and Properties of a Time-Varying GQARCH(1,1)-M Model

Table 2

Bayesian inference results.

Dow-Jones	PM	PSD	𝜙0.5	𝜙min	𝜙max	IF
𝛿	0.052	0.041	0.054	−0.048	0.103	3.001
𝜑	0.812	0.082	0.854	−0.992	0.999	2.115
𝜑^2𝑢	0.010	0.034	0.013	0.002	0.018	1.509
𝜔	0.405	0.071	0.461	0.004	0.816	2.367
𝛼	0.152	0.040	0.291	0.001	0.873	1.048
𝛽	0.651	0.168	0.629	0.003	0.984	2.994
𝛾	0.392	0.112	0.393	−0.681	0.418	5.108
FTSE	PM	PSD	𝜙0.5	𝜙min	𝜙max	IF
𝛿	0.059	0.036	0.059	−0.051	0.395	3.111
𝜑	0.811	0.096	0.839	−0.809	0.999	2.154
𝜑^2𝑢	0.009	0.029	0.012	0.005	0.017	1.995
𝜔	0.205	0.087	0.398	0.003	0.995	1.457
𝛼	0.140	0.055	0.187	0.001	0.931	3.458
𝛽	0.682	0.153	0.701	0.001	0.988	2.721
𝛾	0.374	0.102	0.381	−0.615	0.401	1.254
Nikkei	PM	PSD	𝜙0.5	𝜙min	𝜙max	IF
𝛿	0.068	0.051	0.068	−0.064	0.211	2.998
𝜑	0.809	0.090	0.837	−0.831	0.999	1.211
𝜑^2𝑢	0.010	0.031	0.010	0.004	0.019	2.001
𝜔	0.195	0.079	0.228	0.004	0.501	2.789
𝛼	0.149	0.052	0.197	0.001	0.893	3.974
𝛽	0.634	0.119	0.645	0.006	0.989	1.988
𝛾	0.408	0.123	0.409	−0.587	0.487	4.007

Note: PM denotes posterior mean, PSD posterior standard deviation, 𝜙_0.5 posterior median, 𝜙_min posterior minimum, 𝜙_max posterior maximum, and IF inefficiency factor.