Table 2.

Optimal parameter estimates with time lag $l=2$. One-hundred different initial processes are randomly implemented. The related mean and standard deviation (sd) are calculated based on 100× outcomes.

Estimates	${\mathit{\sigma }}_{\left(\mathit{\lambda }\right)}$	${\mathit{\sigma }}_{\left(\mathit{\psi }\right)}$	${\mathit{\sigma }}_{\left(\mathit{\theta }\right)}$	${\mathit{\sigma }}_{\left(\mathit{\zeta }\right)}$	${\mathit{\alpha }}^{\left(\mathit{\lambda }\right)}$	${\mathit{\alpha }}^{\left(\mathit{\psi }\right)}$	${\mathit{\alpha }}^{\left(\mathit{\theta }\right)}$	${\mathit{\alpha }}^{\left(\mathit{\zeta }\right)}$
mean	0.851	0.836	0.816	0.853	0.220	−0.136	0.173	−0.233
sd	0.121	0.113	0.107	0.124	0.911	0.929	0.958	0.991
estimates	${\beta }_1^{\left(\psi \right)}$	${\beta }_1^{\left(\zeta \right)}$	${\beta }_2^{\left(\zeta \right)}$	${\beta }_3^{\left(\zeta \right)}$	${\beta }_4^{\left(\zeta \right)}$	${\epsilon }_{AL}$	${\epsilon }_{AK}$	${\epsilon }_{AZ}$
mean	−0.300	0.232	−0.064	−0.119	−0.076	0.731	0.774	0.764
sd	0.873	1.068	1.004	1.180	1.085	0.285	0.286	0.269
estimates	${\epsilon }_{AR}$	${\epsilon }_{CA}$	${\epsilon }_{CO}$	${\epsilon }_{CT}$	${\epsilon }_{DE}$	${\epsilon }_{FL}$	${\epsilon }_{GA}$	${\epsilon }_{HI}$
mean	0.739	0.697	0.754	0.776	0.744	0.732	0.730	0.693
sd	0.286	0.296	0.284	0.270	0.285	0.301	0.275	0.297
estimates	${\epsilon }_{ID}$	${\epsilon }_{IL}$	${\epsilon }_{IN}$	${\epsilon }_{IA}$	${\epsilon }_{KS}$	${\epsilon }_{KY}$	${\epsilon }_{LA}$	${\epsilon }_{ME}$
mean	0.707	0.673	0.781	0.715	0.696	0.751	0.816	0.784
sd	0.253	0.278	0.284	0.285	0.292	0.281	0.296	0.290
estimates	${\epsilon }_{MD}$	${\epsilon }_{MA}$	${\epsilon }_{MI}$	${\epsilon }_{MN}$	${\epsilon }_{MS}$	${\epsilon }_{NJ}$	${\epsilon }_{NM}$	${\epsilon }_{NY}$
mean	0.780	0.658	0.740	0.724	0.758	0.708	0.858	0.780
sd	0.301	0.291	0.296	0.289	0.308	0.291	0.273	0.306
estimates	${\epsilon }_{MO}$	${\epsilon }_{MT}$	${\epsilon }_{NE}$	${\epsilon }_{NV}$	${\epsilon }_{NH}$	${\epsilon }_{NC}$	${\epsilon }_{ND}$	${\epsilon }_{OH}$
mean	0.716	0.757	0.732	0.780	0.776	0.793	0.769	0.710
sd	0.299	0.281	0.298	0.303	0.284	0.273	0.284	0.301
estimates	${\epsilon }_{OK}$	${\epsilon }_{OR}$	${\epsilon }_{PA}$	${\epsilon }_{RI}$	${\epsilon }_{TX}$	${\epsilon }_{SC}$	${\epsilon }_{SD}$	${\epsilon }_{TN}$
mean	0.667	0.732	0.742	0.763	0.812	0.765	0.746	0.729
sd	0.294	0.277	0.306	0.283	0.296	0.279	0.273	0.290
estimates	${\epsilon }_{UT}$	${\epsilon }_{VT}$	${\epsilon }_{VA}$	${\epsilon }_{WA}$	${\epsilon }_{WV}$	${\epsilon }_{WI}$	${\epsilon }_{WY}$	${\epsilon }_{DC}$
mean	0.736	0.742	0.687	0.757	0.805	0.779	0.727	0.791
sd	0.291	0.287	0.327	0.283	0.287	0.300	0.289	0.296