Research on the predictive effect of a combined model of ARIMA and neural networks on human brucellosis in Shanxi Province, China: a time series predictive analysis

Table 2 Selection of the optimal model from among the four candidate models

Candidate models	Parameter estimate				Fitting index			Ljung-Box Test
Candidate models	AR1	SAR1	MA1	SMA1	AIC	SBC	R²	χ2	P
ARIMA (1,1,0) (1,1,0)₁₂	−0.0914	− 0.3839*	–	–	− 363.82	− 358.47	0.929	18.42	0.6807
ARIMA (0,1,1) (0,1,1)₁₂	–	–	−0.7900*	−0.9913*	− 374.14	−368.79	0.938	21.60	0.4843
ARIMA (1,1,1) (1,1,0)₁₂	−0.2288	−0.3835*	0.1363	–	− 361.82	− 353.80	0.929	18.43	0.6217
ARIMA (1,1,1) (0,1,1)₁₂	−0.3295	–	−0.2707	0.6712*	−374.03	− 366.00	0.937	24.04	0.2909

*P ≤ 0.05. The residuals of the four candidate models were tested using the Ljung-Box Test

ISSN: 1471-2334