Fig 1.
Monthly incidence of hepatitis from January 2005 to December 2012.
Table 1.
The ADF test of the transformed hepatitis incidence series.
Fig 2.
The ACF and PACF graphs of transformed hepatitis incidence series.
ACF = the autocorrelation function graph and PACF = partial autocorrelation graph. The possible values of q and Q were 1, 2, 3 and 1 basic on the ACF graph, and the possible values of p and P were 1, 2, 3 and 1 basic on the PACF graph.
Table 2.
The parameters of the three ARIMA models.
Table 3.
Estimate parameters of the ARIMA (0,1,2)(1,1,1)12 model.
Fig 3.
The RMSE of each basic GRNN models.
RMSE = root mean square error; N = the number of input of the basic GRNN model. When the N was 9, the basic GRNN model had the minimum RMSE.
Fig 4.
The selection of the basic GRNN model.
GRNN = the generalized regression neural network. (A) The smoothing factor between 0.3 and 3.0 with an interval of 0.1 or 0.2 were selected to find the minimum RMSE for the basic GRNN model. The GRNN model has lowest RMSE when the smoothing factor came to 1.8. (B) The RMSE showed increase trend when the smoothing factor was higher than 0.3 or lower than 3.0.
Fig 5.
The selection of the ARIMA-GRNN model.
ARIMA = the autoregressive integrated moving average; GRNN = the generalized regression neural network. (A) The smoothing factor between 0.01 and 0.40 with an interval of 0.01 were selected to find the minimum RMSE for the GRNN model. The GRNN model has lowest RMSE when the smoothing factor came to 0.07. (B) The RMSE showed increase trend when the smoothing factor was higher than 0.40 or lower than 0.01.
Fig 6.
The fitting curves of the three models and the actual hepatitis incidence series.
ARIMA = the autoregressive integrated moving average; GRNN = the generalized regression neural network.
Fig 7.
The forecasting curves of the three models and the actual hepatitis incidence series.
ARIMA = the autoregressive integrated moving average; GRNN = the generalized regression neural network.
Table 4.
The fitting and forecasting performance of the three models.