Fig 1.
The annual morbidity of tuberculosis from 2008 to 2012 in Xinjiang and in China.
Xinjiang is one of the autonomous regions of China; its morbidity of tuberculosis (TB) is much higher than the national situation.
Fig 2.
Tuberculosis morbidity from January 2004 to June 2014 in Xinjiang.
The Data was obtained from the website of Bureau of Health, Xinjiang Uyghur Autonomous Region, China. The tuberculosis morbidity has roughly seasonal fluctuations and slightly rising trend.
Table 1.
The ADF test of the transformed tuberculosis morbidity series.
Fig 3.
The ACF and PACF graphs of stabilized tuberculosis morbidity series.
ACF = autocorrelation function, PACF = partial autocorrelation function. Based on the ACF, we determine the possible values of q (q = 1, 2 or 3) and Q(Q = 1) of ARIMA (p, d, q) (P, D, Q) 12, and based on PACF, we determine the possible values of p (p = 1, 2 or 3) and P (P = 1) of ARIMA (p, d, q) (P, D, Q)12.
Table 2.
The six ARIMA models with their AIC and SBC values.
Fig 4.
Histogram-Normality test of residual series of the ARIMA (1, 1, 2) (1, 1, 1)12 model.
Skewness is not 0, Kurtosis is more than 3, Probability is 0.000000, all that suggest the residual series do not obey normal distribution and obey heavier-tailed distribution.
Fig 5.
Fitted values of ARIMA (1, 1, 2) (1, 1, 1)12 model and ARIMA (1, 1, 2) (1, 1, 1)12-ARCH (1) model versus the actual monthly morbidity of tuberculosis before December 2013.
We can see fitting performance of the two models by this Figure.
Fig 6.
Forecast values of ARIMA (1, 1, 2) (1, 1, 1)12 model and ARIMA (1, 1, 2) (1, 1, 1)12-ARCH (1) model versus the actual monthly morbidity of tuberculosis from January 2014 to June 2014.
We can see predication performance of the two models by this Figure.
Table 3.
Forecasting performance comparison by RMSE, MAE and MAPE.