| Objective:To analysis the simulation and forecasting results of different temporal distribution model, the incidence data of hepatitis A was fitted by deterministic analysis, randomness analysis, mixed analysis and the model that independent of distribution tendency, to provide reference for the further research and offer scientific basis for making monitoring and prevention and control tactics of hepatitis A.Methods:Report cards of hepatitis A from Jan 2006 to Dec 2014 was collected from national notifiable disease reported system, permanent residents population was collected Zhejiang CDC and compute the monthly incidence of hepatitis A; sequence diagram was used to present the distribution characteristics; ARIMA model, Exponential Smoothing Method, Auto-Regressive Model and Grey Model was used to simulate the incidence from Jan 2006 to Dec 2013 and the incidence from Jan 2006 to Dec 2011,R2, AIC, SBC was taken as the assessment indicators, the models that built in this study was used to forecast the incidence of 2014to 2015 and the incidence of 2012 to 2015, MSE, RMSE and MAPE was taken as the assessment indicators of the optimization model. In this study, the collation of data was processed by Excel 2013, model fitting was processed by SAS 9.2 and SPSS 20.0 statistical analysis software.Results:The monthly incidence from Jan 2006 to Dec 2013 was fitted by ARIMA(2,1,1) (0,1,1)12NOINT, ARIMA(1,1,1)(0,1,1)12 NOINT and ARIMA(0,1,1)(0,1,1)12 NOINT, the parameters was significance in this three ARIMA model, residual series was white noise, according to the criteria of optimization ARIMA model, the fewer parameters the better and the smaller AIC and SBC the better, ARIMA(1,1,1)(0,1,1)12 NOINT was supposed to be the best fitted model. The simulation results of monthly incidence from Jan 2006 to Dec 2013 by exponential smoothing method using damped trend, simple seasonal, winters additive and winters multiplicative showed that the MSE, RMSE, MAPE and BIC of winters multiplicative was the smallest, winters multiplicative was the best fitting exponential smoothing method. The R2 of auto-regressive model was 0.86, which was better than ordinary least squares estimation, DW statistics was 1.94, which means that the residual series was not self-related, the model was fitted well and the seasonal trend general trend was perfectly simulated. The posterior error ratio of the GM(1,1) model that built in this study was 0.4902, small error possibility was 0.8316, refer to the evaluation criteria of grey model, the level of the grey model that built in this study was qualified and could be used for the short-term prediction.The monthly incidence from Jan 2006 to Dec 2011 was fitted by ARIMA((1,12),1, (1,12))NOINT, ARIMA((1,12),1,1)NOINT and ARIMA((12),1,1) NOINT, residual series was white noisein the three ARIMA model, according to the criteria of optimization ARIMA model, ARIMA((12),1,1) NOINT was supposed to be the best fitted model. The simulation results of monthly incidence from Jan 2006 to Dec 2011 by exponential smoothing method using damped trend, simple seasonal, winters additive and winters multiplicative showed that the MSE, RMSE, MAPE and BIC of winters multiplicative was the smallest, winters multiplicative was the best fitting exponential smoothing method. The R2of auto-regressive model was 0.89, which was better than ordinary least squares estimation, DW statistics was 2.03, which means that the residual series was not self-related, the model was fitted well and the seasonal trend general trend was perfectly simulated. The posterior error ratio of the GM (1,1) model that built in this study was 0.5594, small error possibility was 0.7887, refer to the evaluation criteria of grey model, the level of the grey model that built in this study was basic qualification.ARIMA model, winters multiplicative of exponential smoothing method, auto-regressive model and GM(1,1) model, which modeled by the monthly incidence from Jan 2006 to Dec 2013 and the monthly incidence from Jan 2006 to Dec 2011, was used for the incidence forecasting of 2014-2015 and 2012-2015, MSE, RMAE, MAPE of short-term forecast model was smaller than that of long-term forecast model, MSE, RMAE, MAPE of short-term winters multiplicative was 0.0003,0.0181 and 18.2777, the indicator was the smallest among the four model which means the winters multiplicative had the best forecasting effect.Conclusions:The forecast results of different temporal distribution model show that, the models were fitted for short-time forcast, within the short-time forcast, winters multiplicative of exponential smoothing method makes the best fitting of overall trend and seasonal trend; the auto-regressive model is secondary, which makes good forecast of overall trend, however, the seasonal trend is not well predicted; ARIMA model could couple the overall trend and the seasonal trend, but the precision is not so well; grey model have advantage in the analysis of time series without trend, however, the seasonal trend of time series is not well fitted. |
