A Comparison Of The Prediction Effect Between The Single ARIMA Model And The ARIMA-GRNN Combination Model In The Monthly Incidence Of Scarlet Fever

Abstract Objective To arrange the epidemic data of the monthly incidence of scarlet fever in one city, from 1985 to 2008. To explore the application of the single auto regressive integrated moving average model (ARIMA) and the auto regressive integrated moving average-generalized regression neural network (GRNN) combination model in the fitting and forecasting research of the monthly incidence of scarlet fever from 1985 to 2008. Methods Collected the monthly incidence of scarlet fever from 1985 to January 2008 and the monthly data of meteorological factors from 1985 to 2006. The univariate analysis was made between the monthly incidence of scarlet fever and meteorological factors. The epidemic data of the monthly incidence of scarlet fever from 1985 to 2008 was analyzed, and then the appropriate time period data was selected for building model. Firstly, the auto regressive integrated moving average model was established. Then the fitting values of the ARIMA model of the monthly incidence of scarlet fever was used as input of the GRNN, and the actual values of the monthly incidence of scarlet fever was used as output of the GRNN. The GRNN was trained, and then we compared the effect of the single ARIMA model and the ARIMA-GRNN combination model. Results There might be statistical association between the monthly incidence of scarlet fever and the average air temperature, the average relative humidity, the lowest temperature.?The time series analysis had the advantage that the time variable synthetically substituted all factors in the time series analysis. It was not necessary to know the relevant factors affected the outcome variable. So we did not consider the effect of the meteorological factors on the incidence of scarlet fever in the subsequent modeling. After a preliminary analysis, the epidemic data of the monthly incidence of scarlet fever from 1990 to 2008 was chose and used to establish ARIMA model. The Cox-Stuarts trend test indicated that there was no rising or falling trend in epidemic data of the monthly incidence of scarlet fever from 1990 to 2008. Meanwhile, the white noise test also suggested there was a certain amount of information but not white noise in the monthly incidence of scarlet fever from 1990 to 2008. Finally, SPSS19.0 Expert Modeler indicated that ARIMA(0,0,2)×(1,0,1)12 was optimal model,the expression of model was(1 - 0.974 B¹²)X_t= 0.15 +(1 + 0.366 B + 0.363 B² )(1 - 0.863B¹² )ε_t. The white noise test suggested that the residual of ARIMA was white noise (Box-Ljung Q statistic was 15.857, P=0.322). The smooth factor of GRNN was increased from 0.001 to 0.02 by 0.001, then root mean square error (RMSE) was calculated. Finally, the optimal smooth factor was set as 0.007, the RMSE was minimum. The mean error rate (MER) of the single ARIMA model and the ARIMA-GRNN combination model were 35.5%, 31.2%, respectively; determination coefficient (R²) of two models were 0.703, 0.761, respectively. Conclusion The single ARIMA model and the ARIMA-GRNN combination model both could be used in the fitting and forecasting research of the monthly incidence of scarlet fever from 1990 to 2008. However, the fitting efficacy of the ARIMA-GRNN combination model was better than the single ARIMA, which had practical value in the research of time series data such as the incidence of scarlet fever.