2.1 Draw the sequence diagram
Draw the Zhengzhou region from January 2018 to January 2020 HRSV infection incidence of ALRTI time sequence diagram.The Fig. 1 shown in Zhengzhou region from January 2018 to January 2020 HRSV infection ALRTI has obvious seasonal disease (12 months for fashion cycles).Every popular cycle there is a popular boom,peaked in November to February of the next year.This sequence has the characteristics of both the seasonal cyclical fluctuations and has a rising trend year by year,so, we adopt the product of ARIMA model.
2.2 Sequence tranquilization
Zhengzhou region from January 2018 to January 2020 HRSV infection incidence of ALRTI time sequence diagram showed a trend of cyclical fluctuations,it can't meet the requirements of a stabilized.According to the characteristics of the seasonal fluctuation sequence diagram to natural logarithm conversion and the sequence of the primary season one order difference.After the difference of time series autocorrelation function and partial autocorrelation function has no obvious truncation and trailing phenomenon(Fig. 2,3),is also not a linear attenuation trend.Difference after time sequence diagram (Fig. 4) is close to a smooth, after the difference sequence suitable for time series model.
2.3 The parameters of the model estimation and diagnosis
After determining model type, need to determine the P, d, q and P, d, q value,and to formulate stage for the model.According to the sequence of season change characteristics and smooth processing d = 0, D = 1.Based on the autocorrelation function and partial autocorrelation function diagram, P = 1, q = 1.Season model P, Q value is difficult to determine, in accordance with the relevant research , combined with the goodness of fit of the model and residual error and coefficient of correlation between estimates.Using Ljung-Box tests of residual white noise, eliminate the non-white noise model.After the test,model ARIMA(1,0,1)(0,1,1)12 had the minimum standardized BIC (1.457),smooth R2 = 0.216.Residual error sequence of autocorrelation coefficient and partial correlation coefficients within the 95% confidence interval (Fig. 5),Ljung—Box = 20.787, P = 0.160.Therefor,model ARIMA(1, 0, 1)(0, 1, 1)12 was selected as the optimal model.
2.4 Model to predict
According to ARIMA modeling method, the time series of ALRTI incidence caused by HRSV infection from January 2018 to January 2020 in Zhengzhou were modeled.Then, the monthly incidence of ALRTI caused by HRSV infection from March 2021 to January 2022 was used as validation data, and the sequence diagram of actual and predicted values was drawn, as shown in Fig. 6.According to the predicted value and actual value relative error to the assessment of the effect of forecast model (table 1).