Time series analysis-based seasonal autoregressive fractionally integrated moving average to estimate hepatitis B and C epidemics in China

Figure 1 Time series graphs displaying the incidence cases, trend, cyclicity, and seasonality of hepatitis B and C. A: Hepatitis B incidence cases and the decomposed trend and cyclicity by Hodrick-Prescott (HP) method; B: Seasonal factor for hepatitis B series; C: Hepatitis C incidence cases and the decomposed trend and cyclicity by HP method; D: Seasonal factor for hepatitis C series. It is clear that hepatitis B and C have the same seasonal patterns, a peak in March and a trough in February, and the other months remain relatively stable.

Figure 2 Comparison of the hepatitis B incidence cases with the forecasts under the seasonal autoregressive integrated moving average and seasonal autoregressive fractionally integrated moving average. A: Comparison of the 12-step ahead forecasts under the seasonal autoregressive integrated moving average (SARIMA) and seasonal autoregressive fractionally integrated moving average (SARFIMA); B: Comparison of the 90-step ahead forecasts under the SARIMA and SARFIMA; C: Projection into 2030 under the SARFIMA. The predictive results are plotted in the right of the virtual vertical line. It seemed that the forecasts under the SARFIMA are in closer proximity to the actual hepatitis B incidence values and the predictive hepatitis B incidence curves would reach a plateau in the upcoming years. 95%CI: 95% confidence interval; SARFIMA: Seasonal autoregressive fractionally integrated moving average; SARIMA: Seasonal autoregressive integrated moving average.

Figure 3 Comparison of the hepatitis C incidence cases with the forecasts under the seasonal autoregressive integrated moving average and seasonal autoregressive fractionally integrated moving average. A: Comparison of the 12-step ahead forecasts under the seasonal autoregressive integrated moving average (SARIMA) and seasonal autoregressive fractionally integrated moving average (SARFIMA); B: Comparison of the 90-step ahead forecasts under the SARIMA and SARFIMA; C: Projection into 2030 under the SARFIMA. The predictive results are plotted in the right of the virtual vertical line. It appeared that the forecasts under the SARFIMA are in closer proximity to the actual hepatitis C incidence values and the predictive hepatitis C incidence cases would begin to recede in the next years. 95%CI: 95% confidence interval; SARFIMA: Seasonal autoregressive fractionally integrated moving average; SARIMA: Seasonal autoregressive integrated moving average.