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

Table 1 Comparison of the forecasting ability under the seasonal autoregressive integrated moving average and the seasonal autoregressive fractionally integrated moving average

Metrics	Hepatitis B		Hepatitis C
	SARIMA	SARFIMA	SARIMA	SARFIMA
12-step ahead forecasts
MAD	16867.708	15211.939	3355.664	3245.308
MAPE	0.191	0.173	0.208	0.201
RMSE	20775.123	18762.935	4093.553	3940.966
MER	0.165	0.149	0.178	0.172
RMSPE	0.267	0.248	0.285	0.279
90-step ahead forecasts
MAD	13423.963	10446.219	2246.348	1586.973
MAPE	0.134	0.106	0.133	0.096
RMSE	15289.986	12577.033	3379.293	2482.687
MER	0.134	0.105	0.112	0.079
RMSPE	0.155	0.137	0.241	0.192

SARIMA: Seasonal autoregressive integrated moving average; SARFIMA: Seasonal autoregressive fractionally integrated moving average; MAD: Mean absolute deviation; MAPE: Mean absolute percentage error; RMSE: Root mean square error; MER: Mean error rate; RMSPE: Root mean square percentage error.

Table 2 Projection into 2030 for hepatitis B and C incidence cases

Time (yr)	Hepatitis B		Hepatitis C
	Forecasts	95%CI	Forecasts	95%CI
2023	1240031	1041413-1438650	210742	141933-279552
2024	1262930	994670-1531191	209337	149760-268915
2025	1245681	953797-1537566	213123	138049-288198
2026	1234951	929339-1540563	209276	117296-301256
2027	1227438	912670-1542207	208070	101135-315004
2028	1221949	900585-1543314	205350	84304-326395
2029	1217813	891418-1544208	203073	69221-336926
2030	1214607	884203-1545011	200514	54983-346044
Mean	1233175	938512-1527839	207436	107085-307786
Total	9865400	7508093-12222709	1659485	856681-2462290

95%CI: 95%confidence interval.