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.