Multiplicative Holt-Winters method: pseudo-parameter and mean absolute percentage error (MAPE) values.

Median (and inter-quartile range) pseudo-parameter α, β, and γ values—which smooth control level, trend, and seasonal time-series components, respectively—reflect fitting of B = 500 bootstrap-generated full-length pseudo-time-series with the seasonal multiplicative Holt-Winters method. The greater the pseudo-parameter value, the shorter the smoothing memory, i.e., information from the recent-past have more pronounced effects on estimates than those from the distant-past. Generally, the strength of pseudo-parameters follows γ≫α≥β, which is expected for time-series with highly seasonal and negligible trend components. Furthermore, large mean absolute percentage error (MAPE) values between observed monthly consultation rates and their median forecasts imply low accuracy and vice-versa. Thus, 92% of the 24 time-series (TS) forecasts generated here (2 forecast horizons, 3 diseases, and 4 age categories = 24 TS forecasts) are reasonably accurate, i.e., their MAPE values are circa 25%. MAPE values from a seasonal adjustment (SA3) forecasting method [32] are also listed for benchmark comparison. The MHW performance is equal or superior to that of the SA3 forecasting benchmark in 87.5% of the 24 TS forecasts generated here, as implied by equal or smaller MAPE values.

中位数（及四分位距（inter-quartile range））的伪参数（pseudo-parameter）α、β、γ值分别用于平滑控制水平、趋势项与季节性时间序列分量，其取值反映了采用乘法型季节性霍尔特-温特斯（Holt-Winters）方法对B=500条自助法（bootstrap）生成的全长伪时间序列的拟合效果。伪参数的取值越大，平滑记忆长度越短，即近期历史信息对参数估计的影响显著强于远期历史信息。通常，伪参数的强度遵循γ≫α≥β的规律，这对于强季节性且趋势可忽略的时间序列而言符合预期。此外，观测月度就诊率与其中位数预测值之间的平均绝对百分比误差（mean absolute percentage error, MAPE）越大，代表预测精度越低，反之亦然。据此，本次生成的24条时间序列（time series, TS）预测结果中（包含2种预测跨度、3种疾病与4个年龄组，共计24条TS预测），有92%的预测精度处于合理区间，即其MAPE值约为25%。文中还列出了季节性调整（seasonal adjustment, SA3）预测方法[32]的MAPE值作为基准对照。从MAPE值相等或更小的结果来看，本次生成的24条TS预测中，有87.5%的预测结果的MHW性能优于或等于SA3预测基准。