时间异质性下共享单车需求的共形预测——分组覆盖偏差的分解与校准

Conformal Prediction for Bike-Sharing Demand under Temporal Heterogeneity—Decomposition and Calibration of Group Coverage Deviations

摘要: 共享单车需求具有明显的日内周期和时间异质性，预测区间的边际覆盖率达到目标水平，并不意味着不同时段都具有相同的覆盖表现。以首尔共享单车小时需求数据为例，采用线性回归和梯度提升树作为点预测模型，在按时间顺序划分的训练集、校准集和测试集上构造90%的分割共形预测区间，并比较边际覆盖率与分组覆盖率。结果显示，两类模型的边际覆盖率分别为0.974和0.930，均达到目标水平，但梯度提升树在早、晚高峰的分组覆盖率仅为0.800和0.767。为解释这种现象，将用于判定分组是否欠覆盖的相对尺度分解为分组尺度成分和尺度错配成分。结果表明，某一时段是否出现欠覆盖，不仅与该时段误差尺度相对测试集整体的高低有关，也与校准集和测试集之间的整体误差尺度错配有关。进一步采用分组共形校准后，梯度提升树早高峰覆盖率由0.800提高到0.907，而晚高峰仅提高到0.806，两个高峰时段的改善幅度与校准集中各时段的误差尺度差异能否反映测试集中的相应差异有关。上述分析为解释边际覆盖达标而部分时段仍出现欠覆盖的现象提供了一个简单框架，也可作为计量经济学和时间序列课程中由点预测拓展到区间预测与不确定性量化的教学案例。

Abstract: Bike-sharing demand exhibits pronounced intraday patterns and temporal heterogeneity. Achieving the target marginal coverage rate for prediction intervals does not necessarily imply comparable coverage across different time periods. Using hourly bike-sharing demand data from Seoul, linear regression and gradient boosting are employed as point prediction models, and 90% split conformal prediction intervals are constructed using chronologically ordered training, calibration, and test sets. The marginal coverage rates of the two models are 0.974 and 0.930, respectively, both reaching the target level, whereas the group coverage rates of the gradient boosting model are only 0.800 and 0.767 during the morning and evening peak periods. To explain this phenomenon, the relative scale used to determine whether a group is undercovered is decomposed into a group-specific scale component and a scale-mismatch component. The results show that whether a given period is undercovered depends not only on its error scale relative to that of the overall test set, but also on the mismatch in overall error scale between the calibration and test sets. After applying group-wise conformal calibration, the morning-peak coverage rate of the gradient boosting model increases from 0.800 to 0.907, whereas the evening-peak coverage rate rises only to 0.806. The extent of improvement in each peak period is related to whether the between-group differences in error scale observed in the calibration set reflect the corresponding differences in the test set. These findings provide a simple framework for explaining why marginal coverage can reach the target while some time periods remain undercovered, and they also offer a teaching case for extending econometrics and time-series courses from point prediction to interval prediction and uncertainty quantification.