全国碳市场收益率多期分位数预测与区间校准

Multi-Horizon Quantile Forecasting and Interval Calibration of Returns in China’s National Carbon Market

摘要: 本文以中国全国碳市场碳排放配额(CEA)收益率为研究对象，在严格样本外框架下对未来5个和20个交易日的累计对数收益率开展条件分位数预测，并利用0.05和0.95分位数构造名义90%预测区间。针对不同预测期限可能具有不同信息需求的特点，本文构建分期限差异化分位数预测方法：5日预测采用S、SL和SLM三个信息集的同分位数预测等权组合，20日预测采用基于vol₂₀阈值的波动状态门控，以此作为提高多期限分位数预测精度的核心预测结构。在此基础上，进一步采用序贯共形化分位数回归(Sequential Conformalized Quantile Regression, Sequential CQR)作为区间校准工具，根据历史已实现预测误差对原始区间进行动态修正。相较于采用相同Sequential CQR校准规则的基准方法(S_CQR)，本文方法在全滚动样本中的Mean Pinball Loss分别下降约2.13%和7.00%，且相对于基准方法(S_CQR)的平均损失差在多种稳健检验下均达到统计显著水平。未经校准的5日和20日预测区间Coverage分别为80.79%和65.79%，经Sequential CQR校准后提高至89.27%和88.55%，接近90%的名义覆盖水平。进一步研究发现，本文方法的预测优势在2025~2026后段样本中明显减弱，且不再具有统计显著性。研究结果表明，分期限差异化预测结构是提升多期分位数预测精度的主要来源，而Sequential CQR主要用于改善原始预测区间的覆盖可靠性。

Abstract: This study examines the cumulative log returns of China Emission Allowances (CEA) in China’s national carbon market and conducts conditional quantile forecasting for 5- and 20-trading-day horizons under a strict out-of-sample framework. Nominal 90% prediction intervals are constructed using the 0.05 and 0.95 conditional quantiles. To accommodate horizon-specific information needs, this study first constructs a horizon-specific quantile forecasting structure as the core forecasting layer: same-quantile forecasts from S, SL and SLM are equally weighted for the 5-day horizon, whereas a threshold-based volatility-state gating rule is used for the 20-day horizon. On this basis, Sequential CQR is employed as a post-calibration tool to adjust the raw prediction intervals using previously realized forecast errors. Relative to the benchmark method (S_CQR) under the same Sequential CQR calibration rule, the proposed horizon-specific forecasting structure reduces Mean Pinball Loss by approximately 2.13% and 7.00% for the 5-day and 20-day horizons, respectively, and the corresponding average loss differentials are statistically significant under multiple robustness checks. Before calibration, the interval coverage rates are 80.79% and 65.79%; after Sequential CQR calibration, they increase to 89.27% and 88.55%, respectively, approaching the nominal 90% coverage level. Further analysis shows that the method’s forecasting advantage weakens in the later evaluation subsample covering 2025~2026 and is no longer statistically significant. These findings indicate that the horizon-specific differentiated forecasting structure is the primary source of improved multi-horizon quantile forecasting accuracy, whereas Sequential CQR is mainly used to improve the coverage reliability of the raw prediction intervals.