We propose and analyse rolling-origin conformal prediction for time-series forecasting. The method calibrates the conformal quantile against the $m$ most recent pseudo-out-of-sample forecast errors, adapting to serial dependence, volatility clustering, and distributional drift that invalidate classical conformal guarantees. Under Hölder-$β$ local stationarity and $α$-mixing, we establish a four-term coverage-error decomposition and derive the optimal calibration window $m^{\star} \asymp T^{2β/(2β+1)}$ with coverage-error rate $O(T^{-β/(2β+1)})$. A Le Cam two-point construction shows this rate is minimax-optimal over the Hölder-$β$ model class. The Bahadur representation is proved under both $α$-mixing and the physical-dependence framework of Wu (2005). An oracle inequality formalises Winkler cross-validation as an adaptive window selector; the required uniform concentration condition is established in an appendix. Validation on six real series and 93 M4 competition series confirms the theory: rolling-origin calibration outperforms full-history calibration in 86\% of comparisons (median Winkler improvement 12.3\%), maintains coverage within $\pm2\%$ of the 90\% target at short and medium horizons, and the cross-frequency log-log regression slope $0.614$ ($95\%$ CI $[0.424, 0.805]$) is consistent with the theoretical $2/3$ after controlling for frequency fixed effects.

翻译：我们提出并分析了用于时间序列预测的滚动起点共形预测方法。该方法利用最近$m$个伪样本外预测误差对共形分位数进行校正，以自适应序列依赖、波动率聚类和分布漂移——这些因素会破坏经典共形预测的保证。在Hölder-$β$局部平稳性和$α$-混合条件下，我们建立了四项覆盖误差分解公式，并推导出最优校准窗口$m^{\star} \asymp T^{2β/(2β+1)}$，其覆盖误差率为$O(T^{-β/(2β+1)})$。通过Le Cam两点构造法证明该速率在Hölder-$β$模型类上达到极小极大最优性。我们在$α$-混合框架和Wu (2005)的物理依赖框架下均证明了Bahadur表示。一条oracle不等式形式化描述了Winkler交叉验证作为自适应窗口选择器的性质；附录中建立了所需的均匀集中条件。在六个真实序列和93个M4竞赛序列上的验证证实了理论：滚动起点校准在86%的比较中优于全历史校准（Winkler中位数改进12.3%），在短中期预测中保持覆盖概率在90%目标值的$\pm2\%$范围内，且跨频率对数-对数回归斜率$0.614$（95%置信区间$[0.424, 0.805]$）在控制频率固定效应后与理论值$2/3$一致。