Online Conformal Prediction (CP) struggles to balance temporal adaptability and structural stability. Feedback-driven methods (e.g., Adaptive Conformal Inference (ACI)) suffer from systemic marginal under-coverage and high interval variance during abrupt shifts, while temporally discounted Bayesian CP suffers from severe structural lag and uncalibrated interval bloat. We propose State-Adaptive Bayesian Conformal Prediction (SA-BCP) to achieve optimal spatio-temporal decoupling. By gating long-term temporal inertia with spatial kernel-density evidence, SA-BCP proactively expands intervals for recognized historical regimes while maintaining tight efficiency during stable states. We rigorously prove this mechanism's optimality, identifying a minimax bias-variance tradeoff governed by an evidence threshold $K$. Extensive benchmarks on volatile financial datasets (2016--2026), including AMD, Gold, and GBP/USD, demonstrate that SA-BCP consistently minimizes the strictly proper Winkler score across diverse confidence levels. Specifically, SA-BCP resolves the systematic under-coverage inherent to ACI variants while simultaneously reducing the uncalibrated interval bloat of Bayesian CP by 10\% to 37\% under high-confidence requests. By elegantly navigating this tradeoff, SA-BCP achieves an optimal balance between conditional reliability and predictive efficiency.

翻译：在线共形预测（CP）在时间适应性与结构稳定性之间面临权衡。基于反馈的方法（如自适应共形推断（ACI））在突变期间存在系统性边缘覆盖不足和高区间方差的问题，而时间折扣贝叶斯CP则存在严重的结构滞后和未校准的区间膨胀。我们提出状态自适应贝叶斯共形预测（SA-BCP），以实现最优时空解耦。通过使用空间核密度证据门控长期时间惯性，SA-BCP在稳定状态下保持紧缩效率的同时，主动扩展已知历史状态模式下的区间。我们严格证明了该机制的最优性，识别出由证据阈值$K$支配的极小化极大偏差-方差权衡。在波动性金融数据集（2016-2026年）上（包括AMD、黄金和英镑/美元）的大量基准测试表明，SA-BCP在不同置信水平下始终最小化严格正确的温克勒分数。具体而言，SA-BCP解决了ACI变体固有的系统性覆盖不足问题，同时在高置信度需求下将贝叶斯CP的未校准区间膨胀减少10%至37%。通过精巧地驾驭这一权衡，SA-BCP实现了条件可靠性与预测效率之间的最优平衡。