Optimal Spatio-Temporal Decoupling for Bayesian Conformal Prediction

Online conformal prediction must balance fast adaptation to distribution shift against stable coverage: feedback-driven methods react quickly but become volatile, while strongly discounted Bayesian methods lag and inflate intervals at tight coverage. We introduce State-Adaptive Bayesian Conformal Prediction (SA-BCP), which forms the predictive quantile as a gated convex combination of long-term temporal inertia and local spatial evidence from a kernel density estimate, controlled by a single interpretable evidence threshold K. We establish three results: (i) asymptotic marginal validity of the resulting intervals up to a gate-controlled bias that vanishes as spatial evidence accumulates (exact under recurrent states); (ii) a closed-form expression for the MSE-optimal threshold, K^*MSE=α(1-α)/MT, trading the coverage-indicator (Bernoulli) variance against the temporal structural bias MT; and (iii) a rolling-origin procedure for selecting K online -- consistent under stationarity, with O(√Tlog N) regret against the best fixed K and, for a segmented variant, a sublinear dynamic-regret bound under sublinearly many (BT=o(T)) threshold shifts. Across four financial-volatility and weather datasets, three target coverage levels, and eight baselines, SA-BCP attains at-or-above-nominal coverage in most settings while producing substantially sharper intervals -- up to roughly 3× lower Winkler score than discounted Bayesian CP at the tightest coverage -- and a coverage-matched audit confirms these efficiency gains are not an artifact of under-coverage. We disclose our principal limitation: a volatility-specialized CF-GARCH competitor remains more efficient on its home volatility-base series, though it does not transfer across domains.