Many structural breaks are announced in advance, yet adaptive conformal methods learn of them only from their own errors. A reset at the announced date serves one of two audits, conformal reliability of the next interval or frequency calibration of a closed window, and the two can disagree. For independent scores, restarting the empirical quantile at the boundary attains the minimax reliability rate, of order one over the square root of the post-break count. Restarting an adaptive recursion attains a frequency gap of order one over that count on bounded scores when its floor adds a bounded total. That gap bounds nothing about the next interval. After a large synthetic break, the restarted quantile's coverage error at the 50th forecast is 0.035, against 0.052 for the best of five adaptive baselines. The restarted recursion has the smallest frequency gap over the first 50 forecasts after every synthetic break. Real breaks are mostly smaller. The restarted quantile beats two baselines after an electricity market reform and trails all five after monetary policy decisions. Of nine announced breaks screened, only one is large enough for a detectable gain, and there every method misses nominal coverage by more than 0.1.
Figures & tables
Figure 1: Both audits against the post-reset count m on the mean shift of 2.0, as means over 1,000 replications with one standard error each way on logarithmic axes. ACI is adaptive conformal inference and AB-ACI announced-break ACI. DtACI is dynamically-tuned ACI, SAOCP strongly adaptive online conformal prediction, conformal PID a proportional-integral-derivative controller of the coverage error and AgACI aggregated ACI. Panel a is the frequency gap over the first m forecasts, and panel b is the per-time gap at the m -th. AB-ACI appears in form A and in form D, whose step decays as a power of the count. The naive rule is split conformal prediction on every score since calibration. The oracle uses the true post-break quantile, so its per-time gap is zero and falls off panel b.
Figure 2: Form A’s gain over ACI in frequency gap over the first 50 forecasts against the dose, on a synthetic grid of 11 doses at 500 replications each with a band of one standard error. ACI is adaptive conformal inference and AB-ACI announced-break ACI. A positive gain favours form A, and squares mark grid doses. Every other marker sits at a real window’s dose and at the coverage difference its window detects at 80 percent power over the whole post-break window, so gain and floor share one unit. The FOMC marker places the median cell dose and form C’s floor and carries no gain of form A. The star is the one boundary that clears its floor, and open circles are the rest. Labels i to iv are ERCOT’s offer cap, the first and second shifts of its reserve curve and its real-time co-optimization, which the ERCOT window’s marker carries. Labels v to ix are one FOMC decision, the NEM five-minute settlement, the NEM administered and market price caps and PJM Interconnection’s reserve price formation, and Table gives each dose and floor. Panel a spans the grid and panel b the doses near zero, where the real streams and most of the library fall.
Appendix figures & tables5 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 3: Running coverage of form C and ACI when the announced break does not come, averaged over 200 replications of 1,000 steps and drawn from the 25th step after calibration. The shading spans one percentage point either side of nominal coverage, which is dotted, and the dashed line marks the boundary at step 499.
Figure 4: Coverage and width of form A under a misdated boundary on the large mean shift, over 500 replications per offset and the 200 forecasts after the true boundary, with one standard error each way. Panel a gives post-break coverage at each offset of the announced date from the true one, with ACI dashed, since it receives no date, and nominal coverage dotted. Panel b gives the mean width in pre-break noise standard deviations. A negative offset resets before the break.
Figure 5: Frequency gap over the first 50 forecasts against the post-break mean shift, over 500 replications per shift. Panel a shows the two procedures and ACI with one standard error each way. Panel b shows announced-break ACI’s relative reduction of that gap over ACI, with a band of one bootstrap standard error and zero dotted.
Figure 6: Rolling 20-day coverage on the ERCOT evaluation stream under the refit forecaster, with the two procedures and ACI in colour and AgACI and DtACI with the naive rule in grey. AB-ACI runs form A. The dashed line marks the reform of December 5, 2025 and the shading the post-reform window. The dotted line is nominal coverage, and a window prints once it holds 5 days.
Figure 7: Post-reform coverage against mean finite width in USD per MWh on the ERCOT window over 117 days under the refit forecaster, with one moving-block standard error each way at block length 7 over 10,000 draws. The coverage error comes from the day series of coverage indicators and the width error from the finite widths in day order. AB-ACI appears in form A. The four descendants have wider mean intervals than ACI’s 60.43, from 64.77 for SAOCP to 102.16 for AgACI. The reset rule’s mean leaves out its two infinite widths. The warm start covers as the reset rule does at the finite width Table prints, and its marker would coincide with the reset rule’s at print size, so the figure omits it.
Multi-horizon rare-event forecasting is hard under long macroeconomic series' data constraints: labeled events are scarce, and standard uncertainty quantification assumes an exchangeability that autocorrelation violates. A controlled ablation shows an apparent rare-event threshold for Adaptive Conformal Inference instead reflects calibration-set size. Across 200 random calibration sets, support width of the nonconformity-score distribution explains up to 85% of coverage variance versus 2% for rare-event count; the same, not the same magnitude, replicates across synthetic conditions and five countries (five-country Spearman ρ 0.45-0.66 vs. 0.02-0.23). A diversity-maximizing selector built on this is the only strategy tested that improves long-horizon coverage (67.8% to 81.4% at six months); Mondrian, shift-robust, and extreme-value alternatives fail to close it. Mondrian even worsens coverage under oracle labels. A compact proposition explains why: coverage deficit reflects how closely the calibration set's upper quantile reaches the test distribution's. Diversity is necessary, not sufficient. Demonstrated on a two-stage U.S. recession-forecasting framework with RegressorChain, whether six-month coverage reaches 90% under honest scoring remains open, a question this paper quantifies rather than resolves.
Donald Aadithiyan
Department of Computer Science and Engineering, University of Moratuwa, Moratuwa, Sri Lanka
Adaptive Conformal Inference (ACI) provides distribution-free prediction intervals with asymptotic coverage guarantees for time series under distribution shift. However, ACI only adapts the quantile threshold -- it cannot shift the interval center. When a base forecaster develops persistent bias after a regime change, ACI compensates by widening intervals symmetrically, producing unnecessarily conservative bands. We propose Bias-Corrected ACI (BC-ACI), which augments standard ACI with an online exponentially weighted moving average (EWM) estimate of forecast bias. BC-ACI corrects nonconformity scores before quantile computation and re-centers prediction intervals, addressing the root cause of miscalibration rather than its symptom. An adaptive dead-zone threshold suppresses corrections when estimated bias is indistinguishable from noise, ensuring no degradation on well-calibrated data. In controlled experiments across 688 runs spanning two base models, four synthetic regimes, and three real datasets, BC-ACI reduces Winkler interval scores by 13--17% under mean and compound distribution shifts (Wilcoxon p < 0.001) while maintaining equivalent performance on stationary data (ratio 1.002x). We provide finite-sample analysis showing that coverage guarantees degrade gracefully with bias estimation error.
Conformal prediction gives prediction intervals with finite-sample coverage when the data are exchangeable. Many time-indexed datasets are not exchangeable. They have seasons, recurring regimes, changing frequencies, or other forms of structured dependence. This paper studies a simple way to use that structure. We propose spectral adaptive conformal prediction, a method that forms weighted conformal quantiles using local spectral similarity and then updates the target miscoverage level online. The spectral weights choose calibration residuals that look relevant to the current test point. The adaptive update corrects the long-run miss rate when uncertainty changes over time. We give an approximate coverage result for the fixed spectral weighted quantile and a deterministic long-run calibration result for the adaptive update. Simulations with recurring regimes and slowly changing frequencies, together with three U.S. real-data examples, show that the hybrid method can improve on fixed spectral weighting, while also showing that spectral weighting must be monitored through effective sample size diagnostics.
Jeffery Opoku, David Banahene
aUniversity of Texas Rio Grande Valley, United States · bFlorida International University, United States