Dynamic Regime-Aware Conformal Calibration for Reliable Economic Forecast Intervals under Multiple Distribution Shifts

Bogdan Oancea

cs.LGAug 17, 2026

Dynamic Regime-Aware Conformal Calibration for Reliable Economic Forecast Intervals under Multiple Distribution Shifts

Authors: Bogdan Oancea

Organizations: University of Bucharest, Romania, National Institute of Research and Development for Biological Sciences

Abstract

Conformal prediction provides distribution-free prediction intervals but relies on exchangeability, an assumption often violated in economic forecasting because of covariate shift, concept drift, local heterogeneity and latent regimes. We propose Dynamic Regime-Aware Conformal Prediction (DRACP), which combines density-ratio, localized kernel and probabilistic regime-aware weighting with a self-tuning online significance controller in a unified weighted conformal calibration framework. We distinguish three theoretical results: finite-sample validity under oracle importance weights, a coverage-gap bound for estimated weights with rates in effective sample size, and deterministic or regret guarantees for the online controller. We evaluate DRACP against six baselines on 48 real forecasting series covering euro-area and EU-27 HICP inflation, US macroeconomic and energy indicators, and daily financial series. Recent online methods (FACI, strongly-adaptive online conformal prediction and conformal PID) were verified against the authors' implementations. DRACP is not the most efficient method: strongly-adaptive online conformal prediction achieves the best interval score and intervals about 20% narrower. Instead, DRACP provides the most reliable calibration, achieving coverage closest to the nominal 0.90 (0.890), never falling below 0.80 on any series, maintaining the best coverage at all forecast horizons, and performing best during the 2021-2023 inflation surge. The strongly-adaptive method undercovers on 20 of 48 series versus 10 for DRACP. DRACP therefore offers a principled trade-off between calibration and efficiency, favoring reliable coverage when prediction intervals must satisfy coverage standards. An ablation study shows that the online controller and conditional-scale normalization provide most of the performance gain, whereas the weighting components make a smaller contribution.

Figures & tables

Panel of Figure 1 — Figure 1: The DRACP pipeline at a single forecast origin $t$ . A standard point forecaster produces errors on past periods; four weighting mechanisms score how relevant each past period is to the present; the interval is the weighted quantile of those errors. A controller adjusts the working significance level from realised coverage. All quantities are computed from information available at $t$ .

Symbol	Meaning
$(X_{t},Y_{t})$	covariates and outcome at time $t$
$\widehat{\mu},\widehat{\sigma}$	point forecaster and conditional scale estimate
$S_{i}$	scaled conformity score $\|Y_{i}-\widehat{\mu}(X_{i})\|/\widehat{\sigma}(X_{i})$
$\mathcal{D}_{t}$	rolling calibration buffer of size $m$
$w_{i,t},\bar{w}_{i,t}$	composite and normalized calibration weights
$\lambda$	temporal decay factor

Table 1: Notation.

Panel of Figure 2 — Figure 2: The DRACP calibration step. Four weighting components—temporal decay, density-ratio correction for covariate shift, an ESS-adaptive local kernel, and regime-similarity weighting—are combined into a single normalized weight vector that defines a weighted conformal radius $q_{t}$ and interval $C_{t}$ . An online controller adapts the significance level $\alpha_{t}$ from realized coverage, closing the loop.

Group	# series	Source	Content
HICP inflation	28	Eurostat	monthly annual inflation, euro area and EU-27
US macro & energy	13	FRED, UCI	activity, prices, money, sentiment, electricity
Financial (daily)	7	FRED	rates, FX, commodities, equity, volatility

Table 2: The 48 real forecasting series, by group.

Role	Model	Target	Configuration
Point forecaster $\widehat{\mu}$	Hist. gradient boosting	$Y$	learning rate $0.05$ ; $150$ – $200$ iterations
Conditional scale $\widehat{\sigma}$	Random forest	$\|Y-\widehat{\mu}(X)\|$	$150$ trees; min. leaf size $8$
Density ratio $\widetilde{r}_{t}$	Logistic regression	recent vs. older	standardised inputs; clipped to $[r_{\min},r_{\max}]$
Regime posterior $\bm{\pi}$	Gaussian mixture	covariates	$K$ components, full covariance, causal fit
Feature scaling	Standardisation	covariates	used for kernel distances

Table 3: Models used in the experiments. The point forecaster is shared by every method; the nuisance estimators are specific to DRACP.

Method	Score rank	# best	Mean cov.	Mean $\|\text{cov}-0.90\|$	Width rank
SAOCP	2.17	33	0.868	0.046	3.50
FACI	2.71	5	0.883	0.031	3.92
DRACP	3.15	5	0.890	0.027	5.69
Adaptive	4.38	0	0.884	0.031	5.52
C-PID	4.52	3	0.825	0.083	3.88
Rolling	5.52	0	0.841	0.078	3.44

Table 4: Overall comparison across the 48 real series: average interval-score rank (1

=

best), number of series where best, mean empirical coverage against a nominal

0.90

, mean absolute coverage deviation, and average width rank. Ordered by score rank.

Method	Mean cov.	Mean $\|$ dev $\|$	Worst $\|$ dev $\|$	Min cov.	$<0.85$	$<0.80$
DRACP	0.890	0.027	0.092	0.808	10	0
FACI	0.883	0.031	0.092	0.808	12	0
Adaptive	0.884	0.031	0.105	0.795	12	1
SAOCP	0.868	0.046	0.150	0.750	20	5
Rolling	0.841	0.078	0.245	0.655	24	16
C-PID	0.825	0.083	0.245	0.655	25	20

Table 5: Calibration reliability across the 48 real series. “Worst

|

dev

|

” is the largest absolute deviation from nominal on any series and “Min cov.” the lowest empirical coverage attained; the last two columns count series undercovering below

0.85

and below

0.80

. Ordered by mean deviation.

Figure 4: Average interval-score rank of each method over the 48 real series (lower is better; the dotted line marks the Nemenyi critical distance from the best method).

Figure 5: Distribution of DRACP’s interval-score rank across the 48 real series; it is best on five and in the top three on roughly half.

Group	$n$	SAOCP	FACI	DRACP	Adaptive	C-PID	Rolling	Split	DRACP cov.
EU HICP inflation	28	1.14	2.32	2.57	4.18	5.11	6.18	6.50	0.878
US macro & energy	13	3.15	3.69	3.62	4.46	3.92	4.85	4.31	0.908
Financial (daily)	7	4.43	2.43	4.57	5.00	3.29	4.14	4.14	0.905

Table 6: Average interval-score rank by group (1

=

best), with DRACP empirical coverage in the last column. Ordered as in Table 4 .

Figure 6: Average interval-score rank by method within each of the three series groups.

Figure 7: Distribution of empirical coverage across the 48 real series, by method, ordered by mean absolute deviation from nominal. DRACP and FACI are the only methods whose lower whisker stays above

0.80

; the strongly-adaptive procedure, which attains the best interval score, undercovers on twenty series.

Figure 8: Prediction intervals for German and Romanian HICP inflation through the 2021–23 surge (shaded). DRACP (top) widens and re-narrows around the break; FACI (bottom) adapts more slowly. Coverage and score annotations are computed from the single reproducibility run that produced these interval paths, and therefore differ slightly from the 20-seed means in E .

Figure 9: Left: interval width for Germany—DRACP expands at the break and contracts afterwards. Right: the self-tuned significance level

\alpha_{t}

absorbing residual miscoverage.

		Unadjusted		BH-adjusted
Baseline	Tests	better	worse	better	worse
SAOCP	48	2	15	2	9
FACI	48	4	14	4	9
Adaptive	48	19	5	12	2
C-PID	48	10	5	4	2
Rolling	48	6	5	5	2

Table 7: Diebold–Mariano outcomes for DRACP versus each baseline over the 48 real series (synthetic scenarios excluded). “Unadjusted” counts use

p<0.05

per test; “BH-adjusted” counts control the false discovery rate at

5\%

across all 288 tests jointly.

Series	Split	Rolling	Adaptive	FACI	SAOCP	Conf-PID
Electricity	6.6 ∗∗∗†	5.8 ∗∗∗†	6.3 ∗∗∗†	6.1 ∗∗∗†	5.8 ∗∗∗†	5.6 ∗∗∗†
Euro area HICP	1.8	1.7	3.2 ∗∗†	1.9	1.7	1.7
US retail sales	1.0	0.9	1.9	0.6	0.9	0.9
US ind. production	1.4	1.5	1.7	1.5	1.5	1.5
HICP DE	2.0 ∗	1.9	3.1 ∗∗	1.5	1.9	1.9
HICP FR	2.0 ∗	1.9	2.1 ∗	1.6	1.9	1.9

Table 8: Diebold–Mariano statistics on representative structured series (positive favours DRACP).

{}^{*}p<0.05

{}^{**}p<0.01

{}^{***}p<0.001

(unadjusted); † also significant after Benjamini–Hochberg control of the false discovery rate at

5\%

across all 288 tests jointly.

Scenario	Split	Rolling	Adaptive	FACI	SAOCP	C-PID	DRACP
Stationary	0.898	0.902	0.900	0.898	0.902	0.900	0.902
Covariate	0.899	0.902	0.900	0.898	0.903	0.901	0.903
Conditional	0.424	0.840	0.900	0.894	0.841	0.899	0.904
Abrupt	0.523	0.888	0.900	0.897	0.889	0.900	0.904
Gradual	0.797	0.911	0.909	0.907	0.911	0.911	0.912
Regime	0.902	0.903	0.901	0.899	0.903	0.902	0.904

Table 9: Synthetic empirical coverage (20-seed means; nominal

0.90

; closest in bold).

Scenario	Split	Rolling	Adaptive	FACI	SAOCP	C-PID	DRACP
Stationary	4.83	4.84	4.87	4.88	4.84	4.84	5.09
Covariate	4.83	4.83	4.86	4.88	4.83	4.84	5.04
Conditional	17.29	9.73	9.56	9.59	9.74	9.57	10.21
Abrupt	22.10	14.71	14.72	14.75	14.71	14.74	15.77
Gradual	12.57	11.80	11.69	11.71	11.81	11.71	12.43
Regime	8.89	8.87	8.87	8.82	8.88	8.87	8.89

Table 10: Synthetic mean interval score (20-seed means; lowest in bold).

Figure 10: Empirical coverage across synthetic scenarios of increasing shift complexity.

Base forecaster	RMSE	DRACP rk	SAOCP rk	FACI rk	$\Delta$ vs best (%)	DRACP cov.	SAOCP cov.
ridge ar	1.00	3.52	2.69	3.58	+6.5	0.901	0.891
mlp	1.26	4.73	2.08	2.40	+36.5	0.906	0.883
random forest	1.62	3.31	1.98	2.75	+27.2	0.889	0.866
gradient boosting	2.03	3.10	2.21	2.69	+18.8	0.890	0.863
naive	3.67	2.75	2.19	3.14	+13.3	0.892	0.872

Table 11: Comparison repeated with five base forecasters (48 series). “RMSE” is the median point-forecast RMSE relative to the best model on the same series (

1.00=

most accurate). Ranks are average interval-score ranks among the seven conformal methods. “

\Delta

vs best” is the mean per-series percentage difference in interval score between DRACP and the best baseline on that series (positive is worse for DRACP).

	Interval-score rank							Coverage
Horizon	SAOCP	FACI	DRACP	Adapt.	C-PID	Roll.	Split	DRACP	SAOCP	FACI
$h=1$	2.19	2.73	3.10	4.38	4.52	5.52	5.56	0.890	0.868	0.883
$h=3$	2.46	2.73	4.06	4.25	4.29	4.88	5.33	0.887	0.839	0.870
$h=6$	3.42	2.92	4.52	4.52	4.44	4.11	4.07	0.873	0.804	0.844
$h=12$	4.50	3.33	4.92	4.56	4.75	3.05	2.89	0.842	0.786	0.822

Table 12: Average interval-score rank by forecast horizon over the seven methods (48 series, 10 seeds); ranks sum to 28 in every row and are comparable across rows. The last three columns are empirical coverage against a nominal

0.90

for the three leading methods.

Figure 11: Empirical coverage against forecast horizon over the 48 real series. All methods lose coverage as the horizon grows; DRACP loses it most slowly, and its margin over the strongly-adaptive procedure widens from 2.2 coverage points at

h=1

to 5.6 at

h=12

Method	ms / prediction	Relative	Peak memory (MB)
Split	12.5	1.0	1.25
Rolling	22.2	1.8	1.11
Adaptive	21.9	1.8	1.12
FACI	21.8	1.7	1.12
SAOCP	25.2	2.0	1.12
C-PID	25.3	2.0	1.12

Table 13: Measured computational cost per prediction (900 sequential predictions, macOS-26.5.2-arm64-arm-64bit, 10 cores).

Regimes	Coverage	$\|\text{cov}-0.90\|$	Mean width	Interval score	ESS
$K=1$	0.898	0.002	8.58	10.84	81.9
$K=2$	0.898	0.002	8.58	10.79	75.5
$K=3$	0.898	0.002	8.55	10.77	72.1
$K=4$	0.899	0.001	8.51	10.80	72.7
$K=5$	0.898	0.002	8.60	10.71	68.0
$K=6$	0.899	0.001	8.54	10.77	68.0

Table 14: Sensitivity to the number of latent regimes

K

on the combined-shift benchmark (nominal coverage

0.90

). “ESS” is the mean effective calibration sample size.

Variant	$\Delta$ score (%)	Worse on	Mean $\|\text{cov}-0.90\|$
Full DRACP	+0.0	0%	0.027
– density ratio	+0.7	50%	0.028
– regime weighting	+0.7	50%	0.027
– localization	+0.2	62%	0.025
– temporal decay	+4.6	71%	0.037
– adaptive control	+11.8	92%	0.051

Table 15: Component ablation on the real panel (48 series, 20 seeds). “

\Delta

score” is the mean per-series percentage change in interval score relative to full DRACP (positive is worse); “worse on” is the share of series on which removal degrades the score. The last row replaces the fitted conditional scale with a constant, isolating the contribution of scale normalisation from that of the weights and the controller.

Appendix figures & tables15 assets

Supplementary material from the paper’s appendix.

Appendix

Series	Source	Freq.	Transform	Test	Test period
Euro area HICP	Eurostat	M	rate (level)	73	2019-12–2025-12
HICP AT	Eurostat	M	rate (level)	84	2019-01–2025-12
HICP BE	Eurostat	M	rate (level)	84	2019-01–2025-12
HICP BG	Eurostat	M	rate (level)	82	2019-03–2025-12
HICP CY	Eurostat	M	rate (level)	84	2019-01–2025-12
HICP CZ	Eurostat	M	rate (level)	84	2019-01–2025-12

Appendix

Table 16: The 48 real forecasting series, in three blocks: HICP inflation, US macroeconomic and energy, daily financial. Frequency: M monthly, D daily (business days), H hourly. “Transform” is the modelling target; “Test” the number of sequential one-step predictions. The test period is reported at the resolution of the series: calendar month for monthly series, calendar day for the daily financial series, and date and hour for the hourly electricity series.

Series	Split	Rolling	Adaptive	FACI	SAOCP	C-PID	DRACP
Euro area HICP	23.39	19.13	12.53	10.52	19.23	18.71	9.69
HICP AT	25.80	21.57	11.84	11.25	21.61	21.46	11.29
HICP BE	22.55	19.96	13.97	11.51	20.01	19.77	10.13
HICP BG	7.78	7.24	6.52	6.62	7.27	7.03	4.58
HICP CY	9.11	9.14	8.66	8.60	9.27	8.88	7.89
HICP CZ	31.46	28.07	14.34	13.48	28.12	27.85	8.68

Appendix

Table 17: Mean interval score per series (lower is better; best per row in bold).

Series	Split	Rolling	Adaptive	FACI	SAOCP	C-PID	DRACP
Euro area HICP	0.603	0.712	0.795	0.795	0.712	0.726	0.806
HICP AT	0.607	0.750	0.833	0.821	0.750	0.762	0.845
HICP BE	0.571	0.762	0.821	0.810	0.762	0.762	0.847
HICP BG	1.000	1.000	0.976	0.976	1.000	1.000	0.959
HICP CY	0.857	0.857	0.905	0.881	0.857	0.857	0.900
HICP CZ	0.524	0.738	0.833	0.810	0.738	0.738	0.915

Appendix

Table 18: Empirical coverage per series (nominal

0.90

; closest per row in bold).

Series	Split	Rolling	Adaptive	FACI	SAOCP	C-PID	DRACP
Euro area HICP	2.13	5.68	10.28	8.12	5.68	5.90	7.39
HICP AT	1.38	5.19	9.04	7.43	5.19	5.27	8.47
HICP BE	1.62	5.62	10.71	7.55	5.62	5.77	7.52
HICP BG	7.78	7.24	6.43	6.55	7.27	7.03	4.38
HICP CY	5.90	6.22	6.91	6.57	6.23	6.36	6.41
HICP CZ	1.46	7.11	11.39	10.13	7.10	7.24	7.98

Appendix

Table 19: Mean interval width per series (narrowest per row in bold).

Series	Split	Rolling	Adaptive	FACI	SAOCP	Conf-PID
Electricity	6.6 †	5.8 †	6.3 †	6.1 †	5.8 †	5.6 †
Euro area HICP	1.8	1.7	3.2 †	1.9	1.7	1.7
Fed funds (d)	14.4 †	14.4 †	9.8 †	9.7 †	14.4 †	14.4 †
HICP AT	1.7	1.5	1.1	-0.0	1.5	1.5
HICP BE	1.7	1.8	3.4 †	1.4	1.8	1.8
HICP BG	5.9 †	4.9 †	3.5 †	3.7 †	5.0 †	4.4 †

Appendix

Table 20: Complete Diebold–Mariano matrix: DRACP versus each baseline on every one of the 48 real series (positive favours DRACP). ∗ significant at the unadjusted

5\%

level; † significant after Benjamini–Hochberg control of the false discovery rate at

5\%

across all 288 tests jointly (threshold

p\leq 0.0073

). Entries marked † are a subset of those marked ∗ .

Scenario	Split	Rolling	Adaptive	FACI	DRACP
Stationary	3.78	3.83	3.83	3.82	4.08
Covariate	3.79	3.82	3.81	3.81	4.05
Conditional	4.81	7.65	8.37	8.29	8.97
Abrupt	8.15	12.55	12.87	12.86	13.78
Gradual	8.67	10.40	10.25	10.26	10.92
Regime	6.79	6.81	6.79	6.70	7.00

Appendix

Table 21: Synthetic mean interval width (20-seed means; narrowest in bold).

Panel of Figure 12 — Figure 12: Per-series mean interval score (means over 20 repeated fits, 95% paired moving-block bootstrap whiskers) for a representative subset of structured (top rows) and financial (bottom row) series. Full set produced by reporting.mc_report .

Panel of Figure 13 — Figure 13: Per-series empirical coverage (20-seed means, 95% bootstrap whiskers, nominal $0.90$ dashed) for representative structured (top) and financial (bottom) series.

Panel of Figure 14 — Figure 14: Diagnostics. Top: estimated density-ratio contribution and posterior regime probabilities. Bottom: the online significance level $\alpha_{t}$ and the effective calibration sample size versus bandwidth.

Panel of Figure 15 — Figure 15: Further diagnostics: estimated regime transition matrix, localization weights vs. distance, and the normal Q–Q plot and histogram of standardized residuals.

Figure 16: Hyperparameter sensitivity of DRACP (combined-shift scenario): localization bandwidth, temporal forgetting factor, and density-ratio clipping.

Figure 17: Left: coverage across scenarios of increasing shift complexity. Right: distribution of interval widths by method under combined shift.

Figure 18: Computational cost of DRACP: runtime per prediction versus calibration-buffer size (left) and the

\mathcal{O}(Bd)

memory footprint (right).

Figure 19: A synthetic regime-switching series with annotated regimes (left) and DRACP prediction intervals on the combined-shift scenario (right).

Figure 20: DRACP prediction intervals on electricity demand (left) and euro-area inflation (right).

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Institute for Computer Science Freie Universität Berlin Arnimallee 7 14195 Berlin

Weighted Conformal Prediction Time Series Forecasting Conformal Prediction Adaptive Conformal Inference Regression Prediction Intervals

Open paper AskPDF arXiv

Recent advances in uncertainty quantification for time series forecasting show that conformal prediction can provide reliable prediction intervals, yet standard conformal methods are often inefficient under temporal dependence, drift, and heterogeneous error behavior. Existing methods typically either update miscoverage rates over time or learn unconstrained calibration weights, without explicitly separating two central sources of nonstationarity: smoothly drifting error distributions and co-existing distinct error regimes. We introduce RareCP, a regime-aware retrieval method for adaptive conformal time series prediction. RareCP learns local calibration representations through a mixture of cosine-attention experts that each capture distinct error regimes, while a compact hypernetwork adapts the kernel parameters to track temporal drift. Given a new forecasting context, RareCP retrieves the top-k most relevant calibration examples, assigns similarity weights, and forms a weighted conformal quantile over their signed residuals, yielding asymmetric prediction intervals. The adaptive kernel is trained using a smooth interval score objective, with a parameter-space anchor to a lightweight teacher kernel to preserve stable local representations. On the GIFT-Eval benchmark, RareCP improves interval efficiency over recent conformal baselines and foundation model uncertainty estimates while maintaining empirical coverage. Ablations confirm that regime-specific experts, drift-adaptive kernels, sparse retrieval, and teacher anchoring each contribute to the final performance.

Abstract

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