Conformal Prediction for Time Series with Deep Sequence Models

We present Distribution-aware Conformal Prediction (DCP), a unified framework integrating probabilistic predictors like Monte Carlo dropout, deep ensembles, and quantile regression with score-agnostic conformal calibration to produce valid and efficient prediction intervals. Leveraging a numerical inversion approach to construct interval bounds, DCP accommodates arbitrary combinations of distribution generating predictors and nonconformity scores. Benchmark analysis on synthetic and real-world time series data demonstrate DCP's ability to adaptively calibrate prediction intervals under varying uncertainty regimes. Crucially, DCP's modular design facilitates plug-and-play experimentation with different predictor-score pairings, quantitatively supported by a newly introduced modified Winkler score that balances validity and efficiency by explicitly penalizing undercoverage. While DCP generalizes and extends existing approaches like Conformalized Quantile Regression and Conformalized Monte Carlo, its modular design allows further extensions, setting a foundation for advancing uncertainty quantification in dynamic environments and high-risk applications.

We propose Conformal Seasonal Pools (CSP), a training-free probabilistic time-series forecaster that mixes same-season empirical draws with signed residual draws around a seasonal naive forecast. In an audited rolling-origin benchmark on the six time-series datasets where DeepNPTS was originally evaluated (electricity, exchange_rate, solar_energy, taxi, traffic, wikipedia), CSP-Adaptive significantly outperforms DeepNPTS on every metric we report -- CRPS (per-window paired Wilcoxon $p \approx 4 \times 10^{-10}$), normalized mean quantile loss ($p \approx 7 \times 10^{-10}$), and empirical 95% coverage ($p \approx 8 \times 10^{-45}$, mean 0.89 vs 0.66) -- while running over 500x faster on CPU. Coverage is the most decision-critical of these: a 0.95 nominal interval that contains the truth in only ~66% of cases fails the basic calibration desideratum and would not survive deployment in safety- or decision-critical settings. The failure mode is also more severe than aggregate coverage suggests: in the worst 10% of windows, DeepNPTS's prediction interval covers none of the H forecast horizons -- the entire multi-step trajectory misses the truth at every step simultaneously. This poses serious risk in safety- and decision-critical applications such as healthcare, finance, energy operations, and autonomous systems, where prediction intervals that systematically miss the truth across the entire planning horizon translate directly into misclassified patients, regulatory capital failures, grid imbalances, and safety-case violations. CSP achieves all of this with no learned parameters and no training. We argue training-free conformal samplers should be mandatory baselines when evaluating learned non-parametric forecasters.

We introduce Rolling Conformal Prediction (rolling-CP), a distribution-free predictive inference method for the setting of sequential model training. Specifically, given a data stream $(X_1,Y_1),(X_2,Y_2),\dots$, at each time $n$ the trained model may depend on the observed history $\{(X_i,Y_i)\}_{i<n}$. This setting arises naturally in modern sequential training, including one-pass training over massive datasets and continual fine-tuning or test-time adaptation of language models during deployment. Rolling-CP first calibrates each incoming observation against the current predictor and then rolls it into future training. In this way, we avoid the need for data splitting. Remarkably, although the models at times $n=1,2,\dots$ may have entirely different properties and accuracy levels, for exchangeable data it is nonetheless possible to establish a guarantee of marginal coverage, with a familiar universal factor-two guarantee (a worst case guarantee of $1-2α$ coverage, as compared to the target level $1-α$), without any assumptions of stability or any restrictions on the model training process. For i.i.d. data streams, we further prove high-probability training-conditional validity uniformly over time; under stability conditions, coverage guarantees sharpen towards $1-α$. Numerical experiments on sequential regression, multiclass SGD, and one-pass neural-network training further demonstrate the practical effectiveness of rolling-CP.