Conformal Prediction for Time-series Forecasting with Change Points

TL;DR

The paper tackles uncertainty quantification in time-series with abrupt change points by coupling conformal prediction with a switching dynamical systems framework. The CPTC method builds per-state prediction intervals using online conformal calibration, then aggregates them across regimes, delivering valid coverage without strong distributional assumptions and rapid adaptation when shifts align with predicted state changes. Theoretical guarantees include finite-sample validity under exchangeability and asymptotic validity under mild long-term stability, plus robustness to imperfect state predictions. Empirical results on six datasets demonstrate improved calibration and competitive sharpness relative to baselines, with the approach offering a lightweight, modular alternative for regime-aware UQ in nonstationary environments.

Abstract

Conformal prediction has been explored as a general and efficient way to provide uncertainty quantification for time series. However, current methods struggle to handle time series data with change points - sudden shifts in the underlying data-generating process. In this paper, we propose a novel Conformal Prediction for Time-series with Change points (CPTC) algorithm, addressing this gap by integrating a model to predict the underlying state with online conformal prediction to model uncertainties in non-stationary time series. We prove CPTC's validity and improved adaptivity in the time series setting under minimum assumptions, and demonstrate CPTC's practical effectiveness on 6 synthetic and real-world datasets, showing improved validity and adaptivity compared to state-of-the-art baselines.

Figures (8)

• Figure 1: Comparison of the prediction intervals obtained by our algorithm CPTC (purple) against online conformal prediction baselines on synthetic data. The vertical dashed line marks the distribution shifts; ideal behavior is consistent coverage at the horizontal dashed line in the final panel. Bottom right panel shows that CPTC achieves fast adaptation and remains valid when change points occur.
• Figure 2: (Left) Generative model of the SDS dynamics as in Eqn \ref{['eq:sds']}. Shaded circles represent observed variables; hollow circles are latent variables. (Right) Example to illustrate notation. We show a Lorenz attractor, a canonical nonlinear dynamical system, approximated by a linear SDS linderman2023slds.
• Figure 3: Visualization of prediction intervals on the Electricity hourly demand dataset. The red and blue bars in the bottom reflects the underlying switching state of day and night. Our method (purple) adapts to different levels of volatility between day and night, and achieves stabler coverage over time, whereas ACI (yellow) over-covers during the night and under-covers at change points.
• Figure 4: Dancer bees are tracked by a appearance based tracker from video sequences. The tracked bee is shown in green rectangle in the left figure above. The right figure shows a stylized bee dance through which bees talk to the other bees about the orientation and distance to the food sources.
• Figure 5: Examples of datasets and prediction results. Dotted line represents prediction whereas solid lines represents ground truth; background colors represent the different operating modes segmented by our base predictor RED-SDS.

Theorems & Definitions (14)

• Definition 3.1: Validity
• Proposition 4.1: Finite-sample validity under exchangeability
• Theorem 4.2: Asymptotic validity of CPTC
• Theorem 4.3: Finite-Sample Miscoverage Bound with Imperfect State Predictions
• Theorem 4.4: Miscoverage Ratio under State-Coincident Distribution Shift
• Lemma A.1: Adaptive Conformal Inference Miscoverage Bound Within Predicted States
• Theorem : \ref{['thm:asymptotic_validity']} Asymptotic validity of CPTC
• proof : Proof of Theorem \ref{['thm:asymptotic_validity']}
• Theorem : \ref{['thm:imperfect_state_predictions']} Finite-Sample Miscoverage Bound with Imperfect State Predictions
• proof : Proof of Theorem \ref{['thm:imperfect_state_predictions']}