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Conformal Prediction for Time-series Forecasting with Change Points
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Proposes CPTC, a split/online conformal prediction method that maintains per-state nonconformity score sets and state-specific ACI-style miscoverage targets, using an SDS model's state predictions to yield valid, adaptive intervals under change points.
Problem
Online conformal prediction for time series with change points: existing online CP methods react only after distribution shifts, causing prolonged miscoverage, while SDS state predictions go unused for uncertainty quantification.
Approach
Run one online conformal inference instance per latent SDS state, with state-specific nonconformity score sets and adaptive miscoverage levels updated with the sampled state, and aggregate the state-specific intervals weighted by predicted state probabilities so intervals anticipate predicted transitions.
Key results
- On short-horizon benchmarks at 90% target, CPTC achieves coverage of 90.15 (Bouncing Ball obs.), 90.47 (Bouncing Ball dyn.), 94.96 (3-Mode), 92.38 (Traffic), 91.22 (Electricity), and 92.64 (Dancing Bees), while SPCI, HopCPT, CP and RED-SDS are often below 90%.
- CPTC's width on Bouncing Ball dyn. is 1.76 versus 2.26 for SPCI and 2.27 for ACI among valid methods, but on 3-Mode its width (2.45) is much narrower than ACI (6.40).
- Ablation with ground-truth states shows coverage is stable under 20% and 50% injected state-label error, while interval width grows modestly with state error.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use CPTC instead of ACI | Bouncing Ball obs. · Bouncing Ball obs. | coverage: 89.82 \plusminus 2.95 -> 90.15 \plusminus 1.19 | Helped |
| Use CPTC instead of ACI | Bouncing Ball dyn. · Bouncing Ball dyn. | width: 2.27 \plusminus 1.65 -> 1.76 \plusminus 0.71 | Helped |
| Use CPTC instead of ACI | 3-Mode System · 3-Mode System | coverage: 89.90 \plusminus 2.25 -> 94.96 \plusminus 1.96 | Helped |
| Use CPTC instead of ACI | Traffic · Traffic | width: 27.81 \plusminus 54.08 -> 7.92 \plusminus 2.98 | Helped |
| Use CPTC instead of ACI | Electricity · Electricity | coverage: 89.79 \plusminus 0.83 -> 91.22 \plusminus 1.29 | Helped |
| Use CPTC instead of ACI | Dancing Bees · Dancing Bees | coverage: 86.25 \plusminus 8.10 -> 92.64 \plusminus 3.19 | Helped |
| Inject state prediction errors up to 50% instead of using ground-truth states (ablation) | CPTC · Bouncing Ball obs. | coverage: 90.31 \plusminus 1.27 -> 90.13 \plusminus 1.40 | No clear effect |
| Inject state prediction errors up to 50% instead of using ground-truth states (ablation) | CPTC · Bouncing Ball obs. | width: 3.61 \plusminus 0.93 -> 3.94 \plusminus 1.17 | Hurt |
| Inject state prediction errors up to 50% instead of using ground-truth states (ablation) | CPTC · Bouncing Ball dyn. | coverage: 90.34 \plusminus 0.93 -> 90.33 \plusminus 1.05 | No clear effect |
| Inject state prediction errors up to 50% instead of using ground-truth states (ablation) | CPTC · Bouncing Ball dyn. | width: 2.09 \plusminus 0.60 -> 2.18 \plusminus 0.65 | Hurt |
| Inject state prediction errors up to 50% instead of using ground-truth states (ablation) | CPTC · 3-Mode System | coverage: 92.67 \plusminus 1.52 -> 92.53 \plusminus 1.54 | No clear effect |
| Inject state prediction errors up to 50% instead of using ground-truth states (ablation) | CPTC · 3-Mode System | width: 2.04 \plusminus 0.67 -> 2.27 \plusminus 0.89 | Hurt |
Surprising findings
- Coverage remains stable when state labels are corrupted by 50%, suggesting the state-specific calibration is robust to state prediction errors.
- On longer horizons (T=10,000), SPCI and HopCPT achieve sharper intervals than CPTC, which remains valid but wider.
Limitations
- Slower convergence when state transitions are frequent or unpredictable, since each state needs sufficient observations.
- Wider prediction intervals than specialized methods (SPCI, HopCPT) on very long time series.
- Requires a state prediction model, so it is primarily applicable to SDS-like or discrete SSMs.
Experimental setup
Datasets: Bouncing Ball (obs. and dyn.) 3-mode switching linear system Electricity (UCI) Traffic (UCI) Dancing Bees trajectories
Benchmarks: Bouncing Ball obs. Bouncing Ball dyn. 3-Mode System Traffic Electricity Dancing Bees Longer-horizon variants (T=10,000 synthetic, T=4,000 electricity/traffic)
Metrics: empirical coverage interval width
Baselines: RED-SDS CP (online split conformal) ACI SPCI HopCPT DtACI ECI-cutoff L-ARC
Builds on: Adaptive Conformal Inference (ACI) RED-SDS split conformal prediction SPCI HopCPT
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