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Kernel-based Optimally Weighted Conformal Time-Series Prediction
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Proposes KOWCPI, a sequential conformal prediction method for time series that performs kernel (Reweighted Nadaraya-Watson) quantile regression on overlapping blocks of non-conformity scores with data-driven weights, with asymptotic conditional coverage theory under strong mixing.
Problem
Conformal prediction intervals for time series violate exchangeability; existing weighted-quantile methods use pre-specified weights, and it is unclear how to choose weights that handle the dependence in residuals.
Approach
Adapts the Reweighted Nadaraya-Watson estimator (empirical-likelihood-based adjustment weights times kernel weights) to estimate conditional quantiles of non-conformity scores from sliding-window segments, yielding data-driven weights for weighted conformal intervals, with bandwidth chosen by nonparametric AIC.
Key results
- On Electric, KOWCPI achieves 0.90 coverage with width 0.22 versus 0.29 for SPCI and 0.30 for SCP at target 90%.
- On Wind, KOWCPI reaches 0.91 coverage with width 2.41 versus 2.61 for SPCI and 8.20 for SCP.
- On Solar, KOWCPI reaches 0.90 coverage with width 48.8 versus 84.2 for SPCI and 142.0 for SCP.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use KOWCPI instead of SPCI | Time-series conformal intervals · Electric | width: 0.29 -> 0.22 | Helped |
| Use KOWCPI instead of SPCI | Time-series conformal intervals · Wind | width: 2.61 -> 2.41 | Helped |
| Use KOWCPI instead of SPCI | Time-series conformal intervals · Solar | width: 84.2 -> 48.8 | Helped |
| Use KOWCPI instead of Plain NW | Time-series conformal intervals · Solar | coverage: 0.41 -> 0.90 | Helped |
| Use KOWCPI instead of SPCI | Time-series conformal intervals · Solar | coverage: 0.92 -> 0.90 | Hurt |
Surprising findings
- Plain Nadaraya-Watson weights give severely under-covering intervals on solar (0.41 coverage), showing the adjustment weights matter.
- SF-OGD and SAOCP fail to achieve target coverage on several datasets (e.g., SF-OGD 0.00 on solar).
Limitations
- Conditional coverage guarantee is asymptotic and relies on strong mixing, smoothness and bandwidth assumptions; the convergence rate is left open.
- Window length and bandwidth require tuning; adaptive window selection is only preliminary in appendix.
- Fast adaptation can cause brief local coverage failures in some regions.
Experimental setup
Datasets: ELEC2 electricity NSRDB solar radiation Atlanta 2018 MISO wind speed AAPL daily closing prices
Benchmarks: ELEC2 solar wind AAPL stock
Metrics: marginal coverage average interval width rolling coverage
Baselines: SPCI EnbPI ACI AgACI FACI SF-OGD SAOCP SCP Plain NW
Builds on: Sequential Predictive Conformal Inference (SPCI) Reweighted Nadaraya-Watson estimator Weighted conformal prediction Adaptive Conformal Inference (ACI)
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