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SPACE: Sample-cloud Predictive Adaptive Conformal Ellipsoids for Multivariate Time-Series Forecasting

arXiv 2608.17333 ↗First posted 18 Aug 2026stat.ML cs.AI cs.LGcited by 0

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Abstract (arXiv)

Modern probabilistic time-series forecasters often express uncertainty through forecast samples. While typically converted into nominal prediction regions using empirical quantiles, these model-implied sets lack formal coverage guarantees and frequently deviate from nominal targets under distribution shift. Existing multivariate conformal methods can calibrate these regions online, but they typically estimate geometry from historical residuals using fixed or accumulating look-back windows. This reliance on the past limits their ability to exploit the instantaneous dependence structure of current predictions and leaves them vulnerable to stale-regime contamination. To address this, we propose SPACE, a conformal wrapper for sample-generating multivariate forecasters. SPACE constructs ellipsoidal joint prediction regions by estimating time-local covariance geometry directly from the current forecast sample cloud, calibrating the region's radius via a dynamic backward window-selection scheme. Across diverse multivariate datasets, probabilistic forecasters, and conformal baselines, SPACE consistently brings realized joint and rolling coverage closer to the nominal target, achieving superior coverage-efficiency tradeoffs relative to competing wrappers.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 31 of its 48 references that are in the map. First posted on arXiv 18 Aug 2026.

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References · 31

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19 more
  1. 2021Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecastingcited by 337
  2. 2019High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processescited by 148
  3. 2020Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flowscited by 144
  4. 2021Localized Conformal Prediction: A Generalized Inference Framework for Conformal Predictioncited by 114
  5. 2023Conformal PID Control for Time Series Predictioncited by 88
  6. 2021Calibrating Predictions to Decisions: A Novel Approach to Multi-Class Calibrationcited by 79
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  8. 2021Copula-based conformal prediction for Multi-Target Regressioncited by 53
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  12. 2021Calibrated and Sharp Uncertainties in Deep Learning via Density Estimationcited by 33
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  16. 2023Calibration by Distribution Matching: Trainable Kernel Calibration Metricscited by 20
  17. 2022Exact and Approximate Conformal Inference for Multi-Output Regressioncited by 7
  18. 2025Flow-based Conformal Prediction for Multi-dimensional Time Seriescited by 5
  19. 2026Conformal Prediction for Generative Models via Adaptive Cluster-Based Density Estimationcited by 2

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