# Conformal prediction for multi-dimensional time series by ellipsoidal sets

arXiv: https://arxiv.org/abs/2403.03850 · HTML: https://mlsanity.com/paper/2403.03850/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 49 references that are in the map.
- First posted on arXiv 6 Mar 2024.

## Builds on (most cited first, 28 of 28)

- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Conformal Prediction: a Unified Review of Theory and New Challenges](https://mlsanity.com/paper/2005.07972/) (2020)
- [Conformal PID Control for Time Series Prediction](https://mlsanity.com/paper/2307.16895/) (2023)
- [Uncertainty Quantification over Graph with Conformalized Graph Neural Networks](https://mlsanity.com/paper/2305.14535/) (2023)
- [Sequential Predictive Conformal Inference for Time Series](https://mlsanity.com/paper/2212.03463/) (2022)
- [Predictive Inference Is Free with the Jackknife+-after-Bootstrap](https://mlsanity.com/paper/2002.09025/) (2020)
- [Conformal prediction for time series](https://mlsanity.com/paper/2010.09107/) (2020)
- [Copula-based conformal prediction for Multi-Target Regression](https://mlsanity.com/paper/2101.12002/) (2021)
- [Calibrated Multiple-Output Quantile Regression with Representation Learning](https://mlsanity.com/paper/2110.00816/) (2021)
- [Conformal Prediction Bands for Multivariate Functional Data](https://mlsanity.com/paper/2106.01792/) (2021)
- [Conformal Prediction with Temporal Quantile Adjustments](https://mlsanity.com/paper/2205.09940/) (2022)
- [Inductive Conformal Martingales for Change-Point Detection](https://mlsanity.com/paper/1706.03415/) (2017)
- [Conformalized matrix completion](https://mlsanity.com/paper/2305.10637/) (2023)
- [Conformal Anomaly Detection on Spatio-Temporal Observations with Missing Data](https://mlsanity.com/paper/2105.11886/) (2021)
- [Distribution-Free Prediction Bands for Multivariate Functional Time Series: an Application to the Italian Gas Market](https://mlsanity.com/paper/2107.00527/) (2021)
- [Randomization Tests for Adaptively Collected Data](https://mlsanity.com/paper/2301.05365/) (2023)
- [Spatio-Temporal Wildfire Prediction using Multi-Modal Data](https://mlsanity.com/paper/2207.13250/) (2022)
- [Conformal prediction set for time-series](https://mlsanity.com/paper/2206.07851/) (2022)
- [Solar Radiation Ramping Events Modeling Using Spatio-temporal Point Processes](https://mlsanity.com/paper/2101.11179/) (2021)
- [Joint Coverage Regions: Simultaneous Confidence and Prediction Sets](https://mlsanity.com/paper/2303.00203/) (2023)

## Built on by (most cited first, 30 of 37)

- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Kernel-based Optimally Weighted Conformal Time-Series Prediction](https://mlsanity.com/paper/2405.16828/) (2024)
- [Relational Conformal Prediction for Correlated Time Series](https://mlsanity.com/paper/2502.09443/) (2025)
- [Spatial Conformal Inference through Localized Quantile Regression](https://mlsanity.com/paper/2412.01098/) (2024)
- [Volume-Sorted Prediction Set: Efficient Conformal Prediction for Multi-Target Regression](https://mlsanity.com/paper/2503.02205/) (2025)
- [Conformal Prediction for Hierarchical Data](https://mlsanity.com/paper/2411.13479/) (2024)
- [Flow-based Conformal Prediction for Multi-dimensional Time Series](https://mlsanity.com/paper/2502.05709/) (2025)
- [ResCP: Reservoir Conformal Prediction for Time Series Forecasting](https://mlsanity.com/paper/2510.05060/) (2025)
- [Conformal Inference for Time Series over Graphs](https://mlsanity.com/paper/2510.11049/) (2025)
- [Calibrating Decision Robustness via Inverse Conformal Risk Control](https://mlsanity.com/paper/2510.07750/) (2025)
- [Leave a Window Out: Modifying the Jackknife for Predictive Inference in Time Series](https://mlsanity.com/paper/2605.30292/) (2026)
- [Conformal time series decomposition with component-wise exchangeability](https://mlsanity.com/paper/2406.16766/) (2024)
- [JANET: Joint Adaptive predictioN-region Estimation for Time-series](https://mlsanity.com/paper/2407.06390/) (2024)
- [Topology-Aware Conformal Prediction for Stream Networks](https://mlsanity.com/paper/2503.04981/) (2025)
- [Conformal Prediction in The Loop: A Feedback-Based Uncertainty Model for Trajectory Optimization](https://mlsanity.com/paper/2510.16376/) (2025)
- [Hierarchical Probabilistic Conformal Prediction for Distributed Energy Resources Adoption](https://mlsanity.com/paper/2411.12193/) (2024)
- [Conformal and kNN Predictive Uncertainty Quantification Algorithms in Metric Spaces](https://mlsanity.com/paper/2507.15741/) (2025)
- [Zono-Conformal Prediction: Zonotope-Based Uncertainty Quantification for Regression and Classification Tasks](https://mlsanity.com/paper/2508.11025/) (2025)
- [Towards Trustworthy Vital Sign Forecasting: Leveraging Uncertainty for Prediction Intervals](https://mlsanity.com/paper/2509.01319/) (2025)
- [SpeedCP: Fast Kernel-based Conditional Conformal Prediction](https://mlsanity.com/paper/2509.24100/) (2025)
- [Learning Confidence Ellipsoids and Applications to Robust Subspace Recovery](https://mlsanity.com/paper/2512.16875/) (2025)
- [Single Trajectory Conformal Prediction](https://mlsanity.com/paper/2406.01570/) (2024)
- [Conformalised Conditional Normalising Flows for Joint Prediction Regions in time series](https://mlsanity.com/paper/2411.17042/) (2024)
- [Mitigating Data Scarcity in Time Series Analysis: A Foundation Model with Series-Symbol Data Generation](https://mlsanity.com/paper/2502.15466/) (2025)
- [A Kernel Nonconformity Score for Multivariate Conformal Prediction](https://mlsanity.com/paper/2604.21595/) (2026)
- [Learning Polyhedral Conformal Sets for Robust Optimization](https://mlsanity.com/paper/2605.08506/) (2026)
- [CONTINA: Confidence Interval for Traffic Demand Prediction with Coverage Guarantee](https://mlsanity.com/paper/2504.13961/) (2025)
- [Feature Fitted Online Conformal Prediction for Deep Time Series Forecasting Model](https://mlsanity.com/paper/2505.08158/) (2025)
- [Ellipsoidal Time Series Forecasting](https://mlsanity.com/paper/2505.17370/) (2025)
- [Foundation Model Forecasts: Form and Function](https://mlsanity.com/paper/2510.19345/) (2025)

## Abstract (arXiv)

Conformal prediction (CP) has been a popular method for uncertainty quantification because it is distribution-free, model-agnostic, and theoretically sound. For forecasting problems in supervised learning, most CP methods focus on building prediction intervals for univariate responses. In this work, we develop a sequential CP method called textttMultiDimSPCI that builds prediction textitregions for a multivariate response, especially in the context of multivariate time series, which are not exchangeable. Theoretically, we estimate textitfinite-sample high-probability bounds on the conditional coverage gap. Empirically, we demonstrate that textttMultiDimSPCI maintains valid coverage on a wide range of multivariate time series while producing smaller prediction regions than CP and non-CP baselines.