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Conformal Prediction Algorithms for Time Series Forecasting: Methods and Benchmark

Andro Sabashvili

TL;DR

This work addresses uncertainty quantification in time series forecasting by adapting conformal prediction (CP) to sequential data, where temporal dependence breaks exchangeability. It surveys and benchmarks multiple CP strategies—MSCP (multi-horizon SCP), EnbPI, SPCI, Global-CP, and online controllers ACI/AcMCP—against ARIMA-based baselines, focusing on practicality and computational efficiency. Key findings show that horizon-specific calibration (MSCP) delivers the best balance of coverage validity and interval efficiency, with Parametric-PI and ACI also performing well in many settings; some methods like Nixtla-CP, EnbPI, and SPCI can underperform under real-world nonstationarity. The study provides actionable guidance for practitioners deploying distribution-free uncertainty quantification in multi-step time series forecasts with modular, fast wrappers.

Abstract

Reliable uncertainty quantification is of critical importance in time series forecasting, yet traditional methods often rely on restrictive distributional assumptions. Conformal prediction (CP) has emerged as a promising distribution-free framework for generating prediction intervals with rigorous theoretical guarantees. However, applying CP to sequential data presents a primary challenge: the temporal dependencies inherent in time series fundamentally violate the core assumption of data exchangeability, upon which standard CP guarantees are built. This review critically examines the main categories of algorithmic solutions designed to address this conflict. We survey and benchmark methods that relax the exchangeability assumption, those that redefine the data unit to be a collection of independent time series, approaches that explicitly model the dynamics of the prediction residuals, and online learning algorithms that adapt to distribution shifts to maintain long-run coverage. By synthesizing these approaches, we highlight computational efficiency and practical performance on real-world data.

Conformal Prediction Algorithms for Time Series Forecasting: Methods and Benchmark

TL;DR

This work addresses uncertainty quantification in time series forecasting by adapting conformal prediction (CP) to sequential data, where temporal dependence breaks exchangeability. It surveys and benchmarks multiple CP strategies—MSCP (multi-horizon SCP), EnbPI, SPCI, Global-CP, and online controllers ACI/AcMCP—against ARIMA-based baselines, focusing on practicality and computational efficiency. Key findings show that horizon-specific calibration (MSCP) delivers the best balance of coverage validity and interval efficiency, with Parametric-PI and ACI also performing well in many settings; some methods like Nixtla-CP, EnbPI, and SPCI can underperform under real-world nonstationarity. The study provides actionable guidance for practitioners deploying distribution-free uncertainty quantification in multi-step time series forecasts with modular, fast wrappers.

Abstract

Reliable uncertainty quantification is of critical importance in time series forecasting, yet traditional methods often rely on restrictive distributional assumptions. Conformal prediction (CP) has emerged as a promising distribution-free framework for generating prediction intervals with rigorous theoretical guarantees. However, applying CP to sequential data presents a primary challenge: the temporal dependencies inherent in time series fundamentally violate the core assumption of data exchangeability, upon which standard CP guarantees are built. This review critically examines the main categories of algorithmic solutions designed to address this conflict. We survey and benchmark methods that relax the exchangeability assumption, those that redefine the data unit to be a collection of independent time series, approaches that explicitly model the dynamics of the prediction residuals, and online learning algorithms that adapt to distribution shifts to maintain long-run coverage. By synthesizing these approaches, we highlight computational efficiency and practical performance on real-world data.
Paper Structure (17 sections, 4 equations, 3 figures)

This paper contains 17 sections, 4 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Foundational Concepts: Split Conformal Prediction
  3. Exchangeability
  4. Split Conformal Prediction (SCP)
  5. Validity Guarantee
  6. Conformal Prediction Algorithms for Time Series
  7. Split Conformal Prediction Adapted to Multi-Horizon Forecasting (MSCP)
  8. Ensemble Batch Prediction Intervals (EnbPI)
  9. Sequential Predictive Conformal Inference (SPCI)
  10. Conformal Prediction for Time Series Dataset (Global-CP)
  11. Online Learning and Control (ACI, AcMCP)
  12. Standard Baselines
  13. Experimental Design and Benchmarking
  14. Dataset Description
  15. Evaluation Metrics
  16. ...and 2 more sections

Figures (3)

  • Figure 1: Empirical coverage rate (dashed orange line represents target coverage).
  • Figure 2: Critical difference diagram based on the Winkler interval score
  • Figure 3: Critical difference diagram based on the Winkler interval score for top 3 algorithms