# Online conformal inference for multi-step time series forecasting

arXiv: https://arxiv.org/abs/2410.13115 · HTML: https://mlsanity.com/paper/2410.13115/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Oct 2024.

## Built on by (most cited first, 8 of 8)

- [Conformal Information Pursuit for Interactively Guiding Large Language Models](https://mlsanity.com/paper/2507.03279/) (2025)
- [Calibrated Multi-Level Quantile Forecasting](https://mlsanity.com/paper/2512.23671/) (2025)
- [Conformal Prediction Algorithms for Time Series Forecasting: Methods and Benchmarking](https://mlsanity.com/paper/2601.18509/) (2026)
- [Conformal Prediction with Time-Series Data via Sequential Conformalized Density Regions](https://mlsanity.com/paper/2604.07325/) (2026)
- [Simulation-Augmented Multi-Step Split Conformal Prediction for Aggregated Forecasts](https://mlsanity.com/paper/2606.16356/) (2026)
- [Adaptive Multi-Scale Forecasting and Gate-Localized Conformal Prediction for Multivariate Nonstationary Time Series](https://mlsanity.com/paper/2607.23165/) (2026)
- [TRACE-CRC: Trajectory-Adaptive Conformal Risk Control for Multi-Step Channel State Information Prediction](https://mlsanity.com/paper/2608.27124/) (2026)
- [Adaptive Conformal Inference Under Delayed Feedback: Coverage Guarantees and a Delay-to-Memory Diagnostic](https://mlsanity.com/paper/2609.07251/) (2026)

## Abstract (arXiv)

We consider the problem of constructing distribution-free prediction intervals for multi-step time series forecasting, with a focus on the temporal dependencies inherent in multi-step forecast errors. We establish that the optimal h-step-ahead forecast errors exhibit serial correlation up to lag (h-1) under a general non-stationary autoregressive data generating process. To leverage these properties, we propose the Autocorrelated Multi-step Conformal Prediction (AcMCP) method, which effectively incorporates autocorrelations in multi-step forecast errors, resulting in more statistically efficient prediction intervals. This method guarantees asymptotic marginal coverage for multi-step prediction intervals, though we note that, for finite samples, the coverage error admits an upper bound that increases with the forecasting horizon. Additionally, we extend several easy-to-implement conformal prediction methods, originally designed for single-step forecasting, to accommodate multi-step scenarios. Through empirical evaluations, including simulations and applications to data, we demonstrate that AcMCP achieves coverage that closely aligns with the target within local windows, while providing adaptive prediction intervals that effectively respond to varying conditions.