# Predictive inference for time series: why is split conformal effective despite temporal dependence?

arXiv: https://arxiv.org/abs/2510.02471 · HTML: https://mlsanity.com/paper/2510.02471/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 30 references that are in the map.
- First posted on arXiv 2 Oct 2025.

## Builds on (most cited first, 19 of 19)

- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Conditional Time Series Forecasting with Convolutional Neural Networks](https://mlsanity.com/paper/1703.04691/) (2017)
- [Distributional conformal prediction](https://mlsanity.com/paper/1909.07889/) (2019)
- [Theoretical Foundations of Conformal Prediction](https://mlsanity.com/paper/2411.11824/) (2024)
- [Sequential Predictive Conformal Inference for Time Series](https://mlsanity.com/paper/2212.03463/) (2022)
- [Exact and Robust Conformal Inference Methods for Predictive Machine Learning With Dependent Data](https://mlsanity.com/paper/1802.06300/) (2018)
- [Conformal Prediction Under Feedback Covariate Shift for Biomolecular Design](https://mlsanity.com/paper/2202.03613/) (2022)
- [Conformal prediction for time series](https://mlsanity.com/paper/2010.09107/) (2020)
- [Optimal and instance-dependent guarantees for Markovian linear stochastic approximation](https://mlsanity.com/paper/2112.12770/) (2021)
- [Conformal Validity Guarantees Exist for Any Data Distribution (and How to Find Them)](https://mlsanity.com/paper/2405.06627/) (2024)
- [Improving Subseasonal Forecasting in the Western U.S. with Machine Learning](https://mlsanity.com/paper/1809.07394/) (2018)
- [Statistical and Computational Guarantees for the Baum-Welch Algorithm](https://mlsanity.com/paper/1512.08269/) (2015)
- [Estimating stationary mass, frequency by frequency](https://mlsanity.com/paper/2503.12808/) (2025)

## Built on by (most cited first, 10 of 10)

- [Leave a Window Out: Modifying the Jackknife for Predictive Inference in Time Series](https://mlsanity.com/paper/2605.30292/) (2026)
- [Training-Free Probabilistic Time-Series Forecasting with Conformal Seasonal Pools](https://mlsanity.com/paper/2605.03789/) (2026)
- [Optimal Spatio-Temporal Decoupling for Bayesian Conformal Prediction](https://mlsanity.com/paper/2605.00432/) (2026)
- [Doubly Robust Adaptive Conformal Inference for Causal Effects Under Temporal Dependence](https://mlsanity.com/paper/2606.30500/) (2026)
- [Reaching the Tail: Calibration Diversity Drives Conformal Coverage under Data Scarcity](https://mlsanity.com/paper/2608.21591/) (2026)
- [Next-token functional estimation](https://mlsanity.com/paper/2609.19529/) (2026)
- [Rolling Conformal Prediction in Sequential Model Training](https://mlsanity.com/paper/2609.26951/) (2026)
- [Valid and Efficient Split Conformal Regression for Time Series](https://mlsanity.com/paper/2609.33866/) (2026)
- [Conformal Coverage of Time Series: Validity and Inference](https://mlsanity.com/paper/2609.33868/) (2026)
- [Robustly Reliable Learning for Regression](https://mlsanity.com/paper/2610.17381/) (2026)

## Abstract (arXiv)

We consider the problem of uncertainty quantification for prediction in a time series: if we use past data to forecast the next time point, can we provide valid prediction intervals around our forecasts? To avoid placing distributional assumptions on the data, in recent years the conformal prediction method has been a popular approach for predictive inference, since it provides distribution-free coverage for any iid or exchangeable data distribution. However, in the time series setting, the strong empirical performance of conformal prediction methods is not well understood, since even short-range temporal dependence is a strong violation of the exchangeability assumption. Using predictors with "memory" -- i.e., predictors that utilize past observations, such as autoregressive models -- further exacerbates this problem. In this work, we examine the theoretical properties of split conformal prediction in the time series setting, including the case where predictors may have memory. Our results bound the loss of coverage of these methods in terms of a new "switch coefficient", measuring the extent to which temporal dependence within the time series creates violations of exchangeability. Our characterization of the coverage probability is sharp over the class of stationary, β-mixing processes. Along the way, we introduce tools that may prove useful in analyzing other predictive inference methods for dependent data.