Distributional Conformal Prediction for Markov Processes

2026-05-23

AI Summary

This study addresses the challenge of constructing theoretically guaranteed prediction intervals for stationary Markov processes without relying on specific model structures. The authors propose Markov Distributional Conformal Prediction (MDCP), a method that estimates the transition distribution function and applies a probability integral transform to convert the Markov sequence into approximately independent and identically distributed samples, thereby embedding it within a model-free distributional conformal prediction framework. This work is the first to extend distributional conformal prediction to Markov processes, establishing non-asymptotic unconditional coverage error bounds and proving asymptotic validity of conditional prediction intervals under a mild \(L^p\)-m-approximability condition. Empirical results demonstrate that MDCP significantly outperforms baseline approaches such as model-free bootstrap methods in finite-sample settings.

Abstract

We introduce the Markov Distributional Conformal Prediction (MDCP) method that extends the distributional conformal prediction (previously developed for regression) to the setting of a strictly stationary Markov process. Instead of relying on a specific model structure to do prediction, the idea of distributional conformal prediction interval aligns with the Model-Free (MF) Prediction Principle. In analogy to MF prediction of Markov processes, our method exploits the probability integral transform based on estimated transition distribution functions to transform the Markov data to an i.i.d.~dataset. We show a non-asymptotic error bound of MDCPs unconditional coverage rate under a $β$-mixing condition and other standard assumptions on the kernel estimators. The asymptotic validity of the conditional prediction interval is also verified. In addition, we show that our conditional prediction interval is still asymptotically valid with Markov processes being $L^p$-$m$-approximable instead of satisfying the mixing property. Numerical simulations and real data experiments are deployed to empirically illustrate the finite-sample performance of MDCP, and compare it with the MF bootstrap prediction method.

Problem

• Conformal Prediction
• Markov Processes
• Model-Free Prediction
• Distributional Prediction
• Prediction Intervals

Innovation

• Distributional Conformal Prediction
• Markov Processes
• Model-Free Prediction
• Probability Integral Transform
• Non-asymptotic Coverage