A general framework for multi-step ahead adaptive conformal heteroscedastic time series forecasting

TL;DR

This paper presents AEnbMIMOCQR, a distribution-free, model-agnostic algorithm for multi-step ahead time series forecasting that provides reliable, heteroscedastic-aware prediction intervals even under distribution shifts.

Contribution

It introduces a novel conformal prediction framework that does not require data splitting and maintains coverage under non-exchangeable data conditions.

Findings

Outperforms existing methods on real-world datasets

Provides near-exact coverage without data splitting

Remains reliable over time despite distribution shifts

Abstract

This paper introduces a novel model-agnostic algorithm called adaptive ensemble batch multi-input multi-output conformalized quantile regression (AEnbMIMOCQR} that enables forecasters to generate multi-step ahead prediction intervals for a fixed pre-specified miscoverage rate in a distribution-free manner. Our method is grounded on conformal prediction principles, however, it does not require data splitting and provides close to exact coverage even when the data is not exchangeable. Moreover, the resulting prediction intervals, besides being empirically valid along the forecast horizon, do not neglect heteroscedasticity. AEnbMIMOCQR is designed to be robust to distribution shifts, which means that its prediction intervals remain reliable over an unlimited period of time, without entailing retraining or imposing unrealistic strict assumptions on the data-generating process. Through methodically experimentation, we demonstrate that our approach outperforms other competitive methods on both real-world and synthetic datasets. The code used in the experimental part and a tutorial on how to use AEnbMIMOCQR can be found at the following GitHub repository: https://github.com/Quilograma/AEnbMIMOCQR.