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

arXiv: https://arxiv.org/abs/2207.14219 · HTML: https://mlsanity.com/paper/2207.14219/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 75 references that are in the map.
- First posted on arXiv 28 Jul 2022.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Conformal Prediction: a Unified Review of Theory and New Challenges](https://mlsanity.com/paper/2005.07972/) (2020)
- [High-Quality Prediction Intervals for Deep Learning: A Distribution-Free, Ensembled Approach](https://mlsanity.com/paper/1802.07167/) (2018)
- [Exact and Robust Conformal Inference Methods for Predictive Machine Learning With Dependent Data](https://mlsanity.com/paper/1802.06300/) (2018)
- [Adaptive, Distribution-Free Prediction Intervals for Deep Networks](https://mlsanity.com/paper/1905.10634/) (2019)
- [Predictive Inference Is Free with the Jackknife+-after-Bootstrap](https://mlsanity.com/paper/2002.09025/) (2020)
- [Conformal prediction for time series](https://mlsanity.com/paper/2010.09107/) (2020)
- [Machine Learning Advances for Time Series Forecasting](https://mlsanity.com/paper/2012.12802/) (2020)
- [Exchangeability, Conformal Prediction, and Rank Tests](https://mlsanity.com/paper/2005.06095/) (2020)
- [Valid prediction intervals for regression problems](https://mlsanity.com/paper/2107.00363/) (2021)
- [Ensemble Conformalized Quantile Regression for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2202.08756/) (2022)
- [Multivariate Probabilistic Forecasting of Intraday Electricity Prices using Normalizing Flows](https://mlsanity.com/paper/2205.13826/) (2022)
- [Improved conformalized quantile regression](https://mlsanity.com/paper/2207.02808/) (2022)

## Built on by (most cited first, 1 of 1)

- [Beyond Conformal Predictors: Adaptive Conformal Inference with Confidence Predictors](https://mlsanity.com/paper/2409.15548/) (2024)

## Abstract (arXiv)

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.