# Conformal Prediction Bands for Two-Dimensional Functional Time Series

arXiv: https://arxiv.org/abs/2207.13656 · HTML: https://mlsanity.com/paper/2207.13656/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 48 references that are in the map.
- First posted on arXiv 27 Jul 2022.

## Builds on (most cited first, 10 of 10)

- [Learning by Transduction](https://mlsanity.com/paper/1301.7375/) (2013)
- [Conformal Prediction: a Unified Review of Theory and New Challenges](https://mlsanity.com/paper/2005.07972/) (2020)
- [A Conformal Prediction Approach to Explore Functional Data](https://mlsanity.com/paper/1302.6452/) (2013)
- [Exact and Robust Conformal Inference Methods for Predictive Machine Learning With Dependent Data](https://mlsanity.com/paper/1802.06300/) (2018)
- [Multi Split Conformal Prediction](https://mlsanity.com/paper/2103.00627/) (2021)
- [Conformal Prediction Interval Estimations with an Application to Day-Ahead and Intraday Power Markets](https://mlsanity.com/paper/1905.07886/) (2019)
- [Distribution-Free Prediction Bands for Multivariate Functional Time Series: an Application to the Italian Gas Market](https://mlsanity.com/paper/2107.00527/) (2021)
- [Functional time series prediction under partial observation of the future curve](https://mlsanity.com/paper/1906.00281/) (2019)
- [Testing for stationarity of functional time series in the frequency domain](https://mlsanity.com/paper/1701.01741/) (2017)
- [Simultaneous predictive bands for functional time series using minimum entropy sets](https://mlsanity.com/paper/2105.13627/) (2021)

## Built on by (most cited first, 7 of 7)

- [Calibrated Uncertainty Quantification for Operator Learning via Conformal Prediction](https://mlsanity.com/paper/2402.01960/) (2024)
- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [JANET: Joint Adaptive predictioN-region Estimation for Time-series](https://mlsanity.com/paper/2407.06390/) (2024)
- [A Gentle Introduction to Conformal Time Series Forecasting](https://mlsanity.com/paper/2511.13608/) (2025)
- [Flow-Based Conformal Predictive Distributions](https://mlsanity.com/paper/2602.07633/) (2026)
- [Joint Registration and Conformal Prediction for Partially Observed Functional Data](https://mlsanity.com/paper/2502.15000/) (2025)
- [Questioning the Coverage-Length Metric in Conformal Prediction: When Shorter Intervals Are Not Better](https://mlsanity.com/paper/2601.21455/) (2026)

## Abstract (arXiv)

Time evolving surfaces can be modeled as two-dimensional Functional time series, exploiting the tools of Functional data analysis. Leveraging this approach, a forecasting framework for such complex data is developed. The main focus revolves around Conformal Prediction, a versatile nonparametric paradigm used to quantify uncertainty in prediction problems. Building upon recent variations of Conformal Prediction for Functional time series, a probabilistic forecasting scheme for two-dimensional functional time series is presented, while providing an extension of Functional Autoregressive Processes of order one to this setting. Estimation techniques for the latter process are introduced and their performance are compared in terms of the resulting prediction regions. Finally, the proposed forecasting procedure and the uncertainty quantification technique are applied to a real dataset, collecting daily observations of Sea Level Anomalies of the Black Sea