# Distribution-Free Prediction Bands for Multivariate Functional Time Series: an Application to the Italian Gas Market

arXiv: https://arxiv.org/abs/2107.00527 · HTML: https://mlsanity.com/paper/2107.00527/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2021.

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

- [Conformal prediction for multi-dimensional time series by ellipsoidal sets](https://mlsanity.com/paper/2403.03850/) (2024)
- [Conformal Prediction Bands for Two-Dimensional Functional Time Series](https://mlsanity.com/paper/2207.13656/) (2022)
- [Flow-based Conformal Prediction for Multi-dimensional Time Series](https://mlsanity.com/paper/2502.05709/) (2025)
- [JANET: Joint Adaptive predictioN-region Estimation for Time-series](https://mlsanity.com/paper/2407.06390/) (2024)
- [Topology-Aware Conformal Prediction for Stream Networks](https://mlsanity.com/paper/2503.04981/) (2025)
- [A Gentle Introduction to Conformal Time Series Forecasting](https://mlsanity.com/paper/2511.13608/) (2025)
- [Conformal inference for regression on Riemannian Manifolds](https://mlsanity.com/paper/2310.08209/) (2023)

## Abstract (arXiv)

Uncertainty quantification in forecasting represents a topic of great importance in energy trading, as understanding the status of the energy market would enable traders to directly evaluate the impact of their own offers/bids. To this end, we propose a scalable procedure that outputs closed-form simultaneous prediction bands for multivariate functional response variables in a time series setting, which is able to guarantee performance bounds in terms of unconditional coverage and asymptotic exactness, both under some conditions. After evaluating its performance on synthetic data, the method is used to build multivariate prediction bands for daily demand and offer curves in the Italian gas market.