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

TL;DR

This paper introduces a scalable method for constructing multivariate functional prediction bands with guaranteed coverage, demonstrated on synthetic data and applied to forecast Italian gas market demand and offers.

Contribution

It proposes a novel, scalable approach for distribution-free prediction bands for multivariate functional time series with theoretical guarantees.

Findings

Method achieves reliable coverage in synthetic tests.

Successfully applied to Italian gas market data.

Provides closed-form prediction bands with performance guarantees.

Abstract

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.