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

Uncertainty quantification in forecasting represents a topic of great importance in statistics, especially when dealing with complex data characterized by non-trivial dependence structure. Pushed by novel works concerning distribution-free prediction, 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. The prediction framework thus obtained allows traders to directly evaluate the impact of their own offers/bids on the market, providing an intriguing tool for the business practice.