Uncertainty-Aware Deep Learning Models for Functional Time Series Forecasting

Abstract

  Accurate prediction and interpretability of functional time series is important in areas where response is based on running data such as energy systems, health care, and finance. Although deep learning models have achieved impressive results in time-series prediction tasks, they generally do not come with ways to properly quantify predictive uncertainty, which significantly diminishes their robustness in real-world applications. This paper proposes a novel uncertainty-aware deep learning framework for functional time series prediction. We investigate three uncertainty estimation methods: Monte Carlo Dropout, Deep Ensembles, and Quantile Regression embedded to LSTM as well as Transformer models. Functional data are worked via discretized curves and prediction through sequence-to-sequence models. Experimental results on a real-world electricity consumption data show that the uncertainty-aware models are efficient not only in terms of predictive accuracy

but also provide calibrated confidence intervals. Deep ensembles combined with Transformer backbones achieve the best trade-off between accuracy and uncertainty sharpness. Visualizations, including animated and interactive plots, reveal how uncertainty evolves over time and enhances interpretability. These results support the adoption of uncertainty-aware functional forecasting in high-stakes applications where trust and robustness are essential