Conformal Prediction Bands for Two-Dimensional Functional Time Series

Abstract: 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