This article presents a novel method for prediction of stationary functional time series, in particular for trajectories that share a similar pattern but display variable phases. The limitation of most of the existing prediction methodologies for functional time series is that they only consider vertical variation (amplitude, scale, or vertical shift). To overcome this limitation, we develop a shape-preserving (SP) prediction method that incorporates both vertical and horizontal variation. One major advantage of our proposed method is the ability to preserve the shape of functions. Moreover, our proposed SP method does not involve unnatural transformations and can be easily implemented using existing software packages. The utility of the SP method is demonstrated in the analysis of non-metanic hydrocarbons (NMHC) concentration. The analysis demonstrates that the prediction by the SP method captures the common pattern better than the existing prediction methods and also provides competitive prediction accuracy.
We are grateful to the Associate Editor and two referees for their comments and suggestions that led to substantial improvement of the paper.
"Shape-preserving prediction for stationary functional time series." Electron. J. Statist. 15 (2) 3996 - 4026, 2021. https://doi.org/10.1214/21-EJS1882