Shape-Preserving Prediction for Stationary Functional Time Series

This article presents a novel method for prediction of stationary functional time series, for trajectories sharing a similar pattern with phase variability. Existing prediction methodologies for functional time series only consider amplitude variability. To overcome this limitation, we develop a prediction method that incorporates phase variability. One major advantage of our proposed method is the ability to preserve pattern by treating functional trajectories as shape objects defined in a quotient space with respect to time warping and jointly modeling and estimating amplitude and phase variability. Moreover, the method does not involve unnatural transformations and can be easily implemented using existing software. The asymptotic properties of the least squares estimator are studied. The effectiveness of the proposed method is illustrated in simulation study and real data analysis on annual ocean surface temperatures. It is shown that prediction by the proposed SP (shape-preserving) method captures the common pattern better than the existing prediction method, while providing competitive prediction accuracy.