  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.
