Shape-Preserving Prediction for Stationary Functional Time Series

TL;DR

This paper introduces a shape-preserving prediction method for stationary functional time series that effectively captures both vertical and horizontal variations, maintaining the shape of trajectories and outperforming existing methods in pattern preservation.

Contribution

The paper develops a novel shape-preserving prediction approach that incorporates horizontal variation, addressing limitations of existing methods that only consider vertical changes.

Findings

The SP method better preserves the shape of functions.

It provides competitive prediction accuracy.

It is easy to implement with existing software.

Abstract

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.