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2021 Shape-preserving prediction for stationary functional time series
Shuhao Jiao, Hernando Ombao
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Electron. J. Statist. 15(2): 3996-4026 (2021). DOI: 10.1214/21-EJS1882

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.

Acknowledgments

We are grateful to the Associate Editor and two referees for their comments and suggestions that led to substantial improvement of the paper.

Citation

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Shuhao Jiao. Hernando Ombao. "Shape-preserving prediction for stationary functional time series." Electron. J. Statist. 15 (2) 3996 - 4026, 2021. https://doi.org/10.1214/21-EJS1882

Information

Received: 1 November 2020; Published: 2021
First available in Project Euclid: 27 August 2021

Digital Object Identifier: 10.1214/21-EJS1882

Subjects:
Primary: 37M10 , 62R10

Keywords: (spherical)K-means clustering , Functional registration , functional time series , nonlinear dimension reduction , prediction , Shape space , state-space model

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Vol.15 • No. 2 • 2021
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