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    Shape-Preserving Prediction for Stationary Functional Time Series

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    Type
    Preprint
    Authors
    Jiao, Shuhao
    Ombao, Hernando cc
    KAUST Department
    Statistics Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2019-10-26
    Permanent link to this record
    http://hdl.handle.net/10754/660705
    
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    Abstract
    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.
    Sponsors
    The authors sincerely thank Prof. Alexander Aue for the help in finishing the paper.
    Publisher
    arXiv
    arXiv
    1910.12046
    Additional Links
    https://arxiv.org/pdf/1910.12046
    Collections
    Preprints; Statistics Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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