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Forecasting Based on Hankel Singular Value Decomposition

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Multiscale Forecasting Models

Abstract

Hankel Singular Value Decomposition (HSVD) is proposed and described in this chapter to extract components of low and high frequency from a nonstationary time series. HSVD is designed in order to extract components of low and high frequency from a nonstationary time series. The decomposition is evaluated for both linear and nonlinear forecasting.

The SVD application is over a 100 years old in linear algebra and particularly in matrix computations. Popular application of SVD were found for denoising, features reduction, image compression, among others.

At the end of this chapter are presented empirical applications based on HSVD. A problem coming from transportation sector is studied. In the experiment through an ETL (extraction, transformation and load) has been obtained a weekly sampling of injured persons in traffic accidents in Valparaíso to the period 2003:1–2012:12. One step-ahead forecasting of the studied time series are obtained by means of HSVD to improve the accuracy obtained with linear and nonlinear models. In this study case are implemented: ARIMA model and an Artificial Neural Network based on Levenberg Marquardt.

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Authors and Affiliations

  1. Universidad Nacional de Chimborazo, Riobamba, Ecuador

    Lida Mercedes Barba Maggi

  2. Pontifícia Universidad Católica de Valparaíso, Valparaíso, Chile

    Lida Mercedes Barba Maggi

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  1. Lida Mercedes Barba Maggi
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Barba Maggi, L.M. (2018). Forecasting Based on Hankel Singular Value Decomposition. In: Multiscale Forecasting Models. Springer, Cham. https://doi.org/10.1007/978-3-319-94992-5_2

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  • DOI: https://doi.org/10.1007/978-3-319-94992-5_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-94991-8

  • Online ISBN: 978-3-319-94992-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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