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Multivariate and 2D Extensions of Singular Spectrum Analysis with the Rssa Package

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  • Golyandina, Nina
  • Korobeynikov, Anton
  • Shlemov, Alex
  • Usevich, Konstantin

Abstract

Implementation of multivariate and 2D extensions of singular spectrum analysis (SSA) by means of the R package Rssa is considered. The extensions include MSSA for simultaneous analysis and forecasting of several time series and 2D-SSA for analysis of digital images. A new extension of 2D-SSA analysis called shaped 2D-SSA is introduced for analysis of images of arbitrary shape, not necessary rectangular. It is shown that implementation of shaped 2D-SSA can serve as a basis for implementation of MSSA and other generalizations. Efficient implementation of operations with Hankel and Hankel-block-Hankel matrices through the fast Fourier transform is suggested. Examples with code fragments in R, which explain the methodology and demonstrate the proper use of Rssa, are presented.

Suggested Citation

  • Golyandina, Nina & Korobeynikov, Anton & Shlemov, Alex & Usevich, Konstantin, 2015. "Multivariate and 2D Extensions of Singular Spectrum Analysis with the Rssa Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 67(i02).
    • Handle: RePEc:jss:jstsof:v:067:i02
    DOI: http://hdl.handle.net/10.18637/jss.v067.i02
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    References listed on IDEAS

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    1. Hossein Hassani & Saeed Heravi & Anatoly Zhigljavsky, 2013. "Forecasting UK Industrial Production with Multivariate Singular Spectrum Analysis," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(5), pages 395-408, August.
    2. Zeileis, Achim & Grothendieck, Gabor, 2005. "zoo: S3 Infrastructure for Regular and Irregular Time Series," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 14(i06).
    3. Golyandina, Nina & Korobeynikov, Anton, 2014. "Basic Singular Spectrum Analysis and forecasting with R," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 934-954.
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    Cited by:

    1. Ilkka Launonen & Lasse Holmström, 2017. "Multivariate posterior singular spectrum analysis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(3), pages 361-382, August.
    2. Degiannakis, Stavros & Filis, George & Hassani, Hossein, 2018. "Forecasting global stock market implied volatility indices," Journal of Empirical Finance, Elsevier, vol. 46(C), pages 111-129.
    3. Hossein Hassani & Mahdi Kalantari & Zara Ghodsi, 2019. "Evaluating the Performance of Multiple Imputation Methods for Handling Missing Values in Time Series Data: A Study Focused on East Africa, Soil-Carbonate-Stable Isotope Data," Stats, MDPI, vol. 2(4), pages 1-11, December.
    4. Paulo Canas Rodrigues & Olushina Olawale Awe & Jonatha Sousa Pimentel & Rahim Mahmoudvand, 2020. "Modelling the Behaviour of Currency Exchange Rates with Singular Spectrum Analysis and Artificial Neural Networks," Stats, MDPI, vol. 3(2), pages 1-21, June.
    5. Mahdi Kalantari & Hossein Hassani, 2019. "Automatic Grouping in Singular Spectrum Analysis," Forecasting, MDPI, vol. 1(1), pages 1-16, October.
    6. Lei, Heng & Xue, Minggao & Liu, Huiling, 2022. "Probability distribution forecasting of carbon allowance prices: A hybrid model considering multiple influencing factors," Energy Economics, Elsevier, vol. 113(C).
    7. Kalantari, Mahdi, 2021. "Forecasting COVID-19 pandemic using optimal singular spectrum analysis," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    8. de Carvalho, Miguel & Martos, Gabriel, 2020. "Brexit: Tracking and disentangling the sentiment towards leaving the EU," International Journal of Forecasting, Elsevier, vol. 36(3), pages 1128-1137.
    9. Telesca, Luciano & Laib, Mohamed & Guignard, Fabian & Mauree, Dasaraden & Kanevski, Mikhail, 2019. "Linearity versus non-linearity in high frequency multilevel wind time series measured in urban areas," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 234-244.

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