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Structured low-rank matrix completion for forecasting in time series analysis

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  • Gillard, Jonathan
  • Usevich, Konstantin

Abstract

This paper considers the low-rank matrix completion problem, with a specific application to forecasting in time series analysis. Briefly, the low-rank matrix completion problem is the problem of imputing missing values of a matrix under a rank constraint. We consider a matrix completion problem for Hankel matrices and a convex relaxation based on the nuclear norm. Based on new theoretical results and a number of numerical and real examples, we investigate the cases in which the proposed approach can work. Our results highlight the importance of choosing a proper weighting scheme for the known observations.

Suggested Citation

  • Gillard, Jonathan & Usevich, Konstantin, 2018. "Structured low-rank matrix completion for forecasting in time series analysis," International Journal of Forecasting, Elsevier, vol. 34(4), pages 582-597.
    • Handle: RePEc:eee:intfor:v:34:y:2018:i:4:p:582-597
    DOI: 10.1016/j.ijforecast.2018.03.008
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    References listed on IDEAS

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    1. Alexander Dokumentov & Rob J Hyndman, 2014. "Low-dimensional decomposition, smoothing and forecasting of sparse functional data," Monash Econometrics and Business Statistics Working Papers 16/14, Monash University, Department of Econometrics and Business Statistics.
    2. Hassani, Hossein & Heravi, Saeed & Zhigljavsky, Anatoly, 2009. "Forecasting European industrial production with singular spectrum analysis," International Journal of Forecasting, Elsevier, vol. 25(1), pages 103-118.
    3. Papailias, Fotis & Thomakos, Dimitrios, 2017. "EXSSA: SSA-based reconstruction of time series via exponential smoothing of covariance eigenvalues," International Journal of Forecasting, Elsevier, vol. 33(1), pages 214-229.
    4. GILLIS, Nicolas & GLINEUR, François, 2010. "Low-rank matrix approximation with weights or missing data is NP-hard," LIDAM Discussion Papers CORE 2010075, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Khan, M. Atikur Rahman & Poskitt, D.S., 2017. "Forecasting stochastic processes using singular spectrum analysis: Aspects of the theory and application," International Journal of Forecasting, Elsevier, vol. 33(1), pages 199-213.
    6. Jonathan Gillard & Anatoly Zhigljavsky, 2013. "Optimization challenges in the structured low rank approximation problem," Journal of Global Optimization, Springer, vol. 57(3), pages 733-751, November.
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