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Optimal Dimension Reduction for High-dimensional and Functional Time Series

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  • Marc Hallin
  • Siegfried Hörmann
  • Marco Lippi

Abstract

Dimension reduction techniques are at the core of the statistical analysis of high-dimensional and functional observations. Whether the data are vector- or function-valued, principal component techniques, in this context, play a central role. The success of principal components in the dimension reduction problem is explained by the fact that, for any K

Suggested Citation

  • Marc Hallin & Siegfried Hörmann & Marco Lippi, 2017. "Optimal Dimension Reduction for High-dimensional and Functional Time Series," Working Papers ECARES ECARES 2017-39, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:eca:wpaper:2013/260201
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    References listed on IDEAS

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    1. Forni, Mario & Hallin, Marc & Lippi, Marco & Zaffaroni, Paolo, 2015. "Dynamic factor models with infinite-dimensional factor spaces: One-sided representations," Journal of Econometrics, Elsevier, vol. 185(2), pages 359-371.
    2. Daniel Peña & Victor J. Yohai, 2016. "Generalized Dynamic Principal Components," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1121-1131, July.
    3. Forni, Mario & Hallin, Marc & Lippi, Marco & Zaffaroni, Paolo, 2017. "Dynamic factor models with infinite-dimensional factor space: Asymptotic analysis," Journal of Econometrics, Elsevier, vol. 199(1), pages 74-92.
    4. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1113-1141, December.
    5. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2005. "The Generalized Dynamic Factor Model: One-Sided Estimation and Forecasting," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 830-840, September.
    6. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
    7. Forni, Mario & Lippi, Marco, 2011. "The general dynamic factor model: One-sided representation results," Journal of Econometrics, Elsevier, vol. 163(1), pages 23-28, July.
    8. Hallin, Marc & Lippi, Marco, 2013. "Factor models in high-dimensional time series—A time-domain approach," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2678-2695.
    9. Siegfried Hörmann & Łukasz Kidziński & Marc Hallin, 2015. "Dynamic functional principal components," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 319-348, March.
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    Cited by:

    1. Carlos Trucíos & João H. G. Mazzeu & Marc Hallin & Luiz K. Hotta & Pedro L. Valls Pereira & Mauricio Zevallos, 2022. "Forecasting Conditional Covariance Matrices in High-Dimensional Time Series: A General Dynamic Factor Approach," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(1), pages 40-52, December.

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    Keywords

    dimension reduction; time series; principal components; functional principal components; dynamic principal components; Karhunen-Loève expansion;
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