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Forecasting Multiple Time Series With One-Sided Dynamic Principal Components

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  • Daniel Peña
  • Ezequiel Smucler
  • Victor J. Yohai

Abstract

We define one-sided dynamic principal components (ODPC) for time series as linear combinations of the present and past values of the series that minimize the reconstruction mean squared error. Usually dynamic principal components have been defined as functions of past and future values of the series and therefore they are not appropriate for forecasting purposes. On the contrary, it is shown that the ODPC introduced in this article can be successfully used for forecasting high-dimensional multiple time series. An alternating least-squares algorithm to compute the proposed ODPC is presented. We prove that for stationary and ergodic time series the estimated values converge to their population analogs. We also prove that asymptotically, when both the number of series and the sample size go to infinity, if the data follow a dynamic factor model, the reconstruction obtained with ODPC converges in mean square to the common part of the factor model. The results of a simulation study show that the forecasts obtained with ODPC compare favorably with those obtained using other forecasting methods based on dynamic factor models. Supplementary materials for this article are available online.

Suggested Citation

  • Daniel Peña & Ezequiel Smucler & Victor J. Yohai, 2019. "Forecasting Multiple Time Series With One-Sided Dynamic Principal Components," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(528), pages 1683-1694, October.
  • Handle: RePEc:taf:jnlasa:v:114:y:2019:i:528:p:1683-1694
    DOI: 10.1080/01621459.2018.1520117
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    Cited by:

    1. Andriantomanga, Zo, 2023. "The role of survey-based expectations in real-time forecasting of US inflation," MPRA Paper 119904, University Library of Munich, Germany.
    2. Smucler, Ezequiel, 2019. "Consistency of generalized dynamic principal components in dynamic factor models," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    3. Poncela, Pilar & Ruiz, Esther & Miranda, Karen, 2021. "Factor extraction using Kalman filter and smoothing: This is not just another survey," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1399-1425.
    4. Peña, Daniel & Smucler, Ezequiel & Yohai, Victor J., 2021. "Sparse estimation of dynamic principal components for forecasting high-dimensional time series," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1498-1508.

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