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Consistency of generalized dynamic principal components in dynamic factor models

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  • Smucler, Ezequiel

Abstract

This note shows that when the data follows a dynamic factor model, the reconstruction provided by the generalized dynamic principal components introduced in Peña and Yohai (2016) converges in mean square to the common part of the factor model as both the number of time series and the number of observations diverge to infinity at any rate. A simulation study shows that the method indeed provides accurate estimations of the common part, having a mean square error smaller than competitors.

Suggested Citation

  • Smucler, Ezequiel, 2019. "Consistency of generalized dynamic principal components in dynamic factor models," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    • Handle: RePEc:eee:stapro:v:154:y:2019:i:c:7
    DOI: 10.1016/j.spl.2019.06.012
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    References listed on IDEAS

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    1. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    2. 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.
    3. 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.
    4. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-1304, September.
    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. 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.
    8. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
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    Cited by:

    1. 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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