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Dynamic Factor Models with Infinite-Dimensional Factor Space. Asymptotic Analysis

Author

Listed:
  • Mario Forni

    (Università di Modena e Reggio Emilia, CEPR and RECent)

  • Marc Hallin

    (ECARES, Université Libre de Bruxelles)

  • Marco Lippi

    (EIEF)

  • Paolo Zaffaroni

    (Imperial College London and Università di Roma La Sapienza)

Abstract

Factor models, all particular cases of the Generalized Dynamic Factor Model (GDFM) introduced in Forni, Hallin, Lippi and Reichlin (2000), have become extremely popular in the theory and practice of large panels of time series data. The asymptotic properties (consistency and rates) of the corresponding estimators have been studied in Forni, Hallin, Lippi and Reichlin (2004). Those estimators, however, rely on Brillinger's dynamic principal components, and thus involve two-sided filters, which leads to rather poor forecasting performances. No such problem arises with estimators based on standard (static) principal components, which have been dominant in this literature. On the other hand, the consistency of those static estimators requires the assumption that the space spanned by the factors has finite dimension, which severely restricts the generality afforded by the GDFM. This paper derives the asymptotic properties of a semiparametric estimator of the loadings and common shocks based on one-sided filters recently proposed by Forni, Hallin, Lippi and Zaffaroni (2015). Consistency and exact rates of convergence are obtained for this estimator, under a general class of GDFMs that does not require a finite-dimensional factor space. A Monte Carlo experiment and an empirical exercise on US macroeconomic data corroborate those theoretical results and demonstrate the excellent performance of those estimators in out-of-sample forecasting.

Suggested Citation

  • Mario Forni & Marc Hallin & Marco Lippi & Paolo Zaffaroni, 2016. "Dynamic Factor Models with Infinite-Dimensional Factor Space. Asymptotic Analysis," EIEF Working Papers Series 1607, Einaudi Institute for Economics and Finance (EIEF), revised Apr 2016.
  • Handle: RePEc:eie:wpaper:1607
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    References listed on IDEAS

    as
    1. 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.
    2. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1113-1141, December.
    3. 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.
    4. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2004. "The generalized dynamic factor model consistency and rates," Journal of Econometrics, Elsevier, vol. 119(2), pages 231-255, April.
    5. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    6. Forni, Mario & Gambetti, Luca, 2014. "Sufficient information in structural VARs," Journal of Monetary Economics, Elsevier, vol. 66(C), pages 124-136.
    7. 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.
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    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • E0 - Macroeconomics and Monetary Economics - - General

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