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Dynamic Factor Models with Infinite-Dimensional Factor Space: One-Sided Representations

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  • Mario Forni
  • Marc Hallin
  • Marco Lippi
  • Paolo Zaffaroni

Abstract

Abstract. Factor model methods recently have become extremely popular in the theory andpractice of large panels of time series data. Those methods rely on various factor models whichall are particular cases of the Generalized Dynamic Factor Model (GDFM) introduced inForni, Hallin, Lippi and Reichlin (2000). That paper, however, relies on Brillinger's dynamicprincipal components. The corresponding estimators are two-sided filters whose performanceat the end of the observation period or for forecasting purposes is rather poor. No such problem arises with estimators based on standard principal components, which have beendominant in this literature. On the other hand, those estimators require the assumptionthat the space spanned by the factors has finite dimension. In the present paper, we arguethat such an assumption is extremely restrictive and potentially quite harmful. Elaboratingupon recent results by Anderson and Deistler (2008a, b) on singular stationary processes withrational spectrum, we obtain one-sided representations for the GDFM without assuming finitedimension of the factor space. Construction of the corresponding estimators is also brieflyoutlined. In a companion paper, we establish consistency and rates for such estimators, andprovide Monte Carlo results further motivating our approach.

Suggested Citation

  • Mario Forni & Marc Hallin & Marco Lippi & Paolo Zaffaroni, 2012. "Dynamic Factor Models with Infinite-Dimensional Factor Space: One-Sided Representations," Working Papers ECARES ECARES 2012-046, ULB -- Universite Libre de Bruxelles.
  • Handle: RePEc:eca:wpaper:2013/134458
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    Cited by:

    1. Marc Hallin & Siegfried Hörmann & Marco Lippi, 2018. "Optimal dimension reduction for high-dimensional and functional time series," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 385-398, July.
    2. repec:taf:jnlasa:v:111:y:2016:i:515:p:1121-1131 is not listed on IDEAS
    3. Mario Forni & Alessandro Giovannelli & Marco Lippi & Stefano Soccorsi, 2018. "Dynamic factor model with infinite‐dimensional factor space: Forecasting," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(5), pages 625-642, August.
    4. repec:eee:econom:v:205:y:2018:i:1:p:249-279 is not listed on IDEAS
    5. 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.
    6. Fiorentini, Gabriele & Galesi, Alessandro & Sentana, Enrique, 2018. "A spectral EM algorithm for dynamic factor models," Journal of Econometrics, Elsevier, vol. 205(1), pages 249-279.
    7. Matteo Barigozzi & Marc Hallin, 2016. "Generalized dynamic factor models and volatilities: recovering the market volatility shocks," Econometrics Journal, Royal Economic Society, vol. 19(1), pages 33-60, February.
    8. Smeekes, Stephan & Wijler, Etienne, 2018. "Macroeconomic forecasting using penalized regression methods," International Journal of Forecasting, Elsevier, vol. 34(3), pages 408-430.
    9. Barigozzi, Matteo & Lippi, Marco & Luciani, Matteo, 2016. "Non-Stationary Dynamic Factor Models for Large Datasets," Finance and Economics Discussion Series 2016-024, Board of Governors of the Federal Reserve System (U.S.), revised 18 Jul 2017.
    10. Jari Miettinen & Katrin Illner & Klaus Nordhausen & Hannu Oja & Sara Taskinen & Fabian J. Theis, 2016. "Separation of Uncorrelated Stationary time series using Autocovariance Matrices," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(3), pages 337-354, May.
    11. Massacci, Daniele, 2017. "Least squares estimation of large dimensional threshold factor models," Journal of Econometrics, Elsevier, vol. 197(1), pages 101-129.
    12. Matteo Barigozzi & Marco Lippi & Matteo Luciani, 2014. "Dynamic Factor Models, Cointegration and Error Correction Mechanisms," Working Papers ECARES ECARES 2014-14, ULB -- Universite Libre de Bruxelles.
    13. Gross, Christian & Siklos, Pierre, 2018. "Analyzing credit risk transmission to the non-financial sector in Europe: a network approach," ESRB Working Paper Series 78, European Systemic Risk Board.
    14. repec:eee:econom:v:201:y:2017:i:2:p:292-306 is not listed on IDEAS
    15. Barigozzi, Matteo & Hallin, Marc, 2017. "Generalized dynamic factor models and volatilities: estimation and forecasting," Journal of Econometrics, Elsevier, vol. 201(2), pages 307-321.
    16. Matteo Barigozzi & Marc Hallin, 2015. "Networks, Dynamic Factors, and the Volatility Analysis of High-Dimensional Financial Series," Working Papers ECARES ECARES 2015-34, ULB -- Universite Libre de Bruxelles.
    17. F. Della Marra, 2017. "A forecasting performance comparison of dynamic factor models based on static and dynamic methods," Economics Department Working Papers 2017-ME01, Department of Economics, Parma University (Italy).
    18. repec:bla:jorssc:v:66:y:2017:i:3:p:581-605 is not listed on IDEAS
    19. Matteo Barigozzi & Marc Hallin & Stefano Soccorsi, 2017. "Identification of Global and National Shocks in International Financial Markets via General Dynamic Factor Models," Working Papers ECARES ECARES 2017-10, ULB -- Universite Libre de Bruxelles.
    20. Lübbers, Johannes & Posch, Peter N., 2016. "Commodities' common factor: An empirical assessment of the markets' drivers," Journal of Commodity Markets, Elsevier, vol. 4(1), pages 28-40.

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    Keywords

    generalized dynamic factor models; vector processes with singular spectral density; one-sided representations for dynamic models;

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • E00 - Macroeconomics and Monetary Economics - - General - - - General

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