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Fitting dynamic factor models to non-stationary time series

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  • Eichler Michael
  • Motta Giovanni
  • Sachs Rainer von

    (METEOR)

Abstract

Factor modelling of a large time series panel has widely proven useful to reduce its cross-sectional dimensionality. This is done by explaining common co-movements in the panel through the existence of a small number of common components, up to some idiosyncratic behaviour of each individual series. To capture serial correlation in the common components, a dynamic structure is used as in traditional (uni- or multivariate) time series analysis of second order structure, i.e. allowing for infinite-length filtering of the factors via dynamic loadings. In this paper, motivated from economic data observed over long time periods which show smooth transitions over time in their covariance structure, we allow the dynamic structure of the factor model to be non-stationary over time, by proposing a deterministic time variation of its loadings. In this respect we generalise existing recent work on static factor models with time-varying loadings as well as the classical, i.e. stationary, dynamic approximate factor model. Motivated from the stationary case, we estimate the common components of our dynamic factor model by the eigenvectors of a consistent estimator of the now time-varying spectral density matrix of the underlying data-generating process. This can be seen as time-varying principal components approach in the frequency domain. We derive consistency of this estimator in a "double-asymptotic" framework of both cross-section and time dimension tending to infinity. A simulation study illustrates the performance of our estimators.

Suggested Citation

  • Eichler Michael & Motta Giovanni & Sachs Rainer von, 2009. "Fitting dynamic factor models to non-stationary time series," Research Memorandum 002, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  • Handle: RePEc:unm:umamet:2009002
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    References listed on IDEAS

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    1. Peter Molenaar & Jan Gooijer & Bernhard Schmitz, 1992. "Dynamic factor analysis of nonstationary multivariate time series," Psychometrika, Springer;The Psychometric Society, vol. 57(3), pages 333-349, September.
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    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.
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    9. Motta, Giovanni & Hafner, Christian M. & von Sachs, Rainer, 2011. "Locally Stationary Factor Models: Identification And Nonparametric Estimation," Econometric Theory, Cambridge University Press, vol. 27(06), pages 1279-1319, December.
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    Cited by:

    1. Hallin, Marc & Mathias, Charles & Pirotte, Hugues & Veredas, David, 2011. "Market liquidity as dynamic factors," Journal of Econometrics, Elsevier, vol. 163(1), pages 42-50, July.
    2. Martina Hengge & Seton Leonard, 2017. "Factor Models for Non-Stationary Series: Estimates of Monthly U.S. GDP," IHEID Working Papers 13-2017, Economics Section, The Graduate Institute of International Studies.
    3. Ruiz Ortega, Esther & Poncela, Pilar & Corona, Francisco, 2017. "Estimating non-stationary common factors : Implications for risk sharing," DES - Working Papers. Statistics and Econometrics. WS 24585, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Hautsch, Nikolaus & Kyj, Lada M. & Malec, Peter, 2011. "The merit of high-frequency data in portfolio allocation," CFS Working Paper Series 2011/24, Center for Financial Studies (CFS).

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