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Fitting dynamic factor models to non-stationary time series

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Author Info

  • Eichler, Michael
  • Motta, Giovanni
  • von Sachs, Rainer

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 generalize the 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 a 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. The performance of the estimators is illustrated by a simulation study and an application to a macroeconomic data set.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 163 (2011)
Issue (Month): 1 (July)
Pages: 51-70

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Handle: RePEc:eee:econom:v:163:y:2011:i:1:p:51-70

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Approximate factor models Local stationarity Principal components;

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References

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  1. Peter Molenaar & Jan Gooijer & Bernhard Schmitz, 1992. "Dynamic factor analysis of nonstationary multivariate time series," Psychometrika, Springer, vol. 57(3), pages 333-349, September.
  2. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2003. "The Generalized Dynamic Factor Model. One-Sided Estimation and Forecasting," LEM Papers Series 2003/13, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  3. 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.
  4. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(06), pages 1113-1141, December.
  5. Jiazhu Pan & Qiwei Yao, 2008. "Modelling multiple time series via common factors," Biometrika, Biometrika Trust, vol. 95(2), pages 365-379.
  6. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2004. "The generalised dynamic factor model: consistency and rates," ULB Institutional Repository 2013/10133, ULB -- Universite Libre de Bruxelles.
  7. Jushan Bai & Serena Ng, 2000. "Determining the Number of Factors in Approximate Factor Models," Boston College Working Papers in Economics 440, Boston College Department of Economics.
  8. James H. Stock & Mark W. Watson, 2005. "Implications of Dynamic Factor Models for VAR Analysis," NBER Working Papers 11467, National Bureau of Economic Research, Inc.
  9. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 1999. "The Generalized Dynamic Factor Model: Identification and Estimation," CEPR Discussion Papers 2338, C.E.P.R. Discussion Papers.
  10. Marco Del Negro & Christopher Otrok, 2008. "Dynamic factor models with time-varying parameters: measuring changes in international business cycles," Staff Reports 326, Federal Reserve Bank of New York.
  11. Chamberlain, Gary & Rothschild, Michael, 1982. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Scholarly Articles 3230355, Harvard University Department of Economics.
  12. Borus Jungbacker & Siem Jan Koopman, 2008. "Likelihood-based Analysis for Dynamic Factor Models," Tinbergen Institute Discussion Papers 08-007/4, Tinbergen Institute.
  13. Hallin, Marc & Liska, Roman, 2007. "Determining the Number of Factors in the General Dynamic Factor Model," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 603-617, June.
  14. Pan, Jiazhu & Yao, Qiwei, 2008. "Modelling multiple time series via common factors," Open Access publications from London School of Economics and Political Science http://eprints.lse.ac.uk/, London School of Economics and Political Science.
  15. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
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Citations

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Cited by:
  1. Marc Hallin & Charles Mathias & Hugues Pirotte & David Veredas, 2011. "Market liquidity as dynamic factors," ULB Institutional Repository 2013/136188, ULB -- Universite Libre de Bruxelles.
  2. Nikolaus Hautsch & Lada M. Kyj & Peter Malec, 2011. "The Merit of High-Frequency Data in Portfolio Allocation," SFB 649 Discussion Papers SFB649DP2011-059, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  3. repec:eca:wpaper:2009_004 is not listed on IDEAS
  4. repec:sol:wpaper:10-021 is not listed on IDEAS

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