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Fitting dynamic factor models to non-stationary time series

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

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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  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.
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  7. 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.
  8. Chamberlain, Gary & Rothschild, Michael, 1982. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Scholarly Articles 3230355, Harvard University Department of Economics.
  9. Jiazhu Pan & Qiwei Yao, 2008. "Modelling multiple time series via common factors," LSE Research Online Documents on Economics 22876, London School of Economics and Political Science, LSE Library.
  10. 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.
  11. Forni, Mario & Lippi, Marco, 2000. "The Generalized Dynamic Factor Model: Representation Theory," CEPR Discussion Papers 2509, C.E.P.R. Discussion Papers.
  12. Hoffman, Dennis L & Pagan, Adrian R, 1989. "Post-Sample Prediction Tests for Generalized Method of Moments Estimators," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 51(3), pages 333-43, August.
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  15. Peter Molenaar & Jan Gooijer & Bernhard Schmitz, 1992. "Dynamic factor analysis of nonstationary multivariate time series," Psychometrika, Springer, vol. 57(3), pages 333-349, September.
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