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Locally Stationary Factor Models: Identification And Nonparametric Estimation

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  • Motta, Giovanni
  • Hafner, Christian M.
  • von Sachs, Rainer

Abstract

In this paper we propose a new approximate factor model for large cross-section and time dimensions. Factor loadings are assumed to be smooth functions of time, which allows considering the model as locally stationary while permitting empirically observed time-varying second moments. Factor loadings are estimated by the eigenvectors of a nonparametrically estimated covariance matrix. As is well known in the stationary case, this principal components estimator is consistent in approximate factor models if the eigenvalues of the noise covariance matrix are bounded. To show that this carries over to our locally stationary factor model is the main objective of our paper. Under simultaneous asymptotics (cross-section and time dimension go to infinity simultaneously), we give conditions for consistency of our estimators. A simulation study illustrates the performance of these estimators.

Suggested Citation

  • 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.
  • Handle: RePEc:cup:etheor:v:27:y:2011:i:06:p:1279-1319_00
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    Citations

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    Cited by:

    1. Zura Kakushadze, 2015. "Heterotic Risk Models," Papers 1508.04883, arXiv.org, revised Jan 2016.
    2. Su, Liangjun & Wang, Xia, 2017. "On time-varying factor models: Estimation and testing," Journal of Econometrics, Elsevier, pages 84-101.
    3. Eichler, Michael & Motta, Giovanni & von Sachs, Rainer, 2011. "Fitting dynamic factor models to non-stationary time series," Journal of Econometrics, Elsevier, pages 51-70.
    4. Eichler, Michael & Motta, Giovanni & von Sachs, Rainer, 2011. "Fitting dynamic factor models to non-stationary time series," Journal of Econometrics, Elsevier, pages 51-70.
    5. Zura Kakushadze & Willie Yu, 2016. "Statistical Risk Models," Papers 1602.08070, arXiv.org, revised Jan 2017.
    6. Hallin, Marc & Lippi, Marco, 2013. "Factor models in high-dimensional time series—A time-domain approach," Stochastic Processes and their Applications, Elsevier, pages 2678-2695.
    7. Marc Hallin & Marco Lippi, 2013. "Factor Models in High-Dimensional Time Series: A Time-Domain Approach," Working Papers ECARES ECARES 2013-15, ULB -- Universite Libre de Bruxelles.
    8. Zura Kakushadze & Willie Yu, 2016. "Multifactor Risk Models and Heterotic CAPM," Papers 1602.04902, arXiv.org, revised Mar 2016.

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