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Locally Stationary Factor Models: Identification And Nonparametric Estimation


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


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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    Cited by:

    1. Giovanni Motta & Hernando Ombao, 2012. "Evolutionary Factor Analysis of Replicated Time Series," Biometrics, The International Biometric Society, vol. 68(3), pages 825-836, September.
    2. Eichler, Michael & Motta, Giovanni & von Sachs, Rainer, 2011. "Fitting dynamic factor models to non-stationary time series," Journal of Econometrics, Elsevier, vol. 163(1), pages 51-70, July.
    3. Zura Kakushadze, 2015. "Heterotic Risk Models," Papers 1508.04883,, revised Jan 2016.
    4. Matteo Barigozzi & Marc Hallin & Stefano Soccorsi, 2019. "Time-Varying General Dynamic Factor Models and the Measurement of Financial Connectedness," Working Papers 257939806, Lancaster University Management School, Economics Department.
    5. Su, Liangjun & Wang, Xia, 2017. "On time-varying factor models: Estimation and testing," Journal of Econometrics, Elsevier, vol. 198(1), pages 84-101.
    6. Zura Kakushadze & Willie Yu, 2016. "Statistical Risk Models," Papers 1602.08070,, revised Jan 2017.
    7. Hallin, Marc & Lippi, Marco, 2013. "Factor models in high-dimensional time series—A time-domain approach," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2678-2695.
    8. Caro Navarro, Ángela & Peña Sánchez de Rivera, Daniel, 2018. "Estimation of the common component in Dynamic Factor Models," DES - Working Papers. Statistics and Econometrics. WS 27047, Universidad Carlos III de Madrid. Departamento de Estadística.
    9. Zura Kakushadze & Willie Yu, 2016. "Multifactor Risk Models and Heterotic CAPM," Papers 1602.04902,, revised Mar 2016.

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