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Locally Stationary Factor Models: Identification And Nonparametric Estimation

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  • Motta, Giovanni
  • Hafner, Christian
  • 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.
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Suggested Citation

  • Motta, Giovanni & Hafner, Christian & von Sachs, Rainer, 2011. "Locally Stationary Factor Models: Identification And Nonparametric Estimation," LIDAM Reprints ISBA 2011007, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
  • Handle: RePEc:aiz:louvar:2011007
    Note: In : Econometric Theory, vol. 27, no. 6, p. 1279-1319 (2011)
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    Cited by:

    1. Matteo Barigozzi & Daniele Massacci, 2022. "Modelling Large Dimensional Datasets with Markov Switching Factor Models," Papers 2210.09828, arXiv.org, revised Dec 2023.
    2. Zura Kakushadze, 2015. "Heterotic Risk Models," Papers 1508.04883, arXiv.org, revised Jan 2016.
    3. Barigozzi, Matteo & Hallin, Marc & Soccorsi, Stefano & von Sachs, Rainer, 2021. "Time-varying general dynamic factor models and the measurement of financial connectedness," Journal of Econometrics, Elsevier, vol. 222(1), pages 324-343.
    4. Su, Liangjun & Wang, Xia, 2017. "On time-varying factor models: Estimation and testing," Journal of Econometrics, Elsevier, vol. 198(1), pages 84-101.
    5. Matteo Barigozzi & Marc Hallin & Stefano Soccorsi, 2019. "Time-Varying General Dynamic Factor Models and the Measurement of Financial Connectedness," Working Papers ECARES 2019-09, ULB -- Universite Libre de Bruxelles.
    6. Yousuf, Kashif & Ng, Serena, 2021. "Boosting high dimensional predictive regressions with time varying parameters," Journal of Econometrics, Elsevier, vol. 224(1), pages 60-87.
    7. 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.
    8. Giovanni Motta & Hernando Ombao, 2012. "Evolutionary Factor Analysis of Replicated Time Series," Biometrics, The International Biometric Society, vol. 68(3), pages 825-836, September.
    9. Duván Humberto Cataño & Carlos Vladimir Rodríguez-Caballero & Daniel Peña, 2019. "Wavelet Estimation for Dynamic Factor Models with Time-Varying Loadings," CREATES Research Papers 2019-23, Department of Economics and Business Economics, Aarhus University.
    10. Zura Kakushadze & Willie Yu, 2016. "Statistical Risk Models," Papers 1602.08070, arXiv.org, revised Jan 2017.
    11. Wang, Hanchao & Peng, Bin & Li, Degui & Leng, Chenlei, 2021. "Nonparametric estimation of large covariance matrices with conditional sparsity," Journal of Econometrics, Elsevier, vol. 223(1), pages 53-72.
    12. 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.
    13. Matteo Barigozzi & Marc Hallin, 2023. "Dynamic Factor Models: a Genealogy," Working Papers ECARES 2023-15, ULB -- Universite Libre de Bruxelles.
    14. Jaeheon Jung, 2019. "Estimating a Large Covariance Matrix in Time-varying Factor Models," Papers 1910.11965, arXiv.org.
    15. Caro Navarro, Ángela & Peña, 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.
    16. Zura Kakushadze & Willie Yu, 2016. "Multifactor Risk Models and Heterotic CAPM," Papers 1602.04902, arXiv.org, revised Mar 2016.

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