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Quasi-maximum likelihood estimation of break point in high-dimensional factor models

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  • Duan, Jiangtao
  • Bai, Jushan
  • Han, Xu

Abstract

This paper proposes a quasi-maximum likelihood (QML) estimator of the break point for large-dimensional factor models with a single structural break in the factor loading matrix. We show that the QML estimator is consistent for the true break point when the covariance matrix of the pre- or post-break factor loading (or both) is singular. Consistency here means that the deviation of the estimated break date from the true break date k0 converges to zero as the sample size grows. This is a much stronger result than the break fraction kˆ/T being T-consistent (super-consistent) for k0/T. Also, singularity occurs for most types of structural changes, except for a rotational change. Even for a rotational change, the QML estimator is still T-consistent in terms of the break fraction. Simulation results confirm the theoretical properties of our estimator, and it significantly outperforms existing estimators for change points in factor models.

Suggested Citation

  • Duan, Jiangtao & Bai, Jushan & Han, Xu, 2023. "Quasi-maximum likelihood estimation of break point in high-dimensional factor models," Journal of Econometrics, Elsevier, vol. 233(1), pages 209-236.
    • Handle: RePEc:eee:econom:v:233:y:2023:i:1:p:209-236
    DOI: 10.1016/j.jeconom.2021.12.011
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    More about this item

    Keywords

    Change point estimation; Consistency; High-dimensional factor models; Nearly singular covariance matrix;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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