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Likelihood ratio test for structural changes in factor models

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  • Jushan Bai
  • Jiangtao Duan
  • Xu Han

Abstract

A factor model with a break in its factor loadings is observationally equivalent to a model without changes in the loadings but a change in the variance of its factors. This effectively transforms a structural change problem of high dimension into a problem of low dimension. This paper considers the likelihood ratio (LR) test for a variance change in the estimated factors. The LR test implicitly explores a special feature of the estimated factors: the pre-break and post-break variances can be a singular matrix under the alternative hypothesis, making the LR test diverging faster and thus more powerful than Wald-type tests. The better power property of the LR test is also confirmed by simulations. We also consider mean changes and multiple breaks. We apply the procedure to the factor modelling and structural change of the US employment using monthly industry-level-data.

Suggested Citation

  • Jushan Bai & Jiangtao Duan & Xu Han, 2022. "Likelihood ratio test for structural changes in factor models," Papers 2206.08052, arXiv.org, revised Dec 2023.
    • Handle: RePEc:arx:papers:2206.08052
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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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