Jiangtao Duan, Jushan Bai, Xu Han
arXiv 9 Mar 2025 · Econometrics
arXiv:2503.06645 · PDF · DOI · OpenAlex · Extracted main text
This paper investigates the estimation of high-dimensional factor models in which factor loadings undergo an unknown number of structural changes over time. Given that a model with multiple changes in factor loadings can be observationally indistinguishable from one with constant loadings but varying factor variances, this reduces the high-dimensional structural change problem to a lower-dimensional one. Due to the presence of multiple breakpoints, the factor space may expand, potentially causing the pseudo factor covariance matrix within some regimes to be singular. We define two types of breakpoints: {\bf a singular change}, where the number of factors in the combined regime exceeds the minimum number of factors in the two separate regimes, and {\bf a rotational change}, where the number of factors in the combined regime equals that in each separate regime. Under a singular change, we derive the properties of the small eigenvalues and establish the consistency of the QML estimators. Under a rotational change, unlike in the single-breakpoint case, the pseudo factor covariance matrix within each regime can be either full rank or singular, yet the QML estimation error for the breakpoints remains stably bounded. We further propose an information criterion (IC) to estimate the number of breakpoints and show that, with probability approaching one, it accurately identifies the true number of structural changes. Monte Carlo simulations confirm strong finite-sample performance. Finally, we apply our method to the FRED-MD dataset, identifying five structural breaks in factor loadings between 1959 and 2024.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Baltagi, B. and Kao, C. and Wang, F (2021) Estimating and testing high dimensional factor models with multiple structural changes | 1.000 | 7 | 5 | 100% |
| 2 | Ma, S. and Su, L (2018) Estimation of large dimensional factor models with an unknown number of breaks | 1.000 | 5 | 3 | 100% |
| 3 | Bai, J. and Ng, S (2002) Determining the number of factors in approximate factor models self | 0.737 | 3 | 2 | 100% |
| 4 | Baltagi, B. and Kao, C. and Wang, F (2017) Identification and estimation of a large factor model with structural instability | 0.737 | 3 | 2 | 100% |
| 5 | Duan, J. and Bai, J. and Han, X (2023) Quasi-maximum likelihood estimation of break point in high-dimensional factor models self | 0.737 | 3 | 2 | 100% |
| 6 | McCracken, M.W. and Ng, S (2016) FRED-MD: A monthly database for macroeconomic research | 0.737 | 3 | 2 | 100% |
| 7 | Bai, J (2003) Inferential theory for factor models of large dimensions self | 0.693 | 5 | 1 | 100% |
| 8 | Han, X. and Inoue, A (2015) Tests for parameter instability in dynamic factor models self | 0.644 | 4 | 1 | 100% |
| 9 | Barigozzi, M. and Cho, H. and Fryzlewicz, P (2018) Simultaneous multiple change-point and factor analysis for high-dimensional time series | 0.644 | 2 | 2 | 100% |
| 10 | Matteo Barigozzi and Haeran Cho and Lorenzo Trapani (2025) Moving sum procedure for multiple change point detection in large factor models | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 46 scored citations.