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Simpler Proofs for Approximate Factor Models of Large Dimensions

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  • Jushan Bai
  • Serena Ng

Abstract

Estimates of the approximate factor model are increasingly used in empirical work. Their theoretical properties, studied some twenty years ago, also laid the ground work for analysis on large dimensional panel data models with cross-section dependence. This paper presents simplified proofs for the estimates by using alternative rotation matrices, exploiting properties of low rank matrices, as well as the singular value decomposition of the data in addition to its covariance structure. These simplifications facilitate interpretation of results and provide a more friendly introduction to researchers new to the field. New results are provided to allow linear restrictions to be imposed on factor models.

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  • Jushan Bai & Serena Ng, 2020. "Simpler Proofs for Approximate Factor Models of Large Dimensions," Papers 2008.00254, arXiv.org.
    • Handle: RePEc:arx:papers:2008.00254
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    References listed on IDEAS

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    Cited by:

    1. Jonas Krampe & Luca Margaritella, 2021. "Factor Models with Sparse VAR Idiosyncratic Components," Papers 2112.07149, arXiv.org, revised May 2022.
    2. Matteo Barigozzi, 2023. "Quasi Maximum Likelihood Estimation of High-Dimensional Factor Models: A Critical Review," Papers 2303.11777, arXiv.org, revised Dec 2023.
    3. Helena Chuliá & Ignacio Garrón & Jorge M. Uribe, 2021. ""Vulnerable Funding in the Global Economy"," IREA Working Papers 202106, University of Barcelona, Research Institute of Applied Economics, revised Mar 2021.
    4. Matteo Barigozzi, 2022. "On Estimation and Inference of Large Approximate Dynamic Factor Models via the Principal Component Analysis," Papers 2211.01921, arXiv.org, revised Jul 2023.
    5. Yiren Wang & Liangjun Su & Yichong Zhang, 2022. "Low-rank Panel Quantile Regression: Estimation and Inference," Papers 2210.11062, arXiv.org.
    6. Philipp Gersing & Christoph Rust & Manfred Deistler, 2023. "Weak Factors are Everywhere," Papers 2307.10067, arXiv.org, revised Jan 2024.

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