IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v235y2023i2p1981-2004.html
   My bibliography  Save this article

One-way or two-way factor model for matrix sequences?

Author

Listed:
  • He, Yong
  • Kong, Xinbing
  • Trapani, Lorenzo
  • Yu, Long

Abstract

This paper investigates the issue of determining the dimensions of row and column factor spaces in matrix-valued data. Exploiting the eigen-gap in the spectrum of sample second moment matrices of the data, we propose a family of randomised tests to check whether a one-way or two-way factor structure exists or not. Our tests do not require any arbitrary thresholding on the eigenvalues, and can be applied with (virtually) no restrictions on the relative rate of divergence of the cross-sections to the sample sizes as they pass to infinity. Although tests are based on a randomisation which does not vanish asymptotically, we propose a de-randomised, “strong” (based on the Law of the Iterated Logarithm) decision rule to choose in favour or against the presence of common factors. We use the proposed tests and decision rule in two ways. We further cast our individual tests in a sequential procedure whose output is an estimate of the number of common factors. Our tests are built on two variants of the sample second moment matrix of the data: one based on a row (or column) “flattened” version of the matrix-valued sequence, and one based on a projection-based method. Our simulations show that both procedures work well in large samples and, in small samples, the one based on the projection method delivers a superior performance compared to existing methods in virtually all cases considered.

Suggested Citation

  • He, Yong & Kong, Xinbing & Trapani, Lorenzo & Yu, Long, 2023. "One-way or two-way factor model for matrix sequences?," Journal of Econometrics, Elsevier, vol. 235(2), pages 1981-2004.
    • Handle: RePEc:eee:econom:v:235:y:2023:i:2:p:1981-2004
    DOI: 10.1016/j.jeconom.2023.02.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S030440762300074X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2023.02.008?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    2. Rong Chen & Dan Yang & Cun-Hui Zhang, 2022. "Factor Models for High-Dimensional Tensor Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(537), pages 94-116, January.
    3. E. Andreou & P. Gagliardini & E. Ghysels & M. Rubin, 2019. "Inference in Group Factor Models With an Application to Mixed‐Frequency Data," Econometrica, Econometric Society, vol. 87(4), pages 1267-1305, July.
    4. Yoshimasa Uematsu & Takashi Yamagata, 2022. "Estimation of Sparsity-Induced Weak Factor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(1), pages 213-227, December.
    5. Seung C. Ahn & Alex R. Horenstein, 2013. "Eigenvalue Ratio Test for the Number of Factors," Econometrica, Econometric Society, vol. 81(3), pages 1203-1227, May.
    6. Alexei Onatski, 2009. "Testing Hypotheses About the Number of Factors in Large Factor Models," Econometrica, Econometric Society, vol. 77(5), pages 1447-1479, September.
    7. Yu, Long & He, Yong & Kong, Xinbing & Zhang, Xinsheng, 2022. "Projected estimation for large-dimensional matrix factor models," Journal of Econometrics, Elsevier, vol. 229(1), pages 201-217.
    8. Elynn Y. Chen & Ruey S. Tsay & Rong Chen, 2020. "Constrained Factor Models for High-Dimensional Matrix-Variate Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(530), pages 775-793, April.
    9. Tomohiro Ando & Jushan Bai, 2016. "Panel Data Models with Grouped Factor Structure Under Unknown Group Membership," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(1), pages 163-191, January.
    10. Chen, Rong & Xiao, Han & Yang, Dan, 2021. "Autoregressive models for matrix-valued time series," Journal of Econometrics, Elsevier, vol. 222(1), pages 539-560.
    11. Jushan Bai & Peng Wang, 2016. "Econometric Analysis of Large Factor Models," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 53-80, October.
    12. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    13. Lorenzo Trapani, 2018. "A Randomized Sequential Procedure to Determine the Number of Factors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1341-1349, July.
    14. Guggenberger, Patrik & Kleibergen, Frank & Mavroeidis, Sophocles, 2023. "A test for Kronecker Product Structure covariance matrix," Journal of Econometrics, Elsevier, vol. 233(1), pages 88-112.
    15. Wang, Dong & Liu, Xialu & Chen, Rong, 2019. "Factor models for matrix-valued high-dimensional time series," Journal of Econometrics, Elsevier, vol. 208(1), pages 231-248.
    16. Yuefeng Han & Rong Chen & Cun-Hui Zhang, 2020. "Rank Determination in Tensor Factor Model," Papers 2011.07131, arXiv.org, revised May 2022.
    17. Lam, Clifford & Yao, Qiwei, 2012. "Factor modeling for high-dimensional time series: inference for the number of factors," LSE Research Online Documents on Economics 45684, London School of Economics and Political Science, LSE Library.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Li, Yan & Gao, Zhigen & Huang, Wei & Guo, Jianhua, 2023. "Matrix-variate data analysis by two-way factor model with replicated observations," Statistics & Probability Letters, Elsevier, vol. 202(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Yan & Gao, Zhigen & Huang, Wei & Guo, Jianhua, 2023. "Matrix-variate data analysis by two-way factor model with replicated observations," Statistics & Probability Letters, Elsevier, vol. 202(C).
    2. Yuefeng Han & Rong Chen & Cun-Hui Zhang, 2020. "Rank Determination in Tensor Factor Model," Papers 2011.07131, arXiv.org, revised May 2022.
    3. Xin-Bing Kong & Yong-Xin Liu & Long Yu & Peng Zhao, 2022. "Matrix Quantile Factor Model," Papers 2208.08693, arXiv.org, revised May 2023.
    4. Yuefeng Han & Rong Chen & Dan Yang & Cun-Hui Zhang, 2020. "Tensor Factor Model Estimation by Iterative Projection," Papers 2006.02611, arXiv.org, revised May 2022.
    5. Matteo Barigozzi & Marc Hallin, 2023. "Dynamic Factor Models: a Genealogy," Papers 2310.17278, arXiv.org, revised Jan 2024.
    6. Poncela, Pilar & Ruiz, Esther & Miranda, Karen, 2021. "Factor extraction using Kalman filter and smoothing: This is not just another survey," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1399-1425.
    7. Choi, Sung Hoon & Kim, Donggyu, 2023. "Large volatility matrix analysis using global and national factor models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1917-1933.
    8. Yu, Long & He, Yong & Kong, Xinbing & Zhang, Xinsheng, 2022. "Projected estimation for large-dimensional matrix factor models," Journal of Econometrics, Elsevier, vol. 229(1), pages 201-217.
    9. Jianqing Fan & Kunpeng Li & Yuan Liao, 2020. "Recent Developments on Factor Models and its Applications in Econometric Learning," Papers 2009.10103, arXiv.org.
    10. Alain-Philippe Fortin & Patrick Gagliardini & O. Scaillet, 2022. "Eigenvalue tests for the number of latent factors in short panels," Swiss Finance Institute Research Paper Series 22-81, Swiss Finance Institute.
    11. Barigozzi, Matteo & Trapani, Lorenzo, 2020. "Sequential testing for structural stability in approximate factor models," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 5149-5187.
    12. Sung Hoon Choi & Donggyu Kim, 2022. "Large Volatility Matrix Analysis Using Global and National Factor Models," Papers 2208.12323, arXiv.org, revised Dec 2022.
    13. Xiao Huang, 2023. "Composite Quantile Factor Models," Papers 2308.02450, arXiv.org.
    14. Gagliardini, Patrick & Ossola, Elisa & Scaillet, Olivier, 2019. "Estimation of large dimensional conditional factor models in finance," Working Papers unige:125031, University of Geneva, Geneva School of Economics and Management.
    15. Yuefeng Han & Cun-Hui Zhang & Rong Chen, 2021. "CP Factor Model for Dynamic Tensors," Papers 2110.15517, arXiv.org.
    16. Shuquan Yang & Nengxiang Ling & Yulin Gong, 2022. "Robust estimation of the number of factors for the pair-elliptical factor models," Computational Statistics, Springer, vol. 37(3), pages 1495-1522, July.
    17. Cheng Yu & Dong Li & Feiyu Jiang & Ke Zhu, 2023. "Matrix GARCH Model: Inference and Application," Papers 2306.05169, arXiv.org.
    18. Catherine Doz & Peter Fuleky, 2019. "Dynamic Factor Models," PSE Working Papers halshs-02262202, HAL.
    19. Joakim Westerlund, 2020. "A cross‐section average‐based principal components approach for fixed‐T panels," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(6), pages 776-785, September.
    20. Matthew Harding & Carlos Lamarche & Chris Muris, 2022. "Estimation of a Factor-Augmented Linear Model with Applications Using Student Achievement Data," Papers 2203.03051, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:235:y:2023:i:2:p:1981-2004. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.