IDEAS home Printed from https://ideas.repec.org/a/taf/jnlasa/v113y2018i523p1341-1349.html
   My bibliography  Save this article

A Randomized Sequential Procedure to Determine the Number of Factors

Author

Listed:
  • Lorenzo Trapani

Abstract

This article proposes a procedure to estimate the number of common factors k in a static approximate factor model. The building block of the analysis is the fact that the first k eigenvalues of the covariance matrix of the data diverge, while the others stay bounded. On the grounds of this, we propose a test for the null that the ith eigenvalue diverges, using a randomized test statistic based directly on the estimated eigenvalue. The test only requires minimal assumptions on the data, and no assumptions are required on factors, loadings or idiosyncratic errors. The randomized tests are then employed in a sequential procedure to determine k. Supplementary materials for this article are available online.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:jnlasa:v:113:y:2018:i:523:p:1341-1349
    DOI: 10.1080/01621459.2017.1328359
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01621459.2017.1328359
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/01621459.2017.1328359?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.

    Citations

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


    Cited by:

    1. Matteo Barigozzi & Daniele Massacci, 2022. "Modelling Large Dimensional Datasets with Markov Switching Factor Models," Papers 2210.09828, arXiv.org, revised Dec 2023.
    2. 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.
    3. Patrick Gagliardini & Elisa Ossola & O. Scaillet, 2019. "Estimation of Large Dimensional Conditional Factor Models in Finance," Swiss Finance Institute Research Paper Series 19-46, Swiss Finance Institute.
    4. Matteo Barigozzi & Giuseppe Cavaliere & Lorenzo Trapani, 2021. "Inference in heavy-tailed non-stationary multivariate time series," Papers 2107.13894, arXiv.org.
    5. Matteo Barigozzi, 2023. "Asymptotic equivalence of Principal Components and Quasi Maximum Likelihood estimators in Large Approximate Factor Models," Papers 2307.09864, arXiv.org, revised Sep 2023.
    6. Xin-Bing Kong & Yong-Xin Liu & Long Yu & Peng Zhao, 2022. "Matrix Quantile Factor Model," Papers 2208.08693, arXiv.org, revised May 2023.
    7. Ruan Weihua & Hou Qian, 2021. "Determining the Number of Factors in Static Approximate Factor Models Using Discrete Fourier Transforms and Pseudo-Eigenvalues," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 241(1), pages 71-117, February.
    8. Gagliardini, Patrick & Ossola, Elisa & Scaillet, Olivier, 2019. "A diagnostic criterion for approximate factor structure," Journal of Econometrics, Elsevier, vol. 212(2), pages 503-521.
    9. 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.
    10. Noureddine Kouaissah & Sergio Ortobelli Lozza & Ikram Jebabli, 2022. "Portfolio Selection Using Multivariate Semiparametric Estimators and a Copula PCA-Based Approach," Computational Economics, Springer;Society for Computational Economics, vol. 60(3), pages 833-859, October.
    11. Lorenzo Trapani & Emily Whitehouse, 2020. "Sequential monitoring for cointegrating regressions," Papers 2003.12182, arXiv.org.
    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. Matteo Barigozzi & Marc Hallin, 2023. "Dynamic Factor Models: a Genealogy," Papers 2310.17278, arXiv.org, revised Jan 2024.
    14. Noureddine Kouaissah & Amin Hocine, 2021. "Forecasting systemic risk in portfolio selection: The role of technical trading rules," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(4), pages 708-729, July.
    15. Sun, Yucheng & Xu, Wen & Zhang, Chuanhai, 2023. "Identifying latent factors based on high-frequency data," Journal of Econometrics, Elsevier, vol. 233(1), pages 251-270.
    16. 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.
    17. De Vos, Ignace & Everaert, Gerdie & Sarafidis, Vasilis, 2021. "A method for evaluating the rank condition for CCE estimators," MPRA Paper 112305, University Library of Munich, Germany, revised 09 Mar 2022.
    18. 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.
    19. 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.
    20. Matteo Barigozzi, 2023. "Quasi Maximum Likelihood Estimation of High-Dimensional Factor Models: A Critical Review," Papers 2303.11777, arXiv.org, revised Dec 2023.
    21. Yuefeng Han & Rong Chen & Cun-Hui Zhang, 2020. "Rank Determination in Tensor Factor Model," Papers 2011.07131, arXiv.org, revised May 2022.
    22. Matteo Barigozzi & Giuseppe Cavaliere & Lorenzo Trapani, 2020. "Determining the rank of cointegration with infinite variance," Discussion Papers 20/01, University of Nottingham, Granger Centre for Time Series Econometrics.

    More about this item

    Statistics

    Access and download statistics

    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:taf:jnlasa:v:113:y:2018:i:523:p:1341-1349. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UASA20 .

    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.