IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0206551.html
   My bibliography  Save this article

Random selection of factors preserves the correlation structure in a linear factor model to a high degree

Author

Listed:
  • Antti J Tanskanen
  • Jani Lukkarinen
  • Kari Vatanen

Abstract

In a very high-dimensional vector space, two randomly-chosen vectors are almost orthogonal with high probability. Starting from this observation, we develop a statistical factor model, the random factor model, in which factors are chosen stochastically based on the random projection method. Randomness of factors has the consequence that correlation and covariance matrices are well preserved in a linear factor representation. It also enables derivation of probabilistic bounds for the accuracy of the random factor representation of time-series, their cross-correlations and covariances. As an application, we analyze reproduction of time-series and their cross-correlation coefficients in the well-diversified Russell 3,000 equity index.

Suggested Citation

  • Antti J Tanskanen & Jani Lukkarinen & Kari Vatanen, 2018. "Random selection of factors preserves the correlation structure in a linear factor model to a high degree," PLOS ONE, Public Library of Science, vol. 13(12), pages 1-22, December.
    • Handle: RePEc:plo:pone00:0206551
    DOI: 10.1371/journal.pone.0206551
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0206551
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0206551&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0206551?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
    ---><---

    References listed on IDEAS

    as
    1. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    2. Malevergne, Y. & Sornette, D., 2004. "Collective origin of the coexistence of apparent random matrix theory noise and of factors in large sample correlation matrices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 331(3), pages 660-668.
    3. Joël Bun & Jean-Philippe Bouchaud & Marc Potters, 2017. "Cleaning large correlation matrices: tools from random matrix theory," Post-Print hal-01491304, HAL.
    4. Carl Eckart & Gale Young, 1936. "The approximation of one matrix by another of lower rank," Psychometrika, Springer;The Psychometric Society, vol. 1(3), pages 211-218, September.
    5. Boivin, Jean & Ng, Serena, 2006. "Are more data always better for factor analysis?," Journal of Econometrics, Elsevier, vol. 132(1), pages 169-194, May.
    6. G. Livan & S. Alfarano & E. Scalas, 2011. "The fine structure of spectral properties for random correlation matrices: an application to financial markets," Papers 1102.4076, arXiv.org.
    7. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    8. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    9. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    10. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
    Full references (including those not matched with items on IDEAS)

    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. Antti J. Tanskanen & Jani Lukkarinen & Kari Vatanen, 2016. "Random selection of factors preserves the correlation structure in a linear factor model to a high degree," Papers 1604.05896, arXiv.org, revised Dec 2018.
    2. Anshul Verma & Riccardo Junior Buonocore & Tiziana di Matteo, 2017. "A cluster driven log-volatility factor model: a deepening on the source of the volatility clustering," Papers 1712.02138, arXiv.org, revised May 2018.
    3. Jianqing Fan & Yuan Liao & Martina Mincheva, 2013. "Large covariance estimation by thresholding principal orthogonal complements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 603-680, September.
    4. Simon Hediger & Jeffrey Näf & Marc S. Paolella & Paweł Polak, 2023. "Heterogeneous tail generalized common factor modeling," Digital Finance, Springer, vol. 5(2), pages 389-420, June.
    5. Bai, Jushan & Ando, Tomohiro, 2013. "Multifactor asset pricing with a large number of observable risk factors and unobservable common and group-specific factors," MPRA Paper 52785, University Library of Munich, Germany, revised Dec 2013.
    6. Gregory Connor & Robert A. Korajczyk, 2019. "Semi-strong factors in asset returns," Economics Department Working Paper Series n294-19.pdf, Department of Economics, National University of Ireland - Maynooth.
    7. Natalia Bailey & George Kapetanios & M. Hashem Pesaran, 2021. "Measurement of factor strength: Theory and practice," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(5), pages 587-613, August.
    8. Russell Davidson & Niels S. Grønborg, 2018. "Time-varying parameters: New test tailored to applications in finance and macroeconomics," CREATES Research Papers 2018-22, Department of Economics and Business Economics, Aarhus University.
    9. Zhaoxing Gao & Ruey S. Tsay, 2021. "Divide-and-Conquer: A Distributed Hierarchical Factor Approach to Modeling Large-Scale Time Series Data," Papers 2103.14626, arXiv.org.
    10. Bodnar, Taras & Reiß, Markus, 2016. "Exact and asymptotic tests on a factor model in low and large dimensions with applications," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 125-151.
    11. Jiti Gao & Guangming Pan & Yanrong Yang & Bo Zhang, 2019. "Estimation of Cross-Sectional Dependence in Large Panels," Papers 1904.06843, arXiv.org.
    12. Jushan Bai & Shuzhong Shi, 2011. "Estimating High Dimensional Covariance Matrices and its Applications," Annals of Economics and Finance, Society for AEF, vol. 12(2), pages 199-215, November.
    13. Carlos Enrique Carrasco-Gutierrez & Wagner Piazza Gaglianone, 2012. "Evaluating Asset Pricing Models in a Simulated Multifactor Approach," Brazilian Review of Finance, Brazilian Society of Finance, vol. 10(4), pages 425-460.
    14. Jiti Gao & Guangming Pan & Yanrong Yang & Bo Zhang, 2019. "An Integrated Panel Data Approach to Modelling Economic Growth," Monash Econometrics and Business Statistics Working Papers 9/19, Monash University, Department of Econometrics and Business Statistics.
    15. He, Yong & Zhang, Mingjuan & Zhang, Xinsheng & Zhou, Wang, 2020. "High-dimensional two-sample mean vectors test and support recovery with factor adjustment," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    16. Shi, Huai-Long & Zhou, Wei-Xing, 2022. "Factor volatility spillover and its implications on factor premia," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 80(C).
    17. David E. Allen & Michael McAleer & Abhay K. Singh, 2019. "Daily market news sentiment and stock prices," Applied Economics, Taylor & Francis Journals, vol. 51(30), pages 3212-3235, June.
    18. repec:dau:papers:123456789/2514 is not listed on IDEAS
    19. Zura Kakushadze, 2014. "4-Factor Model for Overnight Returns," Papers 1410.5513, arXiv.org, revised Jun 2015.
    20. Francesco Lautizi, 2015. "Large Scale Covariance Estimates for Portfolio Selection," CEIS Research Paper 353, Tor Vergata University, CEIS, revised 07 Aug 2015.
    21. Tinic, Murat & Sensoy, Ahmet & Demir, Muge & Nguyen, Duc Khuong, 2020. "Broker Network Connectivity and the Cross-Section of Expected Stock Returns," MPRA Paper 104719, University Library of Munich, Germany.

    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:plo:pone00:0206551. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.