IDEAS home Printed from https://ideas.repec.org/p/cam/camdae/1808.html
   My bibliography  Save this paper

Asymptotics of the principal components estimator of large factor models with weak factors and i.i.d. Gaussian noise

Author

Listed:
  • Onatski, A.

Abstract

We consider large factor models where factors' explanatory power does not strongly dominate the explanatory power of the idiosyncratic terms asymptotically. We find the first and second order asymptotics of the principal components estimator of such a weak factors as the dimensionality of the data and the number of observations tend to infinity proportionally. The principal components estimator is inconsistent but asymptotically normal.

Suggested Citation

  • Onatski, A., 2018. "Asymptotics of the principal components estimator of large factor models with weak factors and i.i.d. Gaussian noise," Cambridge Working Papers in Economics 1808, Faculty of Economics, University of Cambridge.
    • Handle: RePEc:cam:camdae:1808
    Note: ao319
    as

    Download full text from publisher

    File URL: http://www.econ.cam.ac.uk/research-files/repec/cam/pdf/cwpe1808.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mario Forni & Lucrezia Reichlin, 1998. "Let's Get Real: A Factor Analytical Approach to Disaggregated Business Cycle Dynamics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 453-473.
    2. Bai, Z. D. & Silverstein, Jack W. & Yin, Y. Q., 1988. "A note on the largest eigenvalue of a large dimensional sample covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 26(2), pages 166-168, August.
    3. Boivin, Jean & Ng, Serena, 2006. "Are more data always better for factor analysis?," Journal of Econometrics, Elsevier, vol. 132(1), pages 169-194, May.
    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. Andreou, Elena & Ghysels, Eric, 2021. "Predicting the VIX and the volatility risk premium: The role of short-run funding spreads Volatility Factors," Journal of Econometrics, Elsevier, vol. 220(2), pages 366-398.
    2. Alexei Onatski & Chen Wang, 2021. "Spurious Factor Analysis," Econometrica, Econometric Society, vol. 89(2), pages 591-614, March.
    3. Jungjun Choi & Ming Yuan, 2024. "High Dimensional Factor Analysis with Weak Factors," Papers 2402.05789, arXiv.org.

    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. David Havrlant & Peter Tóth & Julia Wörz, 2016. "On the optimal number of indicators – nowcasting GDP growth in CESEE," Focus on European Economic Integration, Oesterreichische Nationalbank (Austrian Central Bank), issue 4, pages 54-72.
    2. Alhassan Abdullah Mohammed, 2011. "A Coincident Indicator of the Gulf Cooperation Council Business Cycle," Review of Middle East Economics and Finance, De Gruyter, vol. 6(3), pages 1-23, February.
    3. Stock, J.H. & Watson, M.W., 2016. "Dynamic Factor Models, Factor-Augmented Vector Autoregressions, and Structural Vector Autoregressions in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 415-525, Elsevier.
    4. Kelly, Bryan & Pruitt, Seth, 2015. "The three-pass regression filter: A new approach to forecasting using many predictors," Journal of Econometrics, Elsevier, vol. 186(2), pages 294-316.
    5. Marc Hallin & Roman Liska, 2008. "Dynamic Factors in the Presence of Block Structure," Working Papers ECARES 2008_012, ULB -- Universite Libre de Bruxelles.
    6. Simona Delle Chiaie & Laurent Ferrara & Domenico Giannone, 2022. "Common factors of commodity prices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(3), pages 461-476, April.
    7. Gupta, Rangan & Kabundi, Alain, 2011. "A large factor model for forecasting macroeconomic variables in South Africa," International Journal of Forecasting, Elsevier, vol. 27(4), pages 1076-1088, October.
    8. Forni, Mario & Giannone, Domenico & Lippi, Marco & Reichlin, Lucrezia, 2009. "Opening The Black Box: Structural Factor Models With Large Cross Sections," Econometric Theory, Cambridge University Press, vol. 25(5), pages 1319-1347, October.
    9. Rusnák, Marek, 2016. "Nowcasting Czech GDP in real time," Economic Modelling, Elsevier, vol. 54(C), pages 26-39.
    10. Karim Barhoumi & Olivier Darné & Laurent Ferrara, 2014. "Dynamic factor models: A review of the literature," OECD Journal: Journal of Business Cycle Measurement and Analysis, OECD Publishing, Centre for International Research on Economic Tendency Surveys, vol. 2013(2), pages 73-107.
    11. Maldonado, Javier & Ruiz Ortega, Esther, 2017. "Accurate Subsampling Intervals of Principal Components Factors," DES - Working Papers. Statistics and Econometrics. WS 23974, Universidad Carlos III de Madrid. Departamento de Estadística.
    12. Sagaert, Yves R. & Aghezzaf, El-Houssaine & Kourentzes, Nikolaos & Desmet, Bram, 2018. "Tactical sales forecasting using a very large set of macroeconomic indicators," European Journal of Operational Research, Elsevier, vol. 264(2), pages 558-569.
    13. repec:onb:oenbwp:y::i:89:b:1 is not listed on IDEAS
    14. Kihwan Kim & Hyun Hak Kim & Norman R. Swanson, 2023. "Mixing mixed frequency and diffusion indices in good times and in bad: an assessment based on historical data around the great recession of 2008," Empirical Economics, Springer, vol. 64(3), pages 1421-1469, March.
    15. Christophe Van Nieuwenhuyze, 2006. "A generalised dynamic factor model for the Belgian economy - Useful business cycle indicators and GDP growth forecasts," Working Paper Research 80, National Bank of Belgium.
    16. Sokbae Lee & Serena Ng, 2020. "An Econometric Perspective on Algorithmic Subsampling," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 45-80, August.
    17. Kihwan Kim & Norman Swanson, 2013. "Diffusion Index Model Specification and Estimation Using Mixed Frequency Datasets," Departmental Working Papers 201315, Rutgers University, Department of Economics.
    18. Bessonovs, Andrejs, 2011. "GDP Modelling with Factor Model: an Impact of Nested Data on Forecasting Accuracy," MPRA Paper 30211, University Library of Munich, Germany.
    19. Bettina Becker & Stephen G. Hall, 2009. "A new look at economic convergence in Europe: a common factor approach," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 14(1), pages 85-97.
    20. Stock, James H. & Watson, Mark, 2011. "Dynamic Factor Models," Scholarly Articles 28469541, Harvard University Department of Economics.
    21. Helmut Lütkepohl, 2014. "Structural Vector Autoregressive Analysis in a Data Rich Environment: A Survey," SFB 649 Discussion Papers SFB649DP2014-004, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

    More about this item

    Keywords

    Large factor models; principal components; phase transition; weak factors; inconsistency; asymptotic distribution; Marčenko-Pastur law;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:cam:camdae:1808. 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: Jake Dyer (email available below). General contact details of provider: https://www.econ.cam.ac.uk/ .

    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.