IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v186y2015i2p388-406.html
   My bibliography  Save this article

Asymptotic analysis of the squared estimation error in misspecified factor models

Author

Listed:
  • Onatski, Alexei

Abstract

In this paper, we obtain asymptotic approximations to the squared error of the least squares estimator of the common component in large approximate factor models with possibly misspecified number of factors. The approximations are derived under both strong and weak factors asymptotics assuming that the cross-sectional and temporal dimensions of the data are comparable. We develop consistent estimators of these approximations and propose to use them for model comparison and for selection of the number of factors. We show that the estimators of the number of factors that minimize these loss estimators are asymptotically loss efficient in the sense of Shibata (1980), Li (1987), and Shao (1997).

Suggested Citation

  • Onatski, Alexei, 2015. "Asymptotic analysis of the squared estimation error in misspecified factor models," Journal of Econometrics, Elsevier, vol. 186(2), pages 388-406.
    • Handle: RePEc:eee:econom:v:186:y:2015:i:2:p:388-406
    DOI: 10.1016/j.jeconom.2015.02.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407615000408
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2015.02.016?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. Kapetanios, George & Marcellino, Massimiliano, 2010. "Factor-GMM estimation with large sets of possibly weak instruments," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2655-2675, November.
    2. Andrew T. Foerster & Pierre-Daniel G. Sarte & Mark W. Watson, 2011. "Sectoral versus Aggregate Shocks: A Structural Factor Analysis of Industrial Production," Journal of Political Economy, University of Chicago Press, vol. 119(1), pages 1-38.
    3. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    4. Connor, Gregory & Korajczyk, Robert A, 1993. "A Test for the Number of Factors in an Approximate Factor Model," Journal of Finance, American Finance Association, vol. 48(4), pages 1263-1291, 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. Moon, Hyungsik Roger & Weidner, Martin, 2017. "Dynamic Linear Panel Regression Models With Interactive Fixed Effects," Econometric Theory, Cambridge University Press, vol. 33(1), pages 158-195, February.
    7. Huang, Roger D. & Jo, Hoje, 1995. "Data frequency and the number of factors in stock returns," Journal of Banking & Finance, Elsevier, vol. 19(6), pages 987-1003, September.
    8. Alexander Chudik & M. Hashem Pesaran & Elisa Tosetti, 2011. "Weak and strong cross‐section dependence and estimation of large panels," Econometrics Journal, Royal Economic Society, vol. 14(1), pages 45-90, February.
    9. 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.
    10. Phillips, Peter C. B., 1979. "The sampling distribution of forecasts from a first-order autoregression," Journal of Econometrics, Elsevier, vol. 9(3), pages 241-261, February.
    11. De Mol, Christine & Giannone, Domenico & Reichlin, Lucrezia, 2006. "Forecasting using a large number of predictors: is Bayesian regression a valid alternative to principal components?," Discussion Paper Series 1: Economic Studies 2006,32, Deutsche Bundesbank.
    12. A. Belloni & D. Chen & V. Chernozhukov & C. Hansen, 2012. "Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain," Econometrica, Econometric Society, vol. 80(6), pages 2369-2429, November.
    13. Stock, James H. & Watson, Mark W., 2006. "Forecasting with Many Predictors," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 10, pages 515-554, Elsevier.
    14. Stock, James H. & Watson, Mark, 2011. "Dynamic Factor Models," Scholarly Articles 28469541, Harvard University Department of Economics.
    15. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    16. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
    17. Lancaster, Tony, 2000. "The incidental parameter problem since 1948," Journal of Econometrics, Elsevier, vol. 95(2), pages 391-413, April.
    18. De Mol, Christine & Giannone, Domenico & Reichlin, Lucrezia, 2008. "Forecasting using a large number of predictors: Is Bayesian shrinkage a valid alternative to principal components?," Journal of Econometrics, Elsevier, vol. 146(2), pages 318-328, October.
    19. Alexei Onatski, 2010. "Determining the Number of Factors from Empirical Distribution of Eigenvalues," The Review of Economics and Statistics, MIT Press, vol. 92(4), pages 1004-1016, November.
    20. Forni, Mario & Reichlin, Lucrezia, 2001. "Federal policies and local economies: Europe and the US," European Economic Review, Elsevier, vol. 45(1), pages 109-134, January.
    21. Mehmet Caner & Xu Han, 2014. "Selecting the Correct Number of Factors in Approximate Factor Models: The Large Panel Case With Group Bridge Estimators," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(3), pages 359-374, July.
    22. Onatski, Alexei, 2012. "Asymptotics of the principal components estimator of large factor models with weakly influential factors," Journal of Econometrics, Elsevier, vol. 168(2), pages 244-258.
    23. Bai, Jushan & Ng, Serena, 2008. "Large Dimensional Factor Analysis," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(2), pages 89-163, June.
    24. Alessi, Lucia & Barigozzi, Matteo & Capasso, Marco, 2010. "Improved penalization for determining the number of factors in approximate factor models," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1806-1813, December.
    25. Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, July.
    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. Francisco Corona & Pilar Poncela & Esther Ruiz, 2017. "Determining the number of factors after stationary univariate transformations," Empirical Economics, Springer, vol. 53(1), pages 351-372, August.
    2. 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.
    3. Jie Wei & Yonghui Zhang, 2023. "Does Principal Component Analysis Preserve the Sparsity in Sparse Weak Factor Models?," Papers 2305.05934, arXiv.org, revised Nov 2024.
    4. Guo, Xiao & Chen, Yu & Tang, Cheng Yong, 2023. "Information criteria for latent factor models: A study on factor pervasiveness and adaptivity," Journal of Econometrics, Elsevier, vol. 233(1), pages 237-250.
    5. Norman R. Swanson & Weiqi Xiong, 2018. "Big data analytics in economics: What have we learned so far, and where should we go from here?," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 51(3), pages 695-746, August.
    6. Marine Carrasco & Barbara Rossi, 2016. "In-Sample Inference and Forecasting in Misspecified Factor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 313-338, July.
    7. Gregory Connor & Robert A Korajczyk, 2024. "Semi-Strong Factors in Asset Returns," Journal of Financial Econometrics, Oxford University Press, vol. 22(1), pages 70-93.
    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 & Cho, Haeran & Fryzlewicz, Piotr, 2018. "Simultaneous multiple change-point and factor analysis for high-dimensional time series," Journal of Econometrics, Elsevier, vol. 206(1), pages 187-225.
    10. Andrés Sagner, 2020. "Measuring Systemic Risk: A Quantile Factor Analysis," Working Papers Central Bank of Chile 874, Central Bank of Chile.
    11. Allen, David, 2022. "Asset Pricing Tests, Endogeneity issues and Fama-French factors," MPRA Paper 113610, University Library of Munich, Germany.
    12. Sampi Bravo,James Robert Ezequiel & Jooste,Charl, 2020. "Nowcasting Economic Activity in Times of COVID-19 : An Approximation from the Google Community Mobility Report," Policy Research Working Paper Series 9247, The World Bank.
    13. Freyaldenhoven, Simon, 2022. "Factor models with local factors — Determining the number of relevant factors," Journal of Econometrics, Elsevier, vol. 229(1), pages 80-102.
    14. Alexei Onatski & Chen Wang, 2021. "Spurious Factor Analysis," Econometrica, Econometric Society, vol. 89(2), pages 591-614, March.
    15. Norman R. Swanson, 2016. "Comment," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 348-353, July.
    16. James Sampi, 2016. "High Dimensional Factor Models: An Empirical Bayes Approach," Working Papers 75, Peruvian Economic Association.
    17. Marco Avarucci & Paolo Zaffaroni, 2019. "Robust Nearly-Efficient Estimation of Large Panels with Factor Structures," Papers 1902.11181, arXiv.org.
    18. Matteo Barigozzi & Marc Hallin & Stefano Soccorsi, 2017. "Identification of Global and National Shocks in International Financial Markets via General Dynamic Factor Models," Working Papers ECARES ECARES 2017-10, ULB -- Universite Libre de Bruxelles.

    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. Freyaldenhoven, Simon, 2022. "Factor models with local factors — Determining the number of relevant factors," Journal of Econometrics, Elsevier, vol. 229(1), pages 80-102.
    2. Simon Freyaldenhoven, 2017. "A Generalized Factor Model with Local Factors," 2017 Papers pfr361, Job Market Papers.
    3. 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.
    4. 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.
    5. 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.
    6. repec:cte:wsrepe:23974 is not listed on IDEAS
    7. Pilar Poncela & Esther Ruiz, 2016. "Small- Versus Big-Data Factor Extraction in Dynamic Factor Models: An Empirical Assessment," Advances in Econometrics, in: Dynamic Factor Models, volume 35, pages 401-434, Emerald Group Publishing Limited.
    8. Smeekes, Stephan & Wijler, Etienne, 2018. "Macroeconomic forecasting using penalized regression methods," International Journal of Forecasting, Elsevier, vol. 34(3), pages 408-430.
    9. Lütkepohl, Helmut, 2014. "Structural vector autoregressive analysis in a data rich environment: A survey," SFB 649 Discussion Papers 2014-004, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    10. Alexander Chudik & M. Hashem Pesaran, 2013. "Large panel data models with cross-sectional dependence: a survey," Globalization Institute Working Papers 153, Federal Reserve Bank of Dallas.
    11. repec:hum:wpaper:sfb649dp2014-004 is not listed on IDEAS
    12. 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.
    13. Catherine Doz & Peter Fuleky, 2019. "Dynamic Factor Models," Working Papers 2019-4, University of Hawaii Economic Research Organization, University of Hawaii at Manoa.
    14. Yoshimasa Uematsu & Takashi Yamagata, 2019. "Estimation of Weak Factor Models," DSSR Discussion Papers 96, Graduate School of Economics and Management, Tohoku University.
    15. Luciani, Matteo, 2014. "Forecasting with approximate dynamic factor models: The role of non-pervasive shocks," International Journal of Forecasting, Elsevier, vol. 30(1), pages 20-29.
    16. Francisco Corona & Pilar Poncela & Esther Ruiz, 2017. "Determining the number of factors after stationary univariate transformations," Empirical Economics, Springer, vol. 53(1), pages 351-372, August.
    17. Alessandro Barbarino & Efstathia Bura, 2017. "A Unified Framework for Dimension Reduction in Forecasting," Finance and Economics Discussion Series 2017-004, Board of Governors of the Federal Reserve System (U.S.).
    18. Gagliardini, Patrick & Ossola, Elisa & Scaillet, Olivier, 2019. "A diagnostic criterion for approximate factor structure," Journal of Econometrics, Elsevier, vol. 212(2), pages 503-521.
    19. Ergemen, Yunus Emre & Rodríguez-Caballero, C. Vladimir, 2023. "Estimation of a dynamic multi-level factor model with possible long-range dependence," International Journal of Forecasting, Elsevier, vol. 39(1), pages 405-430.
    20. Bai, Jushan & Ng, Serena, 2023. "Approximate factor models with weaker loadings," Journal of Econometrics, Elsevier, vol. 235(2), pages 1893-1916.
    21. Francisco Corona & Graciela González-Farías & Pedro Orraca, 2017. "A dynamic factor model for the Mexican economy: are common trends useful when predicting economic activity?," Latin American Economic Review, Springer;Centro de Investigaciòn y Docencia Económica (CIDE), vol. 26(1), pages 1-35, December.
    22. Cheng, Xu & Hansen, Bruce E., 2015. "Forecasting with factor-augmented regression: A frequentist model averaging approach," Journal of Econometrics, Elsevier, vol. 186(2), pages 280-293.

    More about this item

    Keywords

    Misspecification; Factor model; Number of factors; Loss efficiency;
    All these keywords.

    JEL classification:

    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

    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:eee:econom:v:186:y:2015:i:2:p:388-406. 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.