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Asymptotic analysis of the squared estimation error in misspecified factor models

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  • 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).

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  • 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
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    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.
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    Cited by:

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    3. Jie Wei & Yonghui Zhang, 2023. "Does Principal Component Analysis Preserve the Sparsity in Sparse Weak Factor Models?," Papers 2305.05934, arXiv.org.
    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, 2019. "Semi-strong factors in asset returns," Economics Department Working Paper Series n294-19.pdf, Department of Economics, National University of Ireland - Maynooth.
    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.

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    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

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