IDEAS home Printed from https://ideas.repec.org/p/msh/ebswps/2018-13.html
   My bibliography  Save this paper

Exponent of cross-sectional dependence for residuals

Author

Listed:
  • Natalia Bailey
  • George Kapetanios
  • M. Hashem Pesaran

Abstract

In this paper we focus on estimating the degree of cross-sectional dependence in the error terms of a classical panel data regression model. For this purpose we propose an estimator of the exponent of cross-sectional dependence denoted by alpha, which is based on the number of non-zero pair-wise cross correlations of these errors. We prove that our estimator, tilde(alpha), is consistent and derive the rate at which tilde(alpha) approaches its true value. We evaluate the finite sample properties of the proposed estimator by use of a Monte Carlo simulation study. The numerical results are encouraging and supportive of the theoretical findings. Finally, we undertake an empirical investigation of alpha for the errors of the CAPM model and its Fama-French extensions using 10-year rolling samples from S&P 500 securities over the period Sept 1989 - May 2018.

Suggested Citation

  • Natalia Bailey & George Kapetanios & M. Hashem Pesaran, 2018. "Exponent of cross-sectional dependence for residuals," Monash Econometrics and Business Statistics Working Papers 13/18, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2018-13
    as

    Download full text from publisher

    File URL: https://www.monash.edu/business/ebs/research/publications/ebs/wp13-2018.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. Natalia Bailey & George Kapetanios & M. Hashem Pesaran, 2016. "Exponent of Cross‐Sectional Dependence: Estimation and Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(6), pages 929-960, September.
    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. A. Chudik & G. Kapetanios & M. Hashem Pesaran, 2018. "A One Covariate at a Time, Multiple Testing Approach to Variable Selection in High‐Dimensional Linear Regression Models," Econometrica, Econometric Society, vol. 86(4), pages 1479-1512, July.
    5. 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..
    6. Bailey, Natalia & Pesaran, M. Hashem & Smith, L. Vanessa, 2019. "A multiple testing approach to the regularisation of large sample correlation matrices," Journal of Econometrics, Elsevier, vol. 208(2), pages 507-534.
    7. 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.
    8. Jianhua Z. Huang & Naiping Liu & Mohsen Pourahmadi & Linxu Liu, 2006. "Covariance matrix selection and estimation via penalised normal likelihood," Biometrika, Biometrika Trust, vol. 93(1), pages 85-98, March.
    9. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
    10. Pesaran, M. H. & Yamagata, T., 2012. "Testing CAPM with a Large Number of Assets (Updated 28th March 2012)," Cambridge Working Papers in Economics 1210, Faculty of Economics, University of Cambridge.
    11. 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.
    12. G. Kapetanios, 2008. "A bootstrap procedure for panel data sets with many cross-sectional units," Econometrics Journal, Royal Economic Society, vol. 11(2), pages 377-395, July.
    13. Cai, Tony & Liu, Weidong, 2011. "Adaptive Thresholding for Sparse Covariance Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 672-684.
    14. Chamberlain, Gary, 1983. "Funds, Factors, and Diversification in Arbitrage Pricing Models," Econometrica, Econometric Society, vol. 51(5), pages 1305-1323, September.
    15. Eugene F. Fama & Kenneth R. French, 2004. "The Capital Asset Pricing Model: Theory and Evidence," Journal of Economic Perspectives, American Economic Association, vol. 18(3), pages 25-46, Summer.
    16. Rothman, Adam J. & Levina, Elizaveta & Zhu, Ji, 2009. "Generalized Thresholding of Large Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 177-186.
    17. Pesaran, M. Hashem & Yamagata, Takashi, 2012. "Testing CAPM with a Large Number of Assets," IZA Discussion Papers 6469, Institute of Labor Economics (IZA).
    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. Arnab Bhattacharjee & Jan Ditzen & Sean Holly, 2022. "Spatial and Spatio-Temporal Error Correction, Networks and Common Correlated Effects," Advances in Econometrics, in: Essays in Honor of M. Hashem Pesaran: Panel Modeling, Micro Applications, and Econometric Methodology, volume 43, pages 37-60, Emerald Group Publishing Limited.
    2. Valizadeh, Pourya & Fischer, Bart L. & Bryant, Henry L., 2022. "Investigating the Differential Effects of the Economy on SNAP Participation: A Factor Model Approach," 2022 Annual Meeting, July 31-August 2, Anaheim, California 322367, Agricultural and Applied Economics Association.
    3. 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.
    4. Ge, Shuyi & Li, Shaoran & Linton, Oliver, 2023. "News-implied linkages and local dependency in the equity market," Journal of Econometrics, Elsevier, vol. 235(2), pages 779-815.
    5. Yu-Ke, Chen & Hassan, Muhammad Shahid & Kalim, Rukhsana & Mahmood, Haider & Arshed, Noman & Salman, Muhammad, 2022. "Testing asymmetric influence of clean and unclean energy for targeting environmental quality in environmentally poor economies," Renewable Energy, Elsevier, vol. 197(C), pages 765-775.
    6. Ge, S., 2020. "Text-Based Linkages and Local Risk Spillovers in the Equity Market," Cambridge Working Papers in Economics 20115, Faculty of Economics, University of Cambridge.
    7. Floros Flouros & Victoria Pistikou & Vasilios Plakandaras, 2022. "Geopolitical Risk as a Determinant of Renewable Energy Investments," Energies, MDPI, vol. 15(4), pages 1-21, February.
    8. Tullio Gregori & Marco Giansoldati, 2023. "Do current and capital account liberalizations affect economic growth in the long run?," Empirical Economics, Springer, vol. 65(1), pages 247-273, July.
    9. Arnab Bhattacharjee & Tapabrata Maiti, 2019. "P. C. Mahalanobis in the Context of Current Econometrics Research," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 1-11, September.
    10. Kapetanios, G. & Pesaran, M.H. & Reese, S., 2021. "Detection of units with pervasive effects in large panel data models," Journal of Econometrics, Elsevier, vol. 221(2), pages 510-541.

    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. Bailey, Natalia & Pesaran, M. Hashem & Smith, L. Vanessa, 2019. "A multiple testing approach to the regularisation of large sample correlation matrices," Journal of Econometrics, Elsevier, vol. 208(2), pages 507-534.
    2. 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.
    3. Xi Luo, 2011. "Recovering Model Structures from Large Low Rank and Sparse Covariance Matrix Estimation," Papers 1111.1133, arXiv.org, revised Mar 2013.
    4. Pesaran, M. Hashem & Yamagata, Takashi, 2012. "Testing CAPM with a Large Number of Assets," IZA Discussion Papers 6469, Institute of Labor Economics (IZA).
    5. Lam, Clifford, 2020. "High-dimensional covariance matrix estimation," LSE Research Online Documents on Economics 101667, London School of Economics and Political Science, LSE Library.
    6. 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.
    7. 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.
    8. Aït-Sahalia, Yacine & Xiu, Dacheng, 2017. "Using principal component analysis to estimate a high dimensional factor model with high-frequency data," Journal of Econometrics, Elsevier, vol. 201(2), pages 384-399.
    9. Seung C. Ahn & Alex R. Horenstein, 2017. "Asset Pricing and Excess Returns over the Market Return," Working Papers 2017-12, University of Miami, Department of Economics.
    10. Pesaran, M. H. & Yamagata, T., 2012. "Testing CAPM with a Large Number of Assets (Updated 28th March 2012)," Cambridge Working Papers in Economics 1210, Faculty of Economics, University of Cambridge.
    11. Fan, Jianqing & Liao, Yuan & Shi, Xiaofeng, 2015. "Risks of large portfolios," Journal of Econometrics, Elsevier, vol. 186(2), pages 367-387.
    12. Chen, Jia & Li, Degui & Linton, Oliver, 2019. "A new semiparametric estimation approach for large dynamic covariance matrices with multiple conditioning variables," Journal of Econometrics, Elsevier, vol. 212(1), pages 155-176.
    13. Gautam Sabnis & Debdeep Pati & Anirban Bhattacharya, 2019. "Compressed Covariance Estimation with Automated Dimension Learning," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 466-481, December.
    14. M. Hashem Pesaran & Ron P. Smith, 2021. "Factor Strengths, Pricing Errors, and Estimation of Risk Premia," CESifo Working Paper Series 8947, CESifo.
    15. Yuki Ikeda & Tatsuya Kubokawa, 2015. "Linear Shrinkage Estimation of Large Covariance Matrices with Use of Factor Models," CIRJE F-Series CIRJE-F-958, CIRJE, Faculty of Economics, University of Tokyo.
    16. Huang, Na & Fryzlewicz, Piotr, 2018. "NOVELIST estimator of large correlation and covariance matrices and their inverses," LSE Research Online Documents on Economics 89055, London School of Economics and Political Science, LSE Library.
    17. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    18. George Kapetanios & M. Hashem Pesaran & Simon Reese, 2018. "A Residual-based Threshold Method for Detection of Units that are Too Big to Fail in Large Factor Models," CESifo Working Paper Series 7401, CESifo.
    19. Ikeda, Yuki & Kubokawa, Tatsuya & Srivastava, Muni S., 2016. "Comparison of linear shrinkage estimators of a large covariance matrix in normal and non-normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 95-108.
    20. Mian Huang & Shangbing Yu & Weixin Yao, 2022. "Regularized Factor Portfolio for Cross-sectional Multifactor Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 427-449, August.

    More about this item

    Keywords

    Pair-wise correlations; cross-sectional dependence; cross-sectional averages; weak and strong factor models; CAPM and Fama-French factors.;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

    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:msh:ebswps:2018-13. 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: Professor Xibin Zhang (email available below). General contact details of provider: https://edirc.repec.org/data/dxmonau.html .

    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.