IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v235y2023i2p1337-1354.html
   My bibliography  Save this article

Testing and signal identification for two-sample high-dimensional covariances via multi-level thresholding

Author

Listed:
  • Chen, Song Xi
  • Guo, Bin
  • Qiu, Yumou

Abstract

The paper considers testing and signal identification for covariance matrices from two populations of marginally sub-Gaussian distributed. A multi-level thresholding procedure is proposed for testing the equality of two high-dimensional covariance matrices, which is designed to detect sparse and faint differences between the covariances. A novel U-statistic composition is developed to establish the asymptotic distribution of the thresholding statistics in conjunction with the matrix blocking and the coupling techniques. It is shown that the proposed test is more powerful than the existing tests in detecting sparse and weak signals in covariances. Multiple testing procedures are constructed to discover different covariances and the sub-groups of variables with different covariance structures between the two populations. The proposed procedures are based on the multi-level thresholding test, which are able to control the false discovery proportion (FDP) with high power. Simulation experiments and a case study on the returns of the S&P 500 stocks before and after the COVID-19 pandemic are conducted to demonstrate and compare the utilities of the proposed methods.

Suggested Citation

  • Chen, Song Xi & Guo, Bin & Qiu, Yumou, 2023. "Testing and signal identification for two-sample high-dimensional covariances via multi-level thresholding," Journal of Econometrics, Elsevier, vol. 235(2), pages 1337-1354.
    • Handle: RePEc:eee:econom:v:235:y:2023:i:2:p:1337-1354
    DOI: 10.1016/j.jeconom.2022.10.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407622001944
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2022.10.008?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. Jenish, Nazgul & Prucha, Ingmar R., 2009. "Central limit theorems and uniform laws of large numbers for arrays of random fields," Journal of Econometrics, Elsevier, vol. 150(1), pages 86-98, May.
    2. Adam J. Rothman, 2012. "Positive definite estimators of large covariance matrices," Biometrika, Biometrika Trust, vol. 99(3), pages 733-740.
    3. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    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. Mokkadem, Abdelkader, 1988. "Mixing properties of ARMA processes," Stochastic Processes and their Applications, Elsevier, vol. 29(2), pages 309-315, September.
    6. 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.
    7. Fan, Jianqing & Han, Fang & Liu, Han & Vickers, Byron, 2016. "Robust inference of risks of large portfolios," Journal of Econometrics, Elsevier, vol. 194(2), pages 298-308.
    8. Hakan Yilmazkuday, 2023. "COVID-19 effects on the S&P 500 index," Applied Economics Letters, Taylor & Francis Journals, vol. 30(1), pages 7-13, January.
    9. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    10. Aurore Delaigle & Peter Hall & Jiashun Jin, 2011. "Robustness and accuracy of methods for high dimensional data analysis based on Student's t‐statistic," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(3), pages 283-301, June.
    11. Camillo Lento & Nikola Gradojevic, 2021. "S&P 500 Index Price Spillovers around the COVID-19 Market Meltdown," JRFM, MDPI, vol. 14(7), pages 1-13, July.
    12. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    13. Chen, Songxi, 2012. "Two Sample Tests for High Dimensional Covariance Matrices," MPRA Paper 46026, University Library of Munich, Germany.
    14. Schott, James R., 2007. "A test for the equality of covariance matrices when the dimension is large relative to the sample sizes," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6535-6542, August.
    15. Genovese, Christopher R. & Wasserman, Larry, 2006. "Exceedance Control of the False Discovery Proportion," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1408-1417, December.
    16. Srivastava, Muni S. & Yanagihara, Hirokazu, 2010. "Testing the equality of several covariance matrices with fewer observations than the dimension," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1319-1329, July.
    17. Gongjun Xu & Lifeng Lin & Peng Wei & Wei Pan, 2016. "An adaptive two-sample test for high-dimensional means," Biometrika, Biometrika Trust, vol. 103(3), pages 609-624.
    18. Jinyuan Chang & Wen Zhou & Wen-Xin Zhou & Lan Wang, 2017. "Comparing large covariance matrices under weak conditions on the dependence structure and its application to gene clustering," Biometrics, The International Biometric Society, vol. 73(1), pages 31-41, March.
    19. Tony Cai & Weidong Liu & Yin Xia, 2013. "Two-Sample Covariance Matrix Testing and Support Recovery in High-Dimensional and Sparse Settings," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 265-277, March.
    20. Huitong Qiu & Fang Han & Han Liu & Brian Caffo, 2016. "Joint estimation of multiple graphical models from high dimensional time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 487-504, March.
    21. John D. Storey, 2002. "A direct approach to false discovery rates," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 479-498, August.
    22. Jianqing Fan & Yuan Liao & Jiawei Yao, 2015. "Power Enhancement in High‐Dimensional Cross‐Sectional Tests," Econometrica, Econometric Society, vol. 83(4), pages 1497-1541, July.
    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. 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).
    2. Yu, Xiufan & Yao, Jiawei & Xue, Lingzhou, 2024. "Power enhancement for testing multi-factor asset pricing models via Fisher’s method," Journal of Econometrics, Elsevier, vol. 239(2).
    3. Chen, Xin & Yang, Dan & Xu, Yan & Xia, Yin & Wang, Dong & Shen, Haipeng, 2023. "Testing and support recovery of correlation structures for matrix-valued observations with an application to stock market data," Journal of Econometrics, Elsevier, vol. 232(2), pages 544-564.
    4. Tao Zhang & Zhiwen Wang & Yanling Wan, 2021. "Functional test for high-dimensional covariance matrix, with application to mitochondrial calcium concentration," Statistical Papers, Springer, vol. 62(3), pages 1213-1230, June.
    5. Cai, T. Tony & Zhang, Anru, 2016. "Inference for high-dimensional differential correlation matrices," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 107-126.
    6. Li, Weiming & Qin, Yingli, 2014. "Hypothesis testing for high-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 108-119.
    7. Zhang, Yangchun & Zhou, Yirui & Liu, Xiaowei, 2023. "Applications on linear spectral statistics of high-dimensional sample covariance matrix with divergent spectrum," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    8. Tsukuda, Koji & Matsuura, Shun, 2019. "High-dimensional testing for proportional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 412-420.
    9. Zhidong Bai & Jiang Hu & Chen Wang & Chao Zhang, 2021. "Test on the linear combinations of covariance matrices in high-dimensional data," Statistical Papers, Springer, vol. 62(2), pages 701-719, April.
    10. Benoît Dewaele & Hugues Pirotte & N. Tuchschmid & E. Wallerstein, 2011. "Assessing the Performance of Funds of Hedge Funds," Working Papers CEB 11-041, ULB -- Universite Libre de Bruxelles.
    11. Mingjuan Zhang & Libin Jin, 2024. "High-Dimensional U-Statistics Type Hypothesis Testing via Jackknife Pseudo-Values with Multiplier Bootstrap," Mathematics, MDPI, vol. 12(23), pages 1-20, December.
    12. Allen, David & Lizieri, Colin & Satchell, Stephen, 2020. "A comparison of non-Gaussian VaR estimation and portfolio construction techniques," Journal of Empirical Finance, Elsevier, vol. 58(C), pages 356-368.
    13. Muni S. Srivastava & Hirokazu Yanagihara & Tatsuya Kubokawa, 2014. "Tests for Covariance Matrices in High Dimension with Less Sample Size," CIRJE F-Series CIRJE-F-933, CIRJE, Faculty of Economics, University of Tokyo.
    14. Deepak Nag Ayyala & Santu Ghosh & Daniel F. Linder, 2022. "Covariance matrix testing in high dimension using random projections," Computational Statistics, Springer, vol. 37(3), pages 1111-1141, July.
    15. Chang, Jinyuan & Qiu, Yumou & Yao, Qiwei & Zou, Tao, 2018. "Confidence regions for entries of a large precision matrix," LSE Research Online Documents on Economics 87513, London School of Economics and Political Science, LSE Library.
    16. Cheng, Guanghui & Liu, Baisen & Tian, Guoliang & Zheng, Shurong, 2020. "Testing proportionality of two high-dimensional covariance matrices," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    17. Andrew Martinez, 2017. "Testing for Differences in Path Forecast Accuracy: Forecast-Error Dynamics Matter," Working Papers (Old Series) 1717, Federal Reserve Bank of Cleveland.
    18. Jinyuan Chang & Wen Zhou & Wen-Xin Zhou & Lan Wang, 2017. "Comparing large covariance matrices under weak conditions on the dependence structure and its application to gene clustering," Biometrics, The International Biometric Society, vol. 73(1), pages 31-41, March.
    19. Xie, Jichun & Kang, Jian, 2017. "High-dimensional tests for functional networks of brain anatomic regions," Journal of Multivariate Analysis, Elsevier, vol. 156(C), pages 70-88.
    20. He, Daojiang & Liu, Huanyu & Xu, Kai & Cao, Mingxiang, 2021. "Generalized Schott type tests for complete independence in high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 183(C).

    More about this item

    Keywords

    Detection boundary; High dimensionality; Multiple testing; Rare and faint signal; Thresholding;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

    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:235:y:2023:i:2:p:1337-1354. 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.