IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v137y2015icp119-140.html
   My bibliography  Save this article

On singular value distribution of large-dimensional autocovariance matrices

Author

Listed:
  • Li, Zeng
  • Pan, Guangming
  • Yao, Jianfeng

Abstract

Let (εj)j≥0 be a sequence of independent p-dimensional random vectors and τ≥1 a given integer. From a sample ε1,…,εT+τ of the sequence, the so-called lag-τ auto-covariance matrix is Cτ=T−1∑j=1Tετ+jεjt. When the dimension p is large compared to the sample size T, this paper establishes the limit of the singular value distribution of Cτ assuming that p and T grow to infinity proportionally and the sequence has uniformly bounded (4+δ)th order moments. Compared to existing asymptotic results on sample covariance matrices developed in random matrix theory, the case of an auto-covariance matrix is much more involved due to the fact that the summands are dependent and the matrix Cτ is not symmetric. Several new techniques are introduced for the derivation of the main theorem.

Suggested Citation

  • Li, Zeng & Pan, Guangming & Yao, Jianfeng, 2015. "On singular value distribution of large-dimensional autocovariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 119-140.
  • Handle: RePEc:eee:jmvana:v:137:y:2015:i:c:p:119-140
    DOI: 10.1016/j.jmva.2015.02.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X1500041X
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jmva.2015.02.006?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. Silverstein, J. W., 1995. "Strong Convergence of the Empirical Distribution of Eigenvalues of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 331-339, November.
    2. Lam, Clifford & Yao, Qiwei, 2012. "Factor modeling for high-dimensional time series: inference for the number of factors," LSE Research Online Documents on Economics 45684, London School of Economics and Political Science, LSE Library.
    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. Sanders, Jaron & Van Werde, Alexander, 2023. "Singular value distribution of dense random matrices with block Markovian dependence," Stochastic Processes and their Applications, Elsevier, vol. 158(C), pages 453-504.
    2. Heiny, Johannes & Mikosch, Thomas, 2021. "Large sample autocovariance matrices of linear processes with heavy tails," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 344-375.

    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. Chen, Jiaqi & Zhang, Yangchun & Li, Weiming & Tian, Boping, 2018. "A supplement on CLT for LSS under a large dimensional generalized spiked covariance model," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 57-65.
    2. Yuefeng Han & Rong Chen & Dan Yang & Cun-Hui Zhang, 2020. "Tensor Factor Model Estimation by Iterative Projection," Papers 2006.02611, arXiv.org, revised Jul 2024.
    3. Jianqing Fan & Xu Han, 2017. "Estimation of the false discovery proportion with unknown dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 1143-1164, September.
    4. Matteo Barigozzi & Marc Hallin, 2023. "Dynamic Factor Models: a Genealogy," Papers 2310.17278, arXiv.org, revised Jan 2024.
    5. 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.
    6. Zhao, Zifeng & Zhang, Zhengjun & Chen, Rong, 2018. "Modeling maxima with autoregressive conditional Fréchet model," Journal of Econometrics, Elsevier, vol. 207(2), pages 325-351.
    7. Feng, Guohua & Gao, Jiti & Peng, Bin, 2022. "An integrated panel data approach to modelling economic growth," Journal of Econometrics, Elsevier, vol. 228(2), pages 379-397.
    8. Jian Zhang & Jie Li, 2022. "Factorized estimation of high‐dimensional nonparametric covariance models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 542-567, June.
    9. Tian, Xintao & Lu, Yuting & Li, Weiming, 2015. "A robust test for sphericity of high-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 217-227.
    10. Pan, Guangming, 2010. "Strong convergence of the empirical distribution of eigenvalues of sample covariance matrices with a perturbation matrix," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1330-1338, July.
    11. Tobias Hartl & Roland Weigand, 2018. "Multivariate Fractional Components Analysis," Papers 1812.09149, arXiv.org, revised Jan 2019.
    12. Ma, Shujie & Linton, Oliver & Gao, Jiti, 2021. "Estimation and inference in semiparametric quantile factor models," Journal of Econometrics, Elsevier, vol. 222(1), pages 295-323.
    13. Heiny, Johannes & Mikosch, Thomas, 2017. "Eigenvalues and eigenvectors of heavy-tailed sample covariance matrices with general growth rates: The iid case," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2179-2207.
    14. Bai, Jushan & Liao, Yuan, 2016. "Efficient estimation of approximate factor models via penalized maximum likelihood," Journal of Econometrics, Elsevier, vol. 191(1), pages 1-18.
    15. Hallin, Marc & Lippi, Marco, 2013. "Factor models in high-dimensional time series—A time-domain approach," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2678-2695.
    16. Trucíos, Carlos & Hotta, Luiz K. & Valls Pereira, Pedro L., 2019. "On the robustness of the principal volatility components," Journal of Empirical Finance, Elsevier, vol. 52(C), pages 201-219.
    17. Xiaorong Yang & Jia Chen & Degui Li & Runze Li, 2024. "Functional-Coefficient Quantile Regression for Panel Data with Latent Group Structure," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(3), pages 1026-1040, July.
    18. Poncela, Pilar & Ruiz, Esther & Miranda, Karen, 2021. "Factor extraction using Kalman filter and smoothing: This is not just another survey," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1399-1425.
    19. Simon Beyeler & Sylvia Kaufmann, 2021. "Reduced‐form factor augmented VAR—Exploiting sparsity to include meaningful factors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(7), pages 989-1012, November.
    20. Ledoit, Olivier & Wolf, Michael, 2017. "Numerical implementation of the QuEST function," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 199-223.

    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:jmvana:v:137:y:2015:i:c:p:119-140. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.