IDEAS home Printed from https://ideas.repec.org/a/taf/jnlasa/v112y2017i517p235-253.html
   My bibliography  Save this article

A Dynamic Structure for High-Dimensional Covariance Matrices and Its Application in Portfolio Allocation

Author

Listed:
  • Shaojun Guo
  • John Leigh Box
  • Wenyang Zhang

Abstract

Estimation of high-dimensional covariance matrices is an interesting and important research topic. In this article, we propose a dynamic structure and develop an estimation procedure for high-dimensional covariance matrices. Asymptotic properties are derived to justify the estimation procedure and simulation studies are conducted to demonstrate its performance when the sample size is finite. By exploring a financial application, an empirical study shows that portfolio allocation based on dynamic high-dimensional covariance matrices can significantly outperform the market from 1995 to 2014. Our proposed method also outperforms portfolio allocation based on the sample covariance matrix, the covariance matrix based on factor models, and the shrinkage estimator of covariance matrix. Supplementary materials for this article are available online.

Suggested Citation

  • Shaojun Guo & John Leigh Box & Wenyang Zhang, 2017. "A Dynamic Structure for High-Dimensional Covariance Matrices and Its Application in Portfolio Allocation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 235-253, January.
    • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:517:p:235-253
    DOI: 10.1080/01621459.2015.1129969
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01621459.2015.1129969
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/01621459.2015.1129969?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. Jianqing Fan & Qiwei Yao & Zongwu Cai, 2003. "Adaptive varying‐coefficient linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 57-80, February.
    2. Jianqing Fan & Wenyang Zhang, 2000. "Simultaneous Confidence Bands and Hypothesis Testing in Varying‐coefficient Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 715-731, December.
    3. Li, Jialiang & Zhang, Wenyang, 2011. "A Semiparametric Threshold Model for Censored Longitudinal Data Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 685-696.
    4. Jianqing Fan & Jingjin Zhang & Ke Yu, 2012. "Vast Portfolio Selection With Gross-Exposure Constraints," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 592-606, June.
    5. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    6. Xia, Yingcun & Härdle, Wolfgang, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1162-1184, May.
    7. Lam, Clifford & Fan, Jianqing, 2009. "Sparsistency and rates of convergence in large covariance matrix estimation," LSE Research Online Documents on Economics 31540, London School of Economics and Political Science, LSE Library.
    8. 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.
    9. Fama, Eugene F & French, Kenneth R, 1992. "The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-465, June.
    10. 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.
    11. Wei Biao Wu, 2003. "Nonparametric estimation of large covariance matrices of longitudinal data," Biometrika, Biometrika Trust, vol. 90(4), pages 831-844, December.
    12. Fan, Jianqing & Fan, Yingying & Lv, Jinchi, 2008. "High dimensional covariance matrix estimation using a factor model," Journal of Econometrics, Elsevier, vol. 147(1), pages 186-197, November.
    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. 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.
    2. Li, Jialiang & Zhang, Wenyang & Kong, Efang, 2018. "Factor models for asset returns based on transformed factors," Journal of Econometrics, Elsevier, vol. 207(2), pages 432-448.
    3. Li, Degui, 2024. "Estimation of Large Dynamic Covariance Matrices: A Selective Review," Econometrics and Statistics, Elsevier, vol. 29(C), pages 16-30.
    4. da Silva, Murilo & Sriram, T.N. & Ke, Yuan, 2023. "Dimension reduction in time series under the presence of conditional heteroscedasticity," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    5. Wang, Hanchao & Peng, Bin & Li, Degui & Leng, Chenlei, 2021. "Nonparametric estimation of large covariance matrices with conditional sparsity," Journal of Econometrics, Elsevier, vol. 223(1), pages 53-72.
    6. Lam, Clifford, 2020. "High-dimensional covariance matrix estimation," LSE Research Online Documents on Economics 101667, London School of Economics and Political Science, LSE Library.
    7. Nadège Ribau-Peltre & Pascal Damel & An Lethi, 2018. "A methodology to avoid over-diversification of funds of equity funds An implementation case study for equity funds of funds in bull markets," Post-Print hal-03027770, HAL.

    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. Fan, Qingliang & Wu, Ruike & Yang, Yanrong & Zhong, Wei, 2024. "Time-varying minimum variance portfolio," Journal of Econometrics, Elsevier, vol. 239(2).
    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. Jianqing Fan & Yuan Liao & Han Liu, 2016. "An overview of the estimation of large covariance and precision matrices," Econometrics Journal, Royal Economic Society, vol. 19(1), pages 1-32, February.
    4. 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.
    5. Cai, T. Tony & Hu, Jianchang & Li, Yingying & Zheng, Xinghua, 2020. "High-dimensional minimum variance portfolio estimation based on high-frequency data," Journal of Econometrics, Elsevier, vol. 214(2), pages 482-494.
    6. 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.
    7. Gillen, Benjamin J., 2014. "An empirical Bayesian approach to stein-optimal covariance matrix estimation," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 402-420.
    8. Zhu, Bo & Zhang, Tianlun, 2021. "Long-term wealth growth portfolio allocation under parameter uncertainty: A non-conservative robust approach," The North American Journal of Economics and Finance, Elsevier, vol. 57(C).
    9. Jianqing Fan & Alex Furger & Dacheng Xiu, 2016. "Incorporating Global Industrial Classification Standard Into Portfolio Allocation: A Simple Factor-Based Large Covariance Matrix Estimator With High-Frequency Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 489-503, October.
    10. Petukhina, Alla & Klochkov, Yegor & Härdle, Wolfgang Karl & Zhivotovskiy, Nikita, 2024. "Robustifying Markowitz," Journal of Econometrics, Elsevier, vol. 239(2).
    11. Fan, Jianqing & Liao, Yuan & Shi, Xiaofeng, 2015. "Risks of large portfolios," Journal of Econometrics, Elsevier, vol. 186(2), pages 367-387.
    12. Ammann, Manuel & Coqueret, Guillaume & Schade, Jan-Philip, 2016. "Characteristics-based portfolio choice with leverage constraints," Journal of Banking & Finance, Elsevier, vol. 70(C), pages 23-37.
    13. In, Francis & Kim, Sangbae & Gençay, Ramazan, 2011. "Investment horizon effect on asset allocation between value and growth strategies," Economic Modelling, Elsevier, vol. 28(4), pages 1489-1497, July.
    14. 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.
    15. Jang Ho Kim & Woo Chang Kim & Frank J. Fabozzi, 2017. "Penalizing variances for higher dependency on factors," Quantitative Finance, Taylor & Francis Journals, vol. 17(4), pages 479-489, April.
    16. Pun, Chi Seng & Wong, Hoi Ying, 2019. "A linear programming model for selection of sparse high-dimensional multiperiod portfolios," European Journal of Operational Research, Elsevier, vol. 273(2), pages 754-771.
    17. Jingying Yang, 2024. "Element Aggregation for Estimation of High-Dimensional Covariance Matrices," Mathematics, MDPI, vol. 12(7), pages 1-16, March.
    18. T. Roncalli & G. Weisang, 2016. "Risk parity portfolios with risk factors," Quantitative Finance, Taylor & Francis Journals, vol. 16(3), pages 377-388, March.
    19. Sebastien Valeyre & Sofiane Aboura & Denis Grebenkov, 2019. "The Reactive Beta Model," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 42(1), pages 71-113, March.
    20. Fracasso, Laís Martins & Müller, Fernanda Maria & Ramos, Henrique Pinto & Righi, Marcelo Brutti, 2023. "Is there a risk premium? Evidence from thirteen measures," The Quarterly Review of Economics and Finance, Elsevier, vol. 92(C), pages 182-199.

    More about this item

    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:taf:jnlasa:v:112:y:2017:i:517:p:235-253. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UASA20 .

    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.