IDEAS home Printed from https://ideas.repec.org/p/cam/camdae/0637.html
   My bibliography  Save this paper

Sample Covariance Shrinkage for High Dimensional Dependent Data

Author

Listed:
  • Sancetta, A.

Abstract

For high dimensional data sets the sample covariance matrix is usually unbiased but noisy if the sample is not large enough. Shrinking the sample covariance towards a constrained, low dimensional estimator can be used to mitigate the sample variability. By doing so, we introduce bias, but reduce variance. In this paper, we give details on feasible optimal shrinkage allowing for time series dependent observations.

Suggested Citation

  • Sancetta, A., 2006. "Sample Covariance Shrinkage for High Dimensional Dependent Data," Cambridge Working Papers in Economics 0637, Faculty of Economics, University of Cambridge.
  • Handle: RePEc:cam:camdae:0637
    Note: Em
    as

    Download full text from publisher

    File URL: http://www.econ.cam.ac.uk/research-files/repec/cam/pdf/cwpe0637.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. 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.
    3. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    4. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
    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. Mark Fiecas & Jürgen Franke & Rainer von Sachs & Joseph Tadjuidje Kamgaing, 2017. "Shrinkage Estimation for Multivariate Hidden Markov Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 424-435, January.
    2. Bernardini, Emmanuela & Cubadda, Gianluca, 2015. "Macroeconomic forecasting and structural analysis through regularized reduced-rank regression," International Journal of Forecasting, Elsevier, vol. 31(3), pages 682-691.
    3. Steland, Ansgar & von Sachs, Rainer, 2018. "Asymptotics for high-dimensional covariance matrices and quadratic forms with applications to the trace functional and shrinkage," Stochastic Processes and their Applications, Elsevier, vol. 128(8), pages 2816-2855.
    4. Ansgar Steland, 2018. "Shrinkage for covariance estimation: asymptotics, confidence intervals, bounds and applications in sensor monitoring and finance," Statistical Papers, Springer, vol. 59(4), pages 1441-1462, December.
    5. Monika Bours & Ansgar Steland, 2021. "Large‐sample approximations and change testing for high‐dimensional covariance matrices of multivariate linear time series and factor models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 610-654, June.
    6. Elliot Beck & Damian Kozbur & Michael Wolf, 2023. "Hedging Forecast Combinations With an Application to the Random Forest," Papers 2308.15384, arXiv.org, revised Aug 2023.
    7. Steland, Ansgar & von Sachs, Rainer, 2016. "Asymptotics for High–Dimensional Covariance Matrices and Quadratic Forms with Applications to the Trace Functional and Shrinkage," LIDAM Discussion Papers ISBA 2016038, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Fiecas , Mark & Franke, Jurgen & von Sachs, Rainer & Tadjuidje , Joseph, 2012. "Shrinkage Estimation for Multivariate Hidden Markov Mixture Models," LIDAM Discussion Papers ISBA 2012016, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Cubadda, Gianluca & Guardabascio, Barbara, 2019. "Representation, estimation and forecasting of the multivariate index-augmented autoregressive model," International Journal of Forecasting, Elsevier, vol. 35(1), pages 67-79.
    10. Steland, Ansgar, 2020. "Testing and estimating change-points in the covariance matrix of a high-dimensional time series," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
    11. Sancetta, Alessio, 2013. "Weak conditions for shrinking multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 285-300.

    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. Ansgar Steland, 2018. "Shrinkage for covariance estimation: asymptotics, confidence intervals, bounds and applications in sensor monitoring and finance," Statistical Papers, Springer, vol. 59(4), pages 1441-1462, December.
    2. Jianqing Fan & Ricardo Masini & Marcelo C. Medeiros, 2021. "Bridging factor and sparse models," Papers 2102.11341, arXiv.org, revised Sep 2022.
    3. Hannart, Alexis & Naveau, Philippe, 2014. "Estimating high dimensional covariance matrices: A new look at the Gaussian conjugate framework," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 149-162.
    4. Candelon, B. & Hurlin, C. & Tokpavi, S., 2012. "Sampling error and double shrinkage estimation of minimum variance portfolios," Journal of Empirical Finance, Elsevier, vol. 19(4), pages 511-527.
    5. Fan, Jianqing & Liao, Yuan & Shi, Xiaofeng, 2015. "Risks of large portfolios," Journal of Econometrics, Elsevier, vol. 186(2), pages 367-387.
    6. David R. Bell & Olivier Ledoit & Michael Wolf, 2012. "A new portfolio formation approach to mispricing of marketing performance indicators with an application to customer satisfaction," ECON - Working Papers 079, Department of Economics - University of Zurich, revised Dec 2013.
    7. Tae-Hwy Lee & Ekaterina Seregina, 2020. "Learning from Forecast Errors: A New Approach to Forecast Combination," Working Papers 202024, University of California at Riverside, Department of Economics.
    8. Istvan Varga-Haszonits & Fabio Caccioli & Imre Kondor, 2016. "Replica approach to mean-variance portfolio optimization," Papers 1606.08679, arXiv.org.
    9. Mishra, Anil V., 2015. "Measures of equity home bias puzzle," Journal of Empirical Finance, Elsevier, vol. 34(C), pages 293-312.
    10. Emmanuel Jurczenko & Bertrand Maillet & Paul Merlin, 2008. "Efficient Frontier for Robust Higher-order Moment Portfolio Selection," Post-Print halshs-00336475, HAL.
    11. Jingying Yang, 2024. "Element Aggregation for Estimation of High-Dimensional Covariance Matrices," Mathematics, MDPI, vol. 12(7), pages 1-16, March.
    12. Carvalho, Carlos & Masini, Ricardo & Medeiros, Marcelo C., 2018. "ArCo: An artificial counterfactual approach for high-dimensional panel time-series data," Journal of Econometrics, Elsevier, vol. 207(2), pages 352-380.
    13. Thomas Trier Bjerring & Omri Ross & Alex Weissensteiner, 2017. "Feature selection for portfolio optimization," Annals of Operations Research, Springer, vol. 256(1), pages 21-40, September.
    14. Lin, Ruitao & Liu, Zhongying & Zheng, Shurong & Yin, Guosheng, 2016. "Power computation for hypothesis testing with high-dimensional covariance matrices," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 10-23.
    15. Bollerslev, Tim & Patton, Andrew J. & Quaedvlieg, Rogier, 2018. "Modeling and forecasting (un)reliable realized covariances for more reliable financial decisions," Journal of Econometrics, Elsevier, vol. 207(1), pages 71-91.
    16. Ledoit, Olivier & Wolf, Michael, 2017. "Numerical implementation of the QuEST function," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 199-223.
    17. 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.
    18. G'abor Papp & Fabio Caccioli & Imre Kondor, 2016. "Bias-variance trade-off in portfolio optimization under Expected Shortfall with $\ell_2$ regularization," Papers 1602.08297, arXiv.org, revised Jul 2018.
    19. Kojevnikov, Denis & Marmer, Vadim & Song, Kyungchul, 2021. "Limit theorems for network dependent random variables," Journal of Econometrics, Elsevier, vol. 222(2), pages 882-908.
    20. Theodoros Tsagaris & Ajay Jasra & Niall Adams, 2012. "Robust and adaptive algorithms for online portfolio selection," Quantitative Finance, Taylor & Francis Journals, vol. 12(11), pages 1651-1662, November.

    More about this item

    Keywords

    Sample Covariance Matrix; Shrinkage; Weak Dependence;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:cam:camdae:0637. 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: Jake Dyer (email available below). General contact details of provider: https://www.econ.cam.ac.uk/ .

    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.