IDEAS home Printed from https://ideas.repec.org/a/oup/jfinec/v11y2012i1p154-192.html
   My bibliography  Save this article

Efficient Estimation of Covariance Matrices using Posterior Mode Multiple Shrinkage

Author

Listed:
  • Paolo Giordani
  • Xiuyan Mun
  • Robert Kohn

Abstract

We propose an approach to the regularization of covariance matrices that can be applied to any model for which the likelihood is available in closed form. The approach is based on using mixtures of double exponential or normal distributions as priors for correlation parameters, and on maximizing the resulting log-posterior (or penalized likelihood) using a stochastic optimization algorithm. The mixture priors are capable of clustering the correlations in several groups, each with separate mean and variance, and can therefore capture a large variety of structures besides sparsity. We apply this approach to the normal linear multivariate regression model as well as several other models that are popular in the literature but have not been previously studied for the purpose of regularization, including multivariate t, normal and t copulas, and mixture of normal distributions. Simulation experiments show the potential for large efficiency gains in estimating the density of the observations in all these models. Sizable gains are also obtained in four real applications. Copyright The Author, 2012. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org, Oxford University Press.

Suggested Citation

  • Paolo Giordani & Xiuyan Mun & Robert Kohn, 2012. "Efficient Estimation of Covariance Matrices using Posterior Mode Multiple Shrinkage," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 11(1), pages 154-192, December.
  • Handle: RePEc:oup:jfinec:v:11:y:2012:i:1:p:154-192
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/jjfinec/nbs009
    Download Restriction: Access to full text is restricted to subscribers.

    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. FrancisX. Diebold & Kamil Yilmaz, 2009. "Measuring Financial Asset Return and Volatility Spillovers, with Application to Global Equity Markets," Economic Journal, Royal Economic Society, vol. 119(534), pages 158-171, January.
    2. Victor DeMiguel & Lorenzo Garlappi & Raman Uppal, 2009. "Optimal Versus Naive Diversification: How Inefficient is the 1-N Portfolio Strategy?," Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1915-1953, May.
    3. Villani, Mattias & Kohn, Robert & Giordani, Paolo, 2009. "Regression density estimation using smooth adaptive Gaussian mixtures," Journal of Econometrics, Elsevier, vol. 153(2), pages 155-173, December.
    4. Daniels, Michael J., 2006. "Bayesian modeling of several covariance matrices and some results on propriety of the posterior for linear regression with correlated and/or heterogeneous errors," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1185-1207, May.
    5. Jian Zhang & Faming Liang, 2008. "Convergence of stochastic approximation algorithms under irregular conditions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 62(3), pages 393-403, August.
    6. John C. Liechty, 2004. "Bayesian correlation estimation," Biometrika, Biometrika Trust, vol. 91(1), pages 1-14, March.
    7. Smith M. & Kohn R., 2002. "Parsimonious Covariance Matrix Estimation for Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1141-1153, December.
    8. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    9. 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.
    10. 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.
    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. 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.
    13. Pourahmadi, Mohsen & Daniels, Michael J. & Park, Trevor, 2007. "Simultaneous modelling of the Cholesky decomposition of several covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 568-587, March.
    14. 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.
    15. 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.
    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. Burda, Martin & Prokhorov, Artem, 2014. "Copula based factorization in Bayesian multivariate infinite mixture models," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 200-213.

    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:oup:jfinec:v:11:y:2012:i:1:p:154-192. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Oxford University Press). General contact details of provider: http://edirc.repec.org/data/sofieea.html .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.