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Estimation of time-varying covariance matrices for large datasets

Author

Listed:
  • Yiannis Dendramis

    (Athens University of Economics and Business)

  • Luidas Giraitis

    (Queen Mary University of London)

  • George Kapetanios

    (King's College London)

Abstract

Time variation is a fundamental problem in statistical and econometric analysis of macroeconomic and financial data. Recently there has been considerable focus on developing econometric modelling that enables stochastic structural change in model parameters and on model estimation by Bayesian or non-parametric kernel methods. In the context of the estimation of covariance matrices of large dimensional panels, such data requires taking into account time variation, possible dependence and heavy-tailed distributions. In this paper we introduce a non-parametric version of regularisation techniques for sparse large covariance matrices, developed by Bickel and Levina (2008) and others. We focus on the robustness of such a procedure to time variation, dependence and heavy-tailedness of distributions. The paper includes a set of results on Bernstein type inequalities for dependent unbounded variables which are expected to be applicable in econometric analysis beyond estimation of large covariance matrices. We discuss the utility of the robust thresholding method, comparing it with other estimators in simulations and an empirical application on the design of minimum variance portfolios.

Suggested Citation

  • Yiannis Dendramis & Luidas Giraitis & George Kapetanios, 2020. "Estimation of time-varying covariance matrices for large datasets," Working Papers 916, Queen Mary University of London, School of Economics and Finance.
  • Handle: RePEc:qmw:qmwecw:916
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    File URL: https://www.qmul.ac.uk/sef/media/econ/research/workingpapers/2020/wp916.pdf
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    References listed on IDEAS

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    1. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
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    Cited by:

    1. Yu Bai & Massimiliano Marcellino & George Kapetanios, 2023. "Mean Group Instrumental Variable Estimation of Time-Varying Large Heterogeneous Panels with Endogenous Regressors," Monash Econometrics and Business Statistics Working Papers 13/23, Monash University, Department of Econometrics and Business Statistics.
    2. Hiraki, Kazuhiro & Sun, Chuanping, 2022. "A toolkit for exploiting contemporaneous stock correlations," Journal of Empirical Finance, Elsevier, vol. 65(C), pages 99-124.

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    More about this item

    Keywords

    covariance matrix estimation; large dataset; regularization; thresholding; shrinkage; exponential inequalities; minimum variance portfolio;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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