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Copula shrinkage and portfolio allocation in ultra-high dimensions

Author

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  • Anatolyev, Stanislav
  • Pyrlik, Vladimir
Abstract
Copulas prove to be a convenient tool in modeling joint distributions. As the data dimensionality grows, obtaining precise and well-conditioned estimates of copula-based distributions becomes a challenge. Currently, copula-based high dimensional settings are typically used for as many as a few hundred variables and require large data samples for estimation to be precise. In this paper, we handle the problem of estimation of Gaussian and t copulas in ultra-high dimensions, up to thousands of variables that use up to 30 times shorter sample lengths. Specifically, we employ recently developed large covariance matrix shrinkage tools to obtain precise and well-conditioned estimates of copula matrix parameters. Simulations show that shrinkage copulas significantly outperform traditional estimators, especially in high dimensions. We also illustrate benefits of this approach for the problem of allocation of large portfolios of stocks. Our experiments show that the shrinkage estimators applied to t copula-based dynamic models deliver better portfolios in terms of cumulative return and maximum downfall over portfolio lifetime than traditional benchmarks.

Suggested Citation

  • Anatolyev, Stanislav & Pyrlik, Vladimir, 2022. "Copula shrinkage and portfolio allocation in ultra-high dimensions," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    • Handle: RePEc:eee:dyncon:v:143:y:2022:i:c:s0165188922002123
    DOI: 10.1016/j.jedc.2022.104508
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    References listed on IDEAS

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    More about this item

    Keywords

    Gaussian copula; t copula; High dimensionality; Large covariance matrices; Shrinkage; Portfolio allocation;
    All these keywords.

    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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