Shrinkage for Gaussian and t Copulas in Ultra-High Dimensions

Stanislav Anatolyev and Vladimir Pyrlik ()

CERGE-EI Working Papers from The Center for Economic Research and Graduate Education - Economics Institute, Prague

Abstract: Copulas are a convenient framework to synthesize joint distributions, particularly in higher dimensions. Currently, copula-based high dimensional settings are used for as many as a few hundred variables and require large data samples for estimation to be precise. In this paper, we employ shrinkage techniques for large covariance matrices in the problem of estimation of Gaussian and t copulas whose dimensionality goes well beyond that typical in the literature. Specifically, we use the covariance matrix shrinkage of Ledoit and Wolf to estimate large matrix parameters of Gaussian and t copulas for up to thousands of variables, using up to 20 times lower sample sizes. The simulation study shows that the shrinkage estimation significantly outperforms traditional estimators, both in low and especially high dimensions. We also apply this approach to the problem of allocation of large portfolios.

Keywords: Gaussian copula; t copula; high dimensionality; large covariance matrices; shrinkage; portfolio allocation (search for similar items in EconPapers)
JEL-codes: C31 C46 C55 C58 (search for similar items in EconPapers)
Date: 2021-08
New Economics Papers: this item is included in nep-cwa, nep-ecm and nep-ore
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Persistent link: https://EconPapers.repec.org/RePEc:cer:papers:wp699

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