### Abstract

In this paper, we construct two tests for the weights of the global minimum variance portfolio (GMVP) in a high-dimensional setting, namely, when the number of assets p depends on the sample size n such that p/n → c ∈ (0, 1) as n tends to infinity. In the case of a singular covariance matrix with rank equal to q we assume that q/n → c̅ ∈ (0, 1) as n → ∞. The considered tests are based on the sample estimator and on the shrinkage estimator of the GMVP weights. We derive the asymptotic distributions of the test statistics under the null and alternative hypotheses. Moreover, we provide a simulation study where the power functions and the receiver operating characteristic curves of the proposed tests are compared with other existing approaches. We observe that the test based on the shrinkage estimator performs well even for values of c close to one.

Original language | English |
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Pages (from-to) | 4479-4493 |

Number of pages | 15 |

Journal | IEEE Transactions on Signal Processing |

Volume | 67 |

Issue number | 17 |

DOIs | |

Publication status | Published - 1 Sep 2019 |

### Keywords

- Finance
- portfolio analysis
- global minimum variance portfolio
- statistical test
- shrinkage estimator
- random matrix theory
- singular covariance matrix

## Cite this

Bodnar, T., Dmytriv, S., Parolya, N., & Schmid, W. (2019). Tests for the Weights of the Global Minimum Variance Portfolio in a High-Dimensional Setting.

*IEEE Transactions on Signal Processing*,*67*(17), 4479-4493. https://doi.org/10.1109/TSP.2019.2929964