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Tests for the Weights of the Global Minimum Variance Portfolio in a High-Dimensional Setting
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 42019 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 67, no 17, p. 4479-4493Article in journal (Refereed) Published
Abstract [en]

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 is an element of (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 -> <(c)over tilde is an element of (0,1) as n -> infinity. 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.

Place, publisher, year, edition, pages
2019. Vol. 67, no 17, p. 4479-4493
Keywords [en]
Finance, portfolio analysis, global minimum variance portfolio, statistical test, shrinkage estimator, random matrix theory, singular covariance matrix
National Category
Electrical Engineering, Electronic Engineering, Information Engineering Mathematics
Identifiers
URN: urn:nbn:se:su:diva-173093DOI: 10.1109/TSP.2019.2929964ISI: 000481475000002OAI: oai:DiVA.org:su-173093DiVA, id: diva2:1358397
Available from: 2019-10-07 Created: 2019-10-07 Last updated: 2019-10-07Bibliographically approved

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