Matching Kollo measures

Carol Alexander, Wei Wei and Xi Chen

Journal of the Operational Research Society, 2024, vol. 75, issue 7, 1279-1293

Abstract: We motivate the advantages of using the Kollo measures, relative to other types of third and fourth moments of multivariate systems, and explore their Monte Carlo simulation and bootstrapping errors. Then we derive necessary and sufficient conditions for simultaneously matching any given mean vector, covariance matrix, Kollo skewness, and Kollo kurtosis. The specification of a suitable orthonormal basis greatly simplifies these moment-matching conditions. We offer semi-closed-form solutions to increase computational efficiency. In this respect, we compare our approach to two competing methods, which anyway can only match Kollo skewness and not the kurtosis at the same time. Ours is the first method for exactly matching all four multivariate moments simultaneously.

Date: 2024
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DOI: 10.1080/01605682.2023.2240847

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