Representing Koziol’s Kurtoses
Nicola Loperfido
A chapter in Mathematical and Statistical Methods for Actuarial Sciences and Finance, 2021, pp 323-328 from Springer
Abstract:
Abstract The Koziol’s kurtosis of a random vector is the sum of its squared fourth moments. Similarly, the Koziol’s excess kurtosis of a random vector is the sum of its fourth standardized cumulants. Koziol’s kurtoses provide some insight into several features of the underlying distributions, as for example tails and modes. Moreover, they are invariant with respect to one-to-one affine transformations. We prove that Koziol’s kurtosis is a simple analytical function of the cokurtosis matrix and the covariance matrix. A similar result holds for Koziol’s excess kurtosis. Derivations of both results use fourth moments and cumulants of linearly transformed random vectors, whose properties already appeared in the literature but are formally proved in this paper for the first time, to the best of our knowledge. Applications to financial econometrics and portfolio selection are briefly discussed.
Keywords: Cokurtosis; Fourth cumulant; Koziol’s kurtoses (search for similar items in EconPapers)
Date: 2021
References: Add references at CitEc
Citations:
There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-78965-7_47
Ordering information: This item can be ordered from
http://www.springer.com/9783030789657
DOI: 10.1007/978-3-030-78965-7_47
Access Statistics for this chapter
More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().