Since financial series are usually heavy tailed and skewed, research has formerly considered well-known leptokurtic distributions to model these series and, recently, has focused on the technique of adjusting the moments of a probability law by using its orthogonal polynomials. This paper combines these approaches by modifying the moments of the convoluted hyperbolic secant. The resulting density is a Gram–Charlier-like (GC-like) expansion capable to account for skewness and excess kurtosis. Multivariate extensions of these expansions are obtained on an argument using spherical distributions. Both the univariate and multivariate (GC-like) expansions prove to be effective in modeling heavy-tailed series and computing risk measures.

Gram–Charlier-Like Expansions of the Convoluted Hyperbolic-Secant Density / F. Nicolussi, M.G. Zoia. - In: JOURNAL OF STATISTICAL THEORY AND PRACTICE. - ISSN 1559-8608. - 14:1(2020). [10.1007/s42519-019-0081-4]

Gram–Charlier-Like Expansions of the Convoluted Hyperbolic-Secant Density

F. Nicolussi;
2020

Abstract

Since financial series are usually heavy tailed and skewed, research has formerly considered well-known leptokurtic distributions to model these series and, recently, has focused on the technique of adjusting the moments of a probability law by using its orthogonal polynomials. This paper combines these approaches by modifying the moments of the convoluted hyperbolic secant. The resulting density is a Gram–Charlier-like (GC-like) expansion capable to account for skewness and excess kurtosis. Multivariate extensions of these expansions are obtained on an argument using spherical distributions. Both the univariate and multivariate (GC-like) expansions prove to be effective in modeling heavy-tailed series and computing risk measures.
Convoluted hyperbolic-secant distribution; Orthogonal polynomials; Kurtosis; Skewness; Gram-Charlier-like expansion
Settore SECS-S/01 - Statistica
JOURNAL OF STATISTICAL THEORY AND PRACTICE
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/705326
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