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).
|Titolo:||Gram–Charlier-Like Expansions of the Convoluted Hyperbolic-Secant Density|
NICOLUSSI, FEDERICA (Primo)
|Parole Chiave:||Convoluted hyperbolic-secant distribution; Orthogonal polynomials; Kurtosis; Skewness; Gram-Charlier-like expansion|
|Settore Scientifico Disciplinare:||Settore SECS-S/01 - Statistica|
|Data di pubblicazione:||2020|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1007/s42519-019-0081-4|
|Appare nelle tipologie:||01 - Articolo su periodico|