On estimating the tail index and the spectral measure of multivariate \(\alpha \)-stable distributions
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We propose estimators for the tail index and the spectral measure of multivariate \(\alpha \)-stable distributions and derive their asymptotic properties. Simulation studies reveal the appropriateness of the estimators. Applications to financial data are also considered.
KeywordsAsymptotic distribution Multivariate α-stable distribution Spectral measure Tail index estimation Generalized empirical likelihood estimation
Mathematics Subject Classification60E07 62H12 62G32
The authors would like to thank an anonymous reviewer and Editor, Professor Norbert Henze, for their valuable comments and suggestions to improve the manuscript. They are also grateful to Professor John P. Nolan to provide access to STABLE package in R for improving the computations and Dr. Thaigo do Rego Sousa for his help in running the programs of GEVStableGarch package. The third author was supported by JSPS KAKENHI Grant Number 26870655.
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