2013/06/07 by Habib Esmaeili, Claudia Klüppelberg, Esmaeili, Habib +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #62F10 #62F12 #62M05 #FOS: Computer and information sciences #Financial Risk and Volatility Modeling #Methodology (stat.ME) #Probability and Risk Models #Statistical Distribution Estimation and Applications #msc:62F10 #msc:62F12 #msc:62M05 #stat.ME
paper · pdf · doi:10.48550/arxiv.1306.1725
25 pages
arxiv created 2013/06/07 · openalex publication_date 2013/06/07 · arxiv updated 2013/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Based on the concept of a Lévy copula to describe the dependence structure of a multivariate Lévy process we present a new estimation procedure. We consider a parametric model for the marginal Lévy processes as well as for the Lévy copula and estimate the parameters by a two-step procedure. We first estimate the parameters of the marginal processes, and then estimate in a second step only the dependence structure parameter. For infinite Lévy measures we truncate the small jumps and base our statistical analysis on the large jumps of the model. Prominent example will be a bivariate stable \lp, which allows for analytic calculations and, hence, for a comparison of different methods. We prove asymptotic normality of the parameter estimates from the two-step procedure and, in particular, we derive the Godambe information matrix, whose inverse is the covariance matrix of the normal limit law. A simulation study investigates the loss of efficiency because of the two-step procedure and the truncation.