TWO‐STEP ESTIMATION OF A MULTI‐VARIATE LÉVY PROCESS. (22nd October 2013)

• Record Type: Journal Article
• Authors: Esmaeili, Habib; Klüppelberg, Claudia
• Is Part Of: Journal of time series analysis. Volume 34:Number 6(2013:Nov.)
• Page Start: 668
• Page End: 690
• Publication Date: 2013-10-22
• Subjects: Dependence structure -- Godambe information matrix -- IFM, inference functions for margins -- Lévy copula -- maximum likelihood estimation -- multi‐variate Lévy process -- reduced likelihood -- two‐step parameter estimation; Time-series analysis -- Periodicals; 519.232
• DOI: 10.1111/jtsa.12042
• Languages: English
• ISSNs: 0143-9782

Abstract

Abstract: Based on the concept of a Lévy copula to describe the dependence structure of a multi‐variate 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 Lévy process, 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.