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In this paper we consider a class of time-changed Lévy processes that can be represented in the form Ys = X T (s) , where X is a Lévy process and T is a non-negative and non-decreasing stochastic process independent of X. The aim of this work is to infer on the Blumenthal-Getoor index of the process X from low-frequency observations of the time-changed Lévy process Y . We propose a consistent estimator for this index, derive the minimax rates of convergence and show that these rates can not be improved in general. The performance of the estimator is illustrated by numerical examples.

In this paper, we analyze a Lévy model based on two popular concepts -subordination and Lévy copulas. More precisely, we consider a two-dimensional Lévy process such that each component is a time-changed (subordinated) Brownian motion and the dependence between subordinators is described via some Lévy copula. The main result of this paper is the series representation for our model, which can be efficiently used for simulation purposes.