Expansion of Lévy process functionals and its application in econometric estimation.

Abstract

This research focuses on the estimation of a class of econometric models for involved unknown nonlinear functionals of nonstationary processes. The proxy of nonstationary processes studied here is Lévy processes including Brownian motion as a particular one. A Lévy process is a càdlàg stochastic process which starts at zero almost surely, which has independent increments over disjoint intervals, which has stationary increment distribution meaning that under shift the distributions of increments are identical, which has stochastic continuous trajectory. Obviously, Brownian motion, Poisson process, Gamma process and Pascal process are fundamental examples of Lévy processes. Lévy processes (Z(t); t >0) studied in this thesis possess density or probability distribution functions which verify some properties stated in the text.