Inférence statistique dans les modèles linéaires à temps continu

Abstract

The aim or goal of this work is to study and analyze the structure of the second order and the necessary and sufficient conditions ensuring the existence of causal solutions for ARMA processes with continuous time (CARMA) driven by Lévy processes. It characterizes, explicitly, the covariance function and explores, also, its characteristics and properties. The existence of unit roots in the polynomial associated with the AR part has been, fully, treated and discussed. In addition, some particular representations related to this type of part, have been illustrated and adequately characterized. The estimate in the CARMA model and its asymptotic properties have been, also, elaborated. The illustrated simulation study has shown and has given very satisfying results.