Nonlinear Marked Poisson Autoregression: Stability and Rate of Convergence to Equilibrium

Abstract

We consider nonlinear marked Poisson autoregressions and we prove the existence and uniqueness (in law) of the ergodic version under various assumptions on the transfer function, the coefficient functions, and the mark distribution. Moreover, by means of coupling techniques we discuss the convergence and the rate of convergence to equilibrium of a non-ergodic version of the time series, starting from some “initial condition”, to the ergodic version. The theoretical results are illustrated by examples and numerical simulations