On stability Conditions of Pareto Autoregressive model

Abstract

This paper concerned with studding a stability conditions of the proposed non-linear  autoregressive time series model Known as Pareto Autoregressive model, acronym is defined by Pareto . A dynamical method Known as local linearization approximation method was used to obtain the stability condition of a non-zero singular point of Pareto  model. In addition, we obtain the orbital stability condition of a limit cycle in terms of model parameters when the Pareto  possesses a limit cycle with period  .