Abstract
In this paper we study stability conditions of a non-linear times series model which we proposed and named as smooth transition secant hyperbolic Autoregressive model (STSechAR).We use a local linearization technique which depends essentially in studing stability in the neighborhood of anon zero singular point of the model in order to approximate the proposed model to a linear Autoregressive model (AR) . In addition we study and find a stability conditions of a limit cycle (if exists) for the proposed model . We apply a theoritical results which we obtain in this paper to a real data which represent a monthly mean temperature in Kirkuk city for the years (2000-2013) AC .
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