Stability Study of Exponential Smooth Transition Double Autoregressive Model with Application

In this research, we propose a novel non-linear time series model referred to as the Exponential Smooth TransitionDouble Autoregressive Model of order p denoted as EXPSTDAR (p). This model is predicated on the double autoregressiveframework and incorporates an exponential function. Through the application of a local linearization technique, we derivea stability condition for a non-zero singular point of the model. And applying these conditions to the acquired models bymodeling real data that represents a weekly average closing price of Iron ore powder in dollars for the period from October2010 to May 2025 for several suggested orders of the model.