Stability Analysis of Threshold Autoregressive Distributed Lag (TARDL(1,1,1)) Models Using Dynamical Approach: Applied Study of Limit Cycle Condition and Orbital Oscillations

This research aims to study the stability condition of the Threshold Autoregressive Distributed Lag [TARDL(1,1,1)] model using dynamic Approach. The limit cycle condition was applied to the model, where the stability of the model was analysed through differential equations that reflect oscillations and cycles, firstly will prove and present the limit cycle condition for this model. Two examples were presented: the first one satisfies the stability of limit cycle and stabilizes at a constant value, while the second one does at satisfy the condition and continuous to oscillate. MATLAB programing was used to plot the model trajectories and explain whether it is stable or not. The results showed that the model stabilizes when the condition is satisfied, while not satisfying it leads to continuous oscillations. Finally a practical application was conducted on real data to determine the stability or not of the models at the limit cycle.