Stability analysis and application of threshold autoregressive distributed lag (TARDL) models with dynamic approach and forecasting

In this study, we review and explain the Threshold Autoregressive Distributed lag (TARDL) models, this model combines the concepts of Threshold Autoregressive (TAR) models and Autoregressive Distributed Lag (ARDL) approaches, allowing for different control regimes of data, depending on whether the threshold variable exceeds certain critical values. Also study their stability conditions using a dynamic approach. We discussed finding the conditions for stability and the stability of the non-zero singular point of the model. These conditions were set for the model and proven. Also, the conditions for the stability of the end cycle of the model under study were found, if any, and these conditions were set and proven. As for the applied section of this study, the stability conditions that were found were applied to real data. This application included an analysis of the data in several stages, starting from drawing the time series with the application of stability transformations and choosing the best model using accuracy criteria, reaching the stage of predicting the series for future steps.