Threshold Variable Selection in Open‐loop Threshold Autoregressive Models

An open‐loop threshold autoregressive model is defined as The main difficulty for building such a model is that the threshold variable Z t is usually unknown. In practice, there may exist many possible candidates for the threshold variable Z t . It is difficult and tedious, if not impossible, to search for the best among all the candidates using standard model selection procedures. In this paper, we introduce a digression concept and propose two simple algorithms to classify the observations without knowing the threshold variable. The classification is then used with several graphical procedures to search for the most suitable threshold variable. Simulated and real examples are included to illustrate the proposed procedures.