Smooth Transition Autoregressive (STAR) Models

Non-linear modeling approaches, including Smooth Transition Autoregressive (STAR) models, have attracted a great deal of attention over the last two decades. The empirical application of these models, however, is not always a straightforward task. In particular, parameter estimation and identification of redundant parameters have not been addressed satisfactorily in the literature yet: There are no deterministic numerical methods -- let alone closed form solutions -- to solve these problems reliably. In empirical studies, we find that heuristic approaches such as Threshold Accepting or Evolutionary Methods are capable of solving these problems. Applied to STAR models, we were able to identify solutions that outperform benchmarks provided in the literature. This paper presents how to apply heuristics to the parameter estimation and the model selection problems. Based on computational studies, these methods are compared to traditional approaches