The SETAR Model of Tong and Lim and Advances in Computation

World Scientific
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Exploration of a Nonlinear World: An Appreciation of Howell Tong's Contributions to Statistics., 2009, 1, pp. 85 - 94
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This discussion revisits Tong and Lim's seminal 1980 paper on the SETAR model in the context of advances in computation since that time. Using the Canadian lynx data set from that paper, it compares exact maximum likelihood estimates with those in the original paper. It illustrates the application of Bayesian MCMC methods, developed in the intervening years, to this model and data set. It shows that SETAR is a limiting case of mixture of experts models and studies the application of one variant of those models to the lynx data set. The application is successful, despite the small size of the data set and the complexity of the model. Predictive likelihood ratios favor Tong and Lim's original model.
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