Tree-structured smooth transition regression models

This paper introduces a tree-based model that combines aspects of classification and regression trees (CART) and smooth transition regression (STR). The model is called the STR-tree. The main idea relies on specifying a parametric nonlinear model through a tree-growing procedure. The resulting model can be analyzed as a smooth transition regression with multiple regimes. Decisions about splits are entirely based on a sequence of Lagrange multiplier (LM) tests of hypotheses. An alternative specification strategy based on a 10-fold cross-validation is also discussed and a Monte Carlo experiment is carried out to evaluate the performance of the proposed methodology in comparison with standard techniques. The STR-tree model outperforms CART when the correct selection of the architecture of simulated trees is discussed. Furthermore, the LM test seems to be a promising alternative to 10-fold cross-validation. Function approximation is also analyzed. When put into proof with real and simulated data sets, the STR-tree model has a superior predictive ability than CART.