Tree-structured smooth transition regression models

This paper introduces a tree-based model that combines aspects of CART (Classification and Regression Trees) and STR (Smooth Transition Regression). The model is called the Smooth Transition Regression Tree (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 crossvalidation. Function approximation is also analyzed. When put into proof with real and simulated datasets, the STR-Tree model has a superior predictive ability than CART.