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Three-structured smooth transition regression models based on CART algorithm


  • Joel Corrêa da Rosa

    (Department of Statistics, Federal University of Paraná)

  • Álvaro Veiga

    (Department of Electrical Engineering, PUC-Rio)

  • Marcelo C. Medeiros

    () (Department of Economics PUC-Rio)


In the present work, a tree-based model that combines aspects of CART (Classification and Regression Trees) and STR (Smooth Transition Regression) is proposed. The main idea relies on specifying a parametric nonlinear model through a tree-growing procedure. The resulting model can be analysed either as a fuzzy regression or as a smooth transition regression with multiple regimes. Decisions about splits are entirely based on statistical tests of hypotheses and confidence intervals are constructed for the parameters within the terminal nodes as well as the final predictions. A Monte Carlo Experiment shows the estimators’ properties and the ability of the proposed algorithm to identify correctly several tree architectures. An application to the famous Boston Housing dataset shows that the proposed model provides better explanation with the same number of leaves as the one obtained with the CART algorithm.

Suggested Citation

  • Joel Corrêa da Rosa & Álvaro Veiga & Marcelo C. Medeiros, 2003. "Three-structured smooth transition regression models based on CART algorithm," Textos para discussão 469, Department of Economics PUC-Rio (Brazil).
  • Handle: RePEc:rio:texdis:469

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    References listed on IDEAS

    1. Eitrheim, Oyvind & Terasvirta, Timo, 1996. "Testing the adequacy of smooth transition autoregressive models," Journal of Econometrics, Elsevier, vol. 74(1), pages 59-75, September.
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    3. Cooper, Suzanne J, 1998. "Multiple Regimes in U.S. Output Fluctuations," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(1), pages 92-100, January.
    4. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    5. Ciampi, Antonio, 1991. "Generalized regression trees," Computational Statistics & Data Analysis, Elsevier, vol. 12(1), pages 57-78, August.
    6. Timo Teräsvirta & Marcelo C. Medeiros & Gianluigi Rech, 2006. "Building neural network models for time series: a statistical approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(1), pages 49-75.
    7. Wooldridge, Jeffrey M., 1991. "On the application of robust, regression- based diagnostics to models of conditional means and conditional variances," Journal of Econometrics, Elsevier, vol. 47(1), pages 5-46, January.
    8. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-161, January.
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