A flexible coefficient smooth transition time series model

Marcelo C. Medeiros, Álvaro Veiga

Research output: Contribution to journalArticlepeer-review


In this paper, we consider a flexible smooth transition autoregressive (STAR) model with multiple regimes and multiple transition variables. This formulation can be interpreted as a time varying linear model where the coefficients are the outputs of a single hidden layer feedforward neural network. This proposal has the major advantage of nesting several nonlinear models, such as, the self-exciting threshold autoregressive (SETAR), the autoregressive neural network (AR-NN), and the logistic STAR models. Furthermore, if the neural network is interpreted as a nonparametric universal approximation to any Borel measurable function, our formulation is directly comparable to the functional coefficient autoregressive (FAR) and the single-index coefficient regression models. A model building procedure is developed based on statistical inference arguments. A Monte Carlo experiment showed that the procedure works in small samples, and its performance improves, as it should, in medium size samples. Several real examples are also addressed.

Original languageEnglish (US)
Pages (from-to)97-113
Number of pages17
JournalIEEE Transactions on Neural Networks
Issue number1
StatePublished - Jan 2005
Externally publishedYes


  • Neural networks
  • Smooth transition models
  • Threshold models
  • Time series

ASJC Scopus subject areas

  • Software
  • Computer Science Applications
  • Computer Networks and Communications
  • Artificial Intelligence


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