Building neural network models for time series: A statistical approach

Marcelo C. Medeiros, Timo Teräsvirta, Gianluigi Rech

Research output: Contribution to journalArticlepeer-review


This paper is concerned with modelling time series by single hidden layer feed-forward neural network models. A coherent modelling strategy based on statistical inference is presented. Variable selection is carried out using simple existing techniques. The problem of selecting the number of hidden units is solved by sequentially applying Lagrange multiplier type tests, with the aim of avoiding the estimation of unidentified models. Misspecification tests are derived for evaluating an estimated neural network model. All the tests are entirely based on auxiliary regressions and are easily implemented. A small-sample simulation experiment is carried out to show how the proposed modelling strategy works and how the misspecification tests behave in small samples. Two applications to real time series, one univariate and the other multivariate, are considered as well. Sets of one-step-ahead forecasts are constructed and forecast accuracy is compared with that of other nonlinear models applied to the same series.

Original languageEnglish (US)
Pages (from-to)49-75
Number of pages27
JournalJournal of Forecasting
Issue number1
StatePublished - Jan 2006
Externally publishedYes


  • Model misspecification
  • Neural computing
  • Nonlinear forecasting
  • Nonlinear time series
  • Smooth transition autoregression

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computer Science Applications
  • Strategy and Management
  • Statistics, Probability and Uncertainty
  • Management Science and Operations Research

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