Modelling nonlinear count time series with local mixtures of Poisson autoregressions

Alexandre X. Carvalho*, Martin A. Tanner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


A novel class of nonlinear models is studied based on local mixtures of autoregressive Poisson time series. The proposed model has the following construction: at any given time period, there exist a certain number of Poisson regression models, denoted as experts, where the vector of covariates may include lags of the dependent variable. Additionally, the existence of a latent multinomial variable is assumed, whose distribution depends on the same covariates as the experts. The latent variable determines which Poisson regression is observed. This structure is a special case of the mixtures-of-experts class of models, which is considerably flexible in modelling the conditional mean function. A formal treatment of conditions to guarantee the asymptotic normality of the maximum likelihood estimator is presented, under stationarity and nonstationarity. The performance of common model selection criteria in selecting the number of experts is explored via Monte Carlo simulations. Finally, an application to a real data set is presented, in order to illustrate the ability of the proposed structure to flexibly model the conditional distribution function.

Original languageEnglish (US)
Pages (from-to)5266-5294
Number of pages29
JournalComputational Statistics and Data Analysis
Issue number11
StatePublished - Jul 15 2007


  • Count data
  • Maximum likelihood estimation
  • Mixtures-of-experts
  • Nonlinear time series
  • Poisson regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics


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