International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 19423, 22 pages

Modeling nonlinearities with mixtures-of-experts of time series models

Alexandre X. Carvalho1 and Martin A. Tanner2

1SBS, Quadra 1, Bloco J, Edifício BNDES, Sala 718, Brasília CEP 70076-900, DF, Brazil
2Department of Statistics, Weinberg College of Arts and Sciences, Northwestern University, Evanston 60208, IL, USA

Received 5 February 2006; Revised 21 May 2006; Accepted 28 May 2006

Copyright © 2006 Alexandre X. Carvalho and Martin A. Tanner. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We discuss a class of nonlinear models based on mixtures-of-experts of regressions of exponential family time series models, where the covariates include functions of lags of the dependent variable as well as external covariates. The discussion covers results on model identifiability, stochastic stability, parameter estimation via maximum likelihood estimation, and model selection via standard information criteria. Applications using real and simulated data are presented to illustrate how mixtures-of-experts of time series models can be employed both for data description, where the usual mixture structure based on an unobserved latent variable may be particularly important, as well as for prediction, where only the mixtures-of-experts flexibility matters.