International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 19423, 22 pages
doi:10.1155/IJMMS/2006/19423
Modeling nonlinearities with mixtures-of-experts of time series models
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.
Abstract
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.