We propose the local-global neural networks model within the context of time series models. This formulation encompasses some already existing nonlinear models and also admits the mixture of experts approach. We emphasize the linear expert case and extensively discuss the theoretical aspects of the model: stationarity conditions, existence, consistency and asymptotic normality of the parameter estimates, and model identifiability. The proposed model consists of a mixture of stationary and nonstationary linear models and is able to describe "intermittent" dynamics; the system spends a large fraction of time in a bounded region, but sporadically develops an instability that grows exponentially for some time and then suddenly collapses. Intermittency is a commonly observed behavior in ecology and epidemiology, fluid dynamics, and other natural systems. A model-building strategy is also considered, and the parameters are estimated by concentrated maximum likelihood. The procedure is illustrated with two real time series.

Publicado no Journal of the American Statistical Association, v.99, n. 468, p. 1092-1107, 2004

versão revista publicada em Victor Bulmer-Thomas, John H. Coatsworth e Roberto Cortés-Conde, The Cambridge Economic History of Latin America, Volume II. The Long 20th Century, Cambridge University Press, 2006, p. 101-134

This paper is concerned with modelling time series by single hidden layer feedforward 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

Publicado em Journal of Forecasting, Volume 25, Número 1, pp. 49 - 75, 2006

 publicado no Journal of Development Economics v.69, n.2, p. 393-421, 2002