In this paper a flexible multiple regime GARCH(1,1)-type model is developed to describe the sign and size asymmetries and intermittent dynamics in financial volatility. The results of the paper are important to other nonlinear GARCH models. The proposed model nests some of the previous specifications found in the literature and has the following advantages. First, contrary to most of the previous models, more than two limiting regimes are possible, and the number of regimes is determined by a simple sequence of tests that circumvents identification problems that are usually found in nonlinear time series models. The second advantage is that the novel stationarity restriction on the parameters is relatively weak, thereby allowing for rich dynamics. It is shown that the model may have explosive regimes but can still be strictly stationary and ergodic. A simulation experiment shows that the proposed model can generate series with high kurtosis and low first-order autocorrelation of the squared observations and exhibit the so-called Taylor effect, even with Gaussian errors. Estimation of the parameters is addressed, and the asymptotic properties of the quasi-maximum likelihood estimator are derived under weak conditions. A Monte-Carlo experiment is designed to evaluate the finite-sample properties of the sequence of tests. Empirical examples are also considered.

Publicado em Econometric Theory, v.25, p. 117-161, 2009

publicado na Revista de Economia Política, v.26, n.1, janeiro-março, 2006

publicado como capítulo de livro em  GLEIZER, D. (coord.) Aprimorando o mercado de câmbio brasileiro. São Paulo: Bolsa de Mercadorias & Futuros, 2005

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