Nonlinear regression models have been widely used in practice for a variety of time series and cross-section datasets. For purposes of analyzing univariate and multivariate time series data, in particular, the Smooth Transition Regression (STR) models have been shown to be very useful for representing and capturing asymmetric behavior. Most STR models have been applied to univariate process, and have assumed a variety of assumptions, including stationary or cointegrated processes, uncorrelated and homoskedastic or conditionally heteroskedastic errors, and weakly exogenous regressors. Under the assumption of exogeneity, the standard method of estimation is nonlinear least squares. The primary purpose of this paper is to relax the assumption of weakly exogenous regressors and to discuss instrumental variable methods for estimating STR models. The paper analyzes the properties of the STR model with endogenous variables by providing a diagnostic test of linearity of the underlying process under endogeneity, developing an estimation procedure for the STR model, presenting the results of Monte Carlo simulations to show the usefulness of the model and estimation method, and providing an empirical application for inflation rate targeting in Brazil. We show that STR models with endogenous variables can be specified and estimated by straightforward application of current results in the literature.

Publicado em  Journal of Econometrics, 165, 100-111, 2011

In this paper we consider a nonlinear model based on neural networks as well as linear models to forecast the daily volatility of the S&P 500 and FTSE 100 indexes. As a proxy for daily volatility, we consider a consistent and unbiased estimator of the integrated volatility that is computed from high frequency intra-day returns. We also consider a simple algorithm based on bagging (bootstrap aggregation) in order to specify the models analyzed in this paper

 Publicado em Journal of Economic Surveys, 25, 6-18,2011

Publicado em Fuzzy Sets and Systems, 161, 1836-1851. 

n this paper we propose a smooth transition tree model for both the conditional mean and variance of the short-term interest rate process. The estimation of such models is addressed and the asymptotic properties of the quasi-maximum likelihood estimator are derived. Model specification is also discussed. When the model is applied to the US short-term interest rate we find (1) leading indicators for inflation and real activity are the most relevant predictors in characterizing the multiple regimes’ structure; (2) the optimal model has three limiting regimes. Moreover, we provide empirical evidence of the power of the model in forecasting the first two conditional moments when it is used in connection with bootstrap aggregation (bagging)

Publicado em  Journal of Applied Econometrics.26, 999-1022, 2011

publicado em Pesquisa e Planejamento Econômico, v. 39, n.3, 2009

publicado em Annals of Finance (Print,0), v. 6, p. 51-82, 2009