High-Dimensional Time Series Models:
Most of my current research is focused on the econometrics of high-dimensional time-series models. In Medeiros and Mendes (2016, Journal of Econometrics) we show under which conditions the adaptive LASSO (adaLASSO) method is model selection consistent in large time-series models with errors are are non Gaussian and conditional heteroskedastic.

Models with Flexible Functional Forms:
For many years I have been interested in constructing models with flexible functional forms. More specifically, my goal has been to combine techniques from  statistical learning (machine learning) and econometrics. For example, three of the four papers of my PhD thesis were related to neural networks and smooth transition models; see Medeiros and Veiga (2003, Journal of Time Series Analysis), Medeiros and Veiga (2005, IEEE Transactions on Neural Networks), and Medeiros, Veiga, and Pedreira (2001, IEEE Transactions on Neural Networks). Joint with Timo Teräsvirta and Gianluigi Rech, I co-authored a paper on neural network models where we developed a simple model building strategy solely based on statistical arguments to specify neural network models. In Suarez-Fariñas, Pedreira, and Medeiros (2004, JASA), we also developed a model based on neural networks and smooth transtion specifications. More recently, I have also started to study regression trees under an econometric perspective; see, for example, da Rosa, Veiga, and Medeiros (2008, Computational Statistics and Data Analysis), Audrino and Medeiros (2010, Journal of Applied Econometrics), or Mendes, Veiga, and Medeiros (2009). As these models are reduced-forms, the main application is time-series out-of-sample forecasting. A successful application of such functional forms is realized volatility forecasting; see McAleer and Medeiros (2008, Journal of Econometrics), Scharth and Medeiros (2009, International Journal of Forecasting), Hillebrand and Medeiros (2010, Econometric Reviews), or Hillebrand and Medeiros (2009).
I have been also interested is the detection of structural-breaks. For example, in Hillebrand and Medeiros (2016, JBES), we study the simultaneous occurrence of long memory and nonlinear effects, such as structural breaks and thresholds, in autoregressive moving average (ARMA) time series models and apply our modeling framework to series of daily realized volatility. In Hillebrand, Medeiros, and  Xu (2010, Journal of Time Series Econometrics) we derive the asymptotic properties of the quasi maximum likelihood estimator of smooth transition regressions when time is the transition variable. An important topic of research is the distinction between long memory and nonlinearities.
Estimation of Structural Models:
Recently, my interest has moved towards models with more structure and I am particularly concerned about regime-switching models with endogenous variables. In Areosa, McAleer, and Medeiros (Journal of Econometrics), we relax the assumption of weakly exogenous regressors in smooth transition regression (STR) models and discuss the estimation of such models by the generalized method of moments. We also show that instruments that are strong in the linear case may be quite weak in the nonlinear framework. 

In Preve and Medeiros (Journal of Econometrics), we introduce a linear programming estimator (LPE) for the slope parameter in a constrained linear regression model with a single regressor. The LPE is interesting because it can be superconsistent in the presence of an endogenous regressor and, under some additional assumptions, preferable to the ordinary least squares and instrumental variable estimators.

Estimation of discrete choice models with measurement error is also a current topic of research.