Eduardo F. Mendes

Ricardo P. Masini, Marcelo C. Medeiros, Eduardo F. Mendes

In this paper we survey the most recent advances in supervised machine learning and high-dimensional models for time series forecasting. We consider both linear and nonlinear alternatives. Among the linear methods we pay special attention to penalized regressions and ensemble of models. The nonlinear methods considered in the paper include shallow and deep neural networks, in their feed-forward and recurrent versions, and tree-based methods, such as random forests and boosted trees. We also consider ensemble and hybrid models by combining ingredients from different alternatives. Tests for superior predictive ability are briefly reviewed. Finally, we discuss application of machine learning in economics and finance and provide an illustration with high-frequency financial data.

Ricardo P. Masini, Marcelo C. Medeiros, Eduardo F. Mendes

There has been considerable advance in understanding the properties of sparse regularization procedures in high-dimensional models. In time series context, it is mostly restricted to Gaussian autoregressions or mixing sequences. We study oracle properties of LASSO estimation of weakly sparse vector-autoregressive models with heavy tailed, weakly dependent innovations with virtually no assumption on the conditional heteroskedasticity. In contrast to current literature, our innovation process satisfy an $L^1$ mixingale type condition on the centered conditional covariance matrices. This condition covers $L^1$-NED sequences and strong ($α$-) mixing sequences as particular examples.