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In this paper, we survey the most recent advances in supervised machine learning (ML) 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 feedforward 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 ML in economics and finance and provide an illustration with high‐frequency financial data. [ABSTRACT FROM AUTHOR]

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. In contrast to current literature, our innovation process satisfy an L1 mixingale type condition on the centered conditional covariance matrices. This condition covers L1‐NED sequences and strong (α‐) mixing sequences as particular examples. [ABSTRACT FROM AUTHOR]