The purpose of the Working Papers is to disseminate the results of research conducted by CIRANO research members in order to solicit exchanges and comments. These reports are written in the style of scientific publications. The ideas and opinions expressed in these documents are solely those of the authors.Les cahiers de la série scientifique visent à rendre accessibles les résultats des recherches effectuées par des chercheurs membres du CIRANO afin de susciter échanges et commentaires. Ces cahiers sont rédigés dans le style des publications scientifiques et n'engagent que leurs auteurs.CIRANO is a private non-profit organization incorporated under the Quebec Companies Act. Its infrastructure and research activities are funded through fees paid by member organizations, an infrastructure grant from the government of Quebec, and grants and research mandates obtained by its research teams. Le CIRANO est un organisme sans but lucratif constitué en vertu de la Loi des compagnies duQuébec. Le financement de son infrastructure et de ses activités de recherche provient des cotisations de ses organisations-membres, d'une subvention d'infrastructure du gouvernement du Québec, de même que des subventions et mandats obtenus par ses équipes de recherche. CIRANO Partners -Les partenaires du CIRANO Corporate Partners -Partenaires corporatifs Autorité des marchés financiers Bank of Canada Bell Canada BMO Financial Group Business Development Bank of Canada Caisse de dépôt et placement du Québec

SummaryThe performance of six classes of models in forecasting different types of economic series is evaluated in an extensive pseudo out‐of‐sample exercise. One of these forecasting models, regularized data‐rich model averaging (RDRMA), is new in the literature. The findings can be summarized in four points. First, RDRMA is difficult to beat in general and generates the best forecasts for real variables. This performance is attributed to the combination of regularization and model averaging, and it confirms that a smart handling of large data sets can lead to substantial improvements over univariate approaches. Second, the ARMA(1,1) model emerges as the best to forecast inflation changes in the short run, while RDRMA dominates at longer horizons. Third, the returns on the S&P 500 index are predictable by RDRMA at short horizons. Finally, the forecast accuracy and the optimal structure of the forecasting equations are quite unstable over time.

We move beyond Is Machine Learning Useful for Macroeconomic Forecasting? by adding the how. The current forecasting literature has focused on matching specific variables and horizons with a particularly successful algorithm. To the contrary, we study the usefulness of the underlying features driving ML gains over standard macroeconometric methods. We distinguish four so-called features (nonlinearities, regularization, cross-validation, and alternative loss function) and study their behavior in both the data-rich and data-poor environments. To do so, we design experiments that allow to identify the "treatment" effects of interest. We conclude that (i) nonlinearity is the true game changer for macroeconomic prediction, (ii) the standard factor model remains the best regularization, (iii) K-fold cross-validation is the best practice, and (iv) the L 2 is preferred to the ε-insensitive in-sample loss. The forecasting gains of nonlinear techniques are associated with high macroeconomic uncertainty, financial stress and housing bubble bursts. Furthermore, ML nonlinearities are helpful when considering density forecasts. KEYWORDSbig data, forecasting, machine learning *** 1% significance of Diebold-Mariano test. ** 5% significance of Diebold-Mariano test. * 10% significance of Diebold-Mariano test. * p < 0.05. ** p < 0.01.

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