We investigate whether the use of statistical learning techniques and big data can enhance the accuracy of inflation forecasts. We make use of a large dataset for the disaggregated prices of consumption goods and services, which we partially reconstruct, and a large suite of different statistical learning and traditional time-series models. The results suggest that the statistical learning models are able to compete with most benchmarks over medium to longer horizons, despite the fact that we only have a relatively small sample of available data. This may imply that the ability of statistical learning models to explain nonlinear relationships, or as an alternative, restrict the set of predictors to relevant information, is of importance. These characteristics of the statistical learning models may be particularly useful during periods of crisis, when deviations from the steady state are more persistent. We find that the accuracy of the central bank's near-term inflation forecasts compares favourably with those of The authors would like to thank Patrick Kelly and Marietjie Bennett from Statistics South Africa for their assistance with the data. The insightful comments of the anonymous referees have also lead to a number of improvements, for which the authors are grateful. The remaining errors are those of the authors.