Mixed-causal ARMA processes are known to capture the dynamics of locally explosive behaviour, such as bubble assets in finance. However, the limited knowledge of the predictive density of mixed-causal processes, especially during explosive bubble events, complicates their forecast and thus limits their use in practical applications. Given the lack of closed-form formulae for the conditional prediction density (except in special cases), simulation-based and sample-based methods have been proposed in the literature. Hovewer, these methods can be computationally expensive, especially for longer forecast horizons, and do not accurately capture the dynamics during explosive episodes. In this paper, we introduce Machine-learning algorithms for forecasting during bubble periods and show that K nearest neighbours and random forest learning methods are promising for this task. These approaches are shown to provide an interesting approximation to the true theoretical predictive densities and exhibit better forecasting abilities than existing simulation-based methods.