Although it is conceptually assumed that global models are relatively ineffective in modelling the highly unstable structure of chaotic hydrologic dynamics, there is not a detailed study of comparing the performances of local and global models in a hydrological context, especially with new emerging machine learning models. In this study, the performance of a local model (k-nearest neighbour, k-nn) and, as global models, several recent machine learning models - artificial neural network (ANN), least square-support vector regression (LS-SVR), random forest (RF), M5 model tree (M5), multivariate adaptive regression splines (MARS) - was analysed in multivariate chaotic forecasting of streamflow. The models were developed for Australia's largest river, the River Murray. The results indicate that the k-nn model was more successful than the global models in capturing the streamflow dynamics. Furthermore, coupled with the multivariate phase-space, it was shown that the global models can be successfully used for obtaining reliable uncertainty estimates for streamflow.