Assessing predictability of environmental time series with statistical and machine learning models

The ever increasing popularity of machine learning methods in virtually all areas of science, engineering and beyond is poised to put established statistical modeling approaches into question. Environmental statistics is no exception, as popular constructs such as neural networks and decision trees are now routinely used to provide forecasts of physical processes ranging from air pollution to meteorology. This presents both challenges and opportunities to the statistical community, which could contribute to the machine learning literature with a model-based approach with formal uncertainty quantification. Should, however, classical statistical methodologies be discarded altogether in environmental statistics, and should our contribution be focused on formalizing machine learning constructs? This work aims at providing some answers to this thought-provoking question with two time series case studies where selected models from both the statistical and machine learning literature are compared in terms of forecasting skills, uncertainty quantification and computational time. Relative merits of both class of approaches are discussed, and broad open questions are formulated as a baseline for a discussion on the topic.