Groundwater level prediction is an applied time series forecasting task with important social impacts to optimize water management as well as preventing some natural disasters: for instance, floods or severe droughts. Machine learning methods have been reported in the literature to achieve this task, but they are only focused on the forecast of the groundwater level at a single location. A global forecasting method aims at exploiting the groundwater level time series from a wide range of locations to produce predictions at a single place or at several places at a time. Given the recent success of global forecasting methods in prestigious competitions, it is meaningful to assess them on groundwater level prediction and see how they are compared to local methods. In this work, we created a dataset of 1026 groundwater level time series. Each time series is made of daily measurements of groundwater levels and two exogenous variables, rainfall and evapotranspiration. This dataset is made available to the communities for reproducibility and further evaluation. To identify the best configuration to effectively predict groundwater level for the complete set of time series, we compared different predictors including local and global time series forecasting methods. We assessed the impact of exogenous variables. Our result analysis shows that the best predictions are obtained by training a global method on past groundwater levels and rainfall data.