Streamflow forecasts produced by hydrological models and post-processing approaches provide valuable information for water management and decision-making. Existing post-processing approaches rarely account for temporal correlation in error models and assume their statistical independence. Understanding this correlation is essential for developing robust post-processors of hydrological models, able to provide reliable forecasts across multiple lead times and aggregation timescales. The temporal correlation of errors is complex. It is often non-linear and dynamic, and influenced by many factors. Here, we use a probabilistic framework coupled with a few statistical methods (including among others, machine learning techniques) to estimate the temporal structure of error correlation. We aim to address several research questions: i) detecting and understanding situations that significantly affect the temporal characteristics of errors; ii) improving the reliability of aggregated forecasts by explicitly modelling the autocorrelation structure. We provide an analysis for a large set of French catchments and several reforecast experiments based on the lumped GR6J hydrological model.