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It is unquestionable that time series forecasting is of paramount importance in many fields. The most used machine learning models to address time series forecasting tasks are Recurrent Neural Networks (RNNs). Typically, those models are built using one of the three most popular cells: ELMAN, Long Short-Term Memory (LSTM), or Gated Recurrent Unit (GRU) cells. Each cell has a different structure and implies a different computational cost. However, it is not clear why and when to use each RNN-cell structure. Actually, there is no comprehensive characterization of all the possible time series behaviors and no guidance on what RNN cell structure is the most suitable for each behavior. The objective of this study is twofold: it presents a comprehensive taxonomy of almost all time series behaviors and provides insights into the best RNN cell structure for each time series behavior. We conducted two experiments: (1) We evaluate and analyze the role of each component in the LSTM-Vanilla cell by creating 11 variants based on one alteration in its basic architecture (removing, adding, or substituting one cell component). (2) We evaluate and analyze the performance of 20 possible RNN-cell structures. To evaluate, compare, and select the best model, different statistical metrics were used: error-based metrics, information criterion-based metrics, naive-based metrics, and direction change-based metrics. To further improve our confidence in the models interpretation and selection, the Friedman Wilcoxon-Holm signed-rank test was used. Our results advocate the usage and exploration of the newly created RNN variant, named SLIM, in time series forecasting thanks to its high ability to accurately predict the different time series behaviors, as well as its simple structural design that does not require expensive temporal and computing resources.