This paper presents a systematic approach for solving complex prediction problems with a focus on energy efficiency. The approach involves using neural networks, specifically recurrent and sequential networks, as the main tool for prediction. In order to test the methodology, a case study was conducted in the telecommunications industry to address the problem of energy efficiency in data centers. The case study involved comparing four recurrent and sequential neural networks, including recurrent neural networks (RNNs), long short-term memory (LSTM), gated recurrent units (GRUs), and online sequential extreme learning machine (OS-ELM), to determine the best network in terms of prediction accuracy and computational time. The results show that OS-ELM outperformed the other networks in both accuracy and computational efficiency. The simulation was applied to real traffic data and showed potential energy savings of up to 12.2% in a single day. This highlights the importance of energy efficiency and the potential for the methodology to be applied to other industries. The methodology can be further developed as technology and data continue to advance, making it a promising solution for a wide range of prediction problems.