Time series forecasting is a pivotal tool across various fields, including finance, energy, and healthcare, where accurate predictions can significantly influence decision-making processes. In this study, we introduce an Enhanced Group Method of Data Handling (GMDH) model, which is integrated with a Roulette Neuron Selection Algorithm to bolster forecasting accuracy and efficiency. The enhancements to the GMDH framework are designed to adeptly address the non-linear relationships commonly found in time series data. This is achieved through the introduction of a roulette selection mechanism, which optimizes the neuron selection process during the network training phase. The adaptive nature of the roulette selection strategy is key to this model, as it enhances the diversity of neuron selection and mitigates the risk of premature convergence. Such improvements lead to the development of more robust forecasting models that are capable of delivering superior performance. Through extensive experimental evaluations on benchmark time series datasets, our proposed approach demonstrates clear superiority over traditional GMDH models as well as other contemporary state-of-the-art methods. This superiority is evident in both predictive accuracy and computational efficiency. The findings from our research suggest that incorporating a roulette-based selection mechanism into the GMDH framework provides a promising avenue for tackling complex time series forecasting challenges. By effectively managing the intricacies of non-linear data patterns and enhancing model adaptability, this approach sets a new standard for precision and resource efficiency in the field of time series forecasting.