<p>Time series forecasting is undoubtedly an essential yet challenging issue for researchers in academia and various industries. The superior performance of computational methods, particularly machine learning and deep learning algorithms, over traditional time series techniques, has made them increasingly attractive and successful. However, most current computational approaches focus solely on nonlinear relationships due to the nature of the algorithms employed and utilize all consecutive lagged variables in high-order models. This approach often leads to the inclusion of lagged variables that do not significantly contribute to model performance. This study aims to address these two fundamental issues. Rather than relying on a purely high-order model that can only capture either linear or nonlinear relationships, we propose a deep partial high-order forecasting model capable of modeling both types of relationships simultaneously. The proposed model is called a partial high-order deep-cascaded forecasting model. In the proposed model, a genetic algorithm is used to select the input variables that determine the model order. The relationships between the selected inputs and the target variables are modeled using a deep cascade-forward neural network (D-CFNM), which can capture both linear and nonlinear dependencies. The proposed model was applied to various time series, and the performance of the proposed model was comparatively evaluated with some state-of-the-art models. The results demonstrate that the proposed model significantly outperforms its counterparts across all tested datasets.</p>