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This study presents a partial high-order time series prediction model. In the proposed model, the inputs that determine the model order are determined by the genetic algorithm (GA).The existing relationships between model inputs and targets are specified by a deep-cascade-forward neural network (D-CFNN) that can model relationships having both linear and nonlinear structures. The proposed model can be called a GA-based partial high-order-cascaded-deep time series prediction model (GA-PHO-DC-TSPM). The GA-PHO-DC-TSPM has been applied to different time series. The obtained results were evaluated comparatively with some state-of-the-art models.