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Forecasting dynamic scenes remains a fundamental challenge in computer vision, as limited observations make it difficult to capture coherent object-level motion and long-term temporal evolution. We present Motion Group-aware Gaussian Forecasting (MoGaF), a framework for long-term scene extrapolation built upon the 4D Gaussian Splatting representation. MoGaF introduces motion-aware Gaussian grouping and group-wise optimization to enforce physically consistent motion across both rigid and non-rigid regions, yielding spatially coherent dynamic representations. Leveraging this structured space-time representation, a lightweight forecasting module predicts future motion, enabling realistic and temporally stable scene evolution. Experiments on synthetic and real-world datasets demonstrate that MoGaF consistently outperforms existing baselines in rendering quality, motion plausibility, and long-term forecasting stability. Our project page is available at this https URL