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Abstract: Forecasting motion of a specific target object is a common problem for surgical interventions, e.g. for localization of a target region, guidance for surgical interventions, or motion compensation. Optical coherence tomography (OCT) is an imaging modality with a high spatial and temporal resolution. Recently, deep learning methods have shown promising performance for OCT\-based motion estimation based on two volumetric images. We extend this approach and investigate whether using a time series of volumes enables motion forecasting. We propose 4D spatio-temporal deep learning for end-to-end motion forecasting and estimation using a stream of OCT volumes. We design and evaluate five different 3D and 4D deep learning methods using a tissue data set. Our best performing 4D method achieves motion forecasting with an overall average correlation coefficient of 97.41\%, while also improving motion estimation performance by a factor of 2.5 compared to a previous 3D approach.