We propose a method for disparity estimation in stereo video. We address the problems associated with spatially-temporally-correlated disparity variations (STCDV). STCDV problems are caused by complex motions, e.g., yaw-rotation, pan-tilt-zoom camera movements, etc. The key novelty of this study is to introduce a spatio-temporal disparity hyperplane (STDH) model. The proposed STDH model represents a hyperplane defined in four-dimensional space spanned by disparity, image plane, and time coordinates. Our STDH model is represented by surface normals varying with the spatially-temporally-correlated changes in disparity. Thus, our STDH model is effective in estimating disparity in a stereo video including STCDVs. We estimate video disparity by incorporating our STDH model into the PatchMatch brief propagation framework. Our experiments demonstrate that the proposed method outperforms other methods.