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The paper poses video-to-video face recognition as a dynamical system identification and classification problem. Video-to-video means that both gallery and probe consists of videos. We model a moving face as a linear dynamical system whose appearance changes with pose. An autoregressive and moving average (ARMA) model is used to represent such a system. The choice of ARMA model is based on its ability to take care of the change in appearance while modeling the dynamics of pose, expression etc. Recognition is performed using the concept of subspace angles to compute distances between probe and gallery video sequences. The results obtained are very promising given the extent of pose, expression and illumination variation in the video data used for experiments.