Abstract As the rank of Volterra adaptive filter interferes with predictive performance, how to determine the optimal rank of Volterra adaptive filter becomes a key problem in practical prediction. Using theory of phase space reconstruction, this paper derives that the optimal rank of Volterra adaptive filter equals the lowest embedding dimension of chaotic dynamical systems. It is shown through some chaotic series experiments that this method is successful in Volterra adaptive predication and robust to the noise of different levels added to the chaotic time series.