In this work, we propose a novel non parametric method for the temporally consistent inpainting of dynamic texture sequences. The inpainting of texture image sequences is stated as a stochastic assimilation issue, for which a novel model-free and data-driven Ensemble Kalman method is introduced. Our model is inspired by the Analog Ensemble Kalman Filter (AnEnKF) recently proposed for the assimilation of geophysical space-time dynamics, where the physical model is replaced by the use of statistical analogs or nearest neighbours. Such a non-parametric framework is of key interest for image processing applications, as prior models are seldom available in general. We present experimental evidence for real dynamic texture that using only a catalog database of historical data and without having any assumption on the model, the proposed method provides relevant dynamically-consistent interpolation and outperforms the classical parametric (autoregressive) dynamical prior.