Overembedding method for modeling nonstationary systems

We propose a general overembedding method for modeling and prediction of nonstationary systems. It basically enlarges the standard time-delay-embedding space by inclusion of the (unknown) slow driving signal, which is estimated simultaneously with the intrinsic stationary dynamics. Our method can be implemented with any modeling tool. Using, in particular, artificial neural networks, its application to both synthetic and real-world time series shows that it is highly efficient, leading to much more accurate results and longer prediction horizons than other existing overembedding methods in the literature.