Coping with Nonstationarity by Overembedding

We discuss how nonstationarity in observed time series data due to pronounced fluctuations of system parameters can be resolved by making use of embedding techniques for scalar data. If a $D$-dimensional deterministic system is driven by $P$ slowly time dependent parameters, a $(D+P)$-dimensional manifold has to be reconstructed from the scalar time series, which is done by an $m>\mathrm{}2\mathrm{}(D+P)$-dimensional time delay embedding. We show that in this space essential aspects of determinism are restored. We demonstrate the validity of the idea heuristically, for numerical examples and for human speech data.