  In this work we propose an objective function to guide the search for a state
space reconstruction of a dynamical system from a time series of measurements.
This statistics can be evaluated on any reconstructed attractor, thereby
allowing a direct comparison among different approaches: (uniform or
non-uniform) delay vectors, PCA, Legendre coordinates, etc. It can also be used
to select the most appropriate parameters of a reconstruction strategy. In the
case of delay coordinates this translates into finding the optimal delay time
and embedding dimension from the absolute minimum of the advocated cost
function. Its definition is based on theoretical arguments on noise
amplification, the complexity of the reconstructed attractor and a direct
measure of local stretch which constitutes a novel irrelevance measure. The
proposed method is demonstrated on synthetic and experimental time series.
