The method of delays is widely used for reconstructing chaotic attractors from experimental observations. Many studies have used a fixed delay time ${\tau }_d$ as the embedding dimension m is increased, but this is not necessarily the best choice for obtaining good convergence of the correlation dimension. Recently, some researchers have suggested that it is better to fix the delay time window ${\tau }_w$ instead. Unfortunately, ${\tau }_w$ cannot be estimated using either the autocorrelation function or the mutual information, and no standard procedure for estimating ${\tau }_w$ has yet emerged. However, the recently introduced $C-C$ method can be used to estimate either ${\tau }_d$ or ${\tau }_w.$ Using this method, we show that, for small data sets, fixing ${\tau }_w,$ rather than ${\tau }_d,$ does indeed lead to a more rapid convergence of the correlation dimension as the embedding dimension m is increased.

• Received 9 January 1998

DOI:https://doi.org/10.1103/PhysRevE.58.5676