DELAY-TIME WINDOW AND PLATEAU ONSET OF THE CORRELATION DIMENSION FOR SMALL DATA SETS

The method of delays is widely used for reconstructing chaotic attract ors from experimental observations. Many studies have used a fixed del ay time rd as the embedding dimension in is increased, but this is not necessarily the best choice for obtaining good convergence of the cor relation 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 o r the mutual information, and no standard procedure for estimating tau (w) has yet emerged. However, the recently introduced C-C method can b e 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 in deed lead to a more rapid convergence of the correlation dimension as the embedding dimension m is increased. [S1063-651X(98)05111-3].