Effect of constant intervals of a time series on the computation of the correlation dimension

The author discusses the computation of the correlation dimension (D₂) of a time series in the particular case of a signal which is constant for a significant fraction of its length. Two examples are investigated, a periodical signal obtained from a synthesized electrocardiogram (ECG) and the z variable of a Rossler nonlinear system. Such signals are chosen because their correlation dimension values are known. It is shown that the D ₂ obtained by using the algorithm of P. Grassberger and I. Procaccia yields, in both cases, an underestimation of the correct D ₂ value. This problem is discussed and a slight modification of the basic algorithm to reduce this error is proposed