On the embedding‐dimension analysis of AE and AL time series

Abstract

Several authors have employed the embedding‐dimension method to analyze time series of geomagnetic indices, with differing results for the value of the correlation dimension ν. It is argued that these differences may arise from corresponding differences in the length and construction of the various data sets used. Practical application of the method to sets of discretized data requires use of a delay time scale set by the autocorrelation time of the data set. It is found that a particular data set containing 35 days of AE exhibits an autocorrelation time τc longer by an order of magnitude than that of a short‐duration (<5 days) set, raising the possibility that extant analyses of long‐duration sets may have employed delay times shorter than τc. In addition, the power spectrum of AE reveals modulation at a period of 24 hr. A numerical experiment on the logistic map shows that such modulation introduces an extra degree of freedom in the data, resulting in an augmented correlation dimension.