Time series and dependent variables (Q805119)

We present a new method for analyzing time series which is designed to extract inherent deterministic dependencies in the series. The method is particularly suited to series with broad-band spectra such as chaotic series with or without noise. We derive quantities, \(\delta_ j(\epsilon)\), based on conditional probabilities, whose magnitude, roughly speaking, is an indicator of the extent to which the kth element in the series is a deterministic function of the (k-j)th element to within a measurement uncertainty, \(\epsilon\). We apply our method to a number of deterministic time series generated by chaotic processes such as the tent, logistic and Hénon maps, as well as to sequences of quasi- random numbers.