TIME-SERIES AND DEPENDENT-VARIABLES

被引:82
作者
SAVIT, R
GREEN, M
机构
[1] Physics Department, The University of Michigan, Ann Arbor
来源
PHYSICA D | 1991年 / 50卷 / 01期
关键词
D O I
10.1016/0167-2789(91)90083-L
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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 k th 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 Henon maps, as well as to sequences of quasi-random numbers. In all cases the delta-j correctly indicate the expected dependencies. We also show that the delta-j are robust to the addition of substantial noise in a deterministic process. In addition, we derive a predictability index which is a measure of the extent to which a time series is predictable given some tolerance, epsilon. Finally, we discuss the behavior of the delta-j as epsilon approaches zero.
引用
收藏
页码:95 / 116
页数:22
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