TESTING FOR NONLINEARITY IN TIME-SERIES - THE METHOD OF SURROGATE DATA
TESTING FOR NONLINEARITY IN TIME-SERIES - THE METHOD OF SURROGATE DATA
复制标题
DOI：
10.1016/0167-2789(92)90102-s
复制
发表时间：
1992-09-15
期刊：
影响因子：
4
通讯作者：
FARMER, JD
中科院分区：
文献类型：
--
作者：
THEILER, J;EUBANK, S;FARMER, JD
我们描述了一种识别时间序列中的非线性的统计方法。该方法首先将某个线性过程指定为零假设，然后生成与该零假设一致的代理数据集，最后计算原始数据集和每个代理数据集的区分统计量。如果为原始数据计算的值与为代理数据计算的值的集合显著不同，则拒绝零假设并检测非线性。我们讨论了各种零假设和区别统计量。对已知混沌系统产生的数值数据进行了验证，并应用于超流体、脑波和太阳黑子测量中出现的一些实验时间序列；我们评估了每种情况下非线性结构证据的统计意义，并举例说明了该方法识别的数据的各个方面。
We describe a statistical approach for identifying nonlinearity in time series. The method first specifies some linear process as a null hypothesis, then generates surrogate data sets which are consistent with this null hypothesis, and finally computes a discriminating statistic for the original and for each of the surrogate data sets. If the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data, then the null hypothesis is rejected and nonlinearity is detected. We discuss various null hypotheses and discriminating statistics. The method is demonstrated for numerical data generated by known chaotic systems, and applied to a number of experimental time series which arise in the measurement of superfluids, brain waves, and sunspots; we evaluate the statistical significance of the evidence for nonlinear structure in each case, and illustrate aspects of the data which this approach identifies.