Detecting determinism in time series: the method of surrogate data
Detecting determinism in time series: the method of surrogate data
复制标题
DOI：
10.1109/tcsi.2003.811020
复制
发表时间：
2003-06
影响因子：
5.1
通讯作者：
M. Small;C. Tse
中科院分区：
文献类型：
--
作者：
M. Small;C. Tse
我们回顾了一种相对较新的统计检验，该检验可用于确定观察到的时间序列是否与特定类型的动力系统不一致。这些替代数据方法可以针对以下假设来检验观察到的时间序列：i)独立且同分布的噪声；ii)线性滤波的噪声；以及iii)线性滤波的噪声的单调非线性变换。还描述了最近提出的第四种算法，该算法用于检验具有不相关噪声的周期轨道的假设。我们提出了这些方法在各种工程问题上的几个新的应用，包括：识别噪声时间序列中的确定性(消息)信号；以及分离确定性和随机分量。当被用来分离确定性分量和噪声分量时，我们证明了将代理方法应用于非线性模型的残差相当于在信息论模型选择标准下对该模型进行拟合。
We review a relatively new statistical test that may be applied to determine whether an observed time series is inconsistent with a specific class of dynamical systems. These surrogate data methods may test an observed time series against the hypotheses of: i) independent and identically distributed noise; ii) linearly filtered noise; and iii) a monotonic nonlinear transformation of linearly filtered noise. A recently suggested fourth algorithm for testing the hypothesis of a periodic orbit with uncorrelated noise is also described. We propose several novel applications of these methods for various engineering problems, including: identifying a deterministic (message) signal in a noisy time series; and separating deterministic and stochastic components. When employed to separate deterministic and noise components, we show that the application of surrogate methods to the residuals of nonlinear models is equivalent to fitting that model subject to an information theoretic model selection criteria.