Guarín Diego, Delgado Edilson, Orozco Álvaro
Department of Electrical Eng,Universidad Tecnológica de Pereira, Vereda la Julita, Pereira, Colombia.
Annu Int Conf IEEE Eng Med Biol Soc. 2011;2011:2671-4. doi: 10.1109/IEMBS.2011.6090734.
Testing for nonlinearity is one of the most important preprocessing steps in nonlinear time series analysis. Typically, this is done by means of the linear surrogate data methods. But it is a known fact that the validity of the results heavily depends on the stationarity of the time series. Since most physiological signals are non-stationary, it is easy to falsely detect nonlinearity using the linear surrogate data methods. In this document, we propose a methodology to extend the procedure for generating constrained surrogate time series in order to assess nonlinearity in non-stationary data. The method is based on the band-phase-randomized surrogates, which consists (contrary to the linear surrogate data methods) in randomizing only a portion of the Fourier phases in the high frequency domain. Analysis of simulated time series showed that in comparison to the linear surrogate data method, our method is able to discriminate between linear stationarity, linear non-stationary and nonlinear time series. Applying our methodology to heart rate variability (HRV) records of five healthy patients, we encountered that nonlinear correlations are present in this non-stationary physiological signals.
非线性检验是非线性时间序列分析中最重要的预处理步骤之一。通常，这是通过线性替代数据方法来完成的。但众所周知，结果的有效性在很大程度上取决于时间序列的平稳性。由于大多数生理信号都是非平稳的，因此使用线性替代数据方法很容易错误地检测到非线性。在本文中，我们提出了一种方法来扩展生成受限替代时间序列的过程，以便评估非平稳数据中的非线性。该方法基于带相位随机化替代数据，与线性替代数据方法不同的是，它只在高频域中对一部分傅里叶相位进行随机化。对模拟时间序列的分析表明，与线性替代数据方法相比，我们的方法能够区分线性平稳、线性非平稳和非线性时间序列。将我们的方法应用于五名健康患者的心率变异性（HRV）记录，我们发现这种非平稳生理信号中存在非线性相关性。
