子空间分割指数熵及其在非线性检验中的应用研究

Subspace Exponent Entropy and Its Application in Nonlinearity Test

检测时间序列的非线性特性是时间序列分析的必要前提,而非线性检验特征对检测结果的有效性至关重要。提出时间序列重构相空间中点轨迹分布的复杂性测度-子空间分割指数熵,并将子空间分割指数熵与时间反转不对称指数、三阶自相关系数、非线性预测误差和近似熵这四种常用的非线性检验特征进行对比分析。对三阶AR信号、Henon信号、Lorenz信号、心电和皮肤电信号的非线性检测结果表明,子空间分割指数熵能够正确检测各类信号的非线性特性,并且具有较高的抗噪性能,是一种区分度高、鲁棒性好的非线性检验特征。

Detecting the nonlinearity of the time series is a prerequisite for time series analysis, while the selection of nonlinearity test statistics is crucial for the validity of the test results. We propose a new test statistic for nonlinearity test named subspace exponent entropy. Subspace exponent entropy divides the reconstructed state space of the time series into subspaees, and then measures the complexity of the phase point distribution in the subspaces. The nonlinearity test experi- ment tests the nonlinearity of five kinds of signals, including AR signal, Henon signal, Lorenz signal, ECG and SCR sig- nal. The length of all the signals is 1000 points. In addition to subspace exponent entropy, we used other four test statistics commonly used in nonlinearity test named time reversibility, higher order autocovariance, nonlinear prediction error and ap- proximate entropy. The experiment results show that the subspace exponent entropy can distinguish the nonlinearity of all signals, and has a high level of anti-noise performance. The subspace exponent entropy is an effective and stable test statis- tic for the nonlinearity test of short and noisy time series.