一种基于Fisher投影的时间序列非线性检验

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摘要为进一步提升替代数据法非线性检验的性能和稳定性，本文引入Fisher投影将不同的非线性检验统计量进行组合并投影，使不同非线性统计量的检验性能互补。利用6类非线性混沌序列和线性高斯白噪声序列进行实验，检验该方法的有效性，结果表明，基于Fisher投影的替代数据法对各类信号正确检验的能力明显提升，且稳定性较好，具有较强的数据适应性；尤其是三阶自协方差统计量、峭度和三阶自相关统计量的三维组合，相对于其他的统计量组合，对非线性混沌序列及线性高斯白噪声序列的检验能力更强，数据适应性更高。

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	卢世坤李夕海牛超曾小牛杨晓芸

关键词 ：非线性检验, 替代数据, 检验统计量, Fisher投影

Abstract：In order to enhance the performance and stability of surrogate data method, we introduce Fisher projection method to combine and project the different nonlinear statistics. In this way, the performance of different statistics can complement each other. In this paper, six kinds of nonlinear chaotic series and linear Gaussian white noise are used to experiment. The results show that the performance of the surrogate data method has been significantly improved. The stability and suitability of the method become better. Specially, comparing with others, the combination of third-order autocovariance, kurtosis and third-order auocorrelation statistics has better performance and suitability.

Key words： Nonlinear test surrogate data test statistics Fisher projection;

收稿日期: 2013-07-02 出版日期: 2015-03-15

引用本文:

卢世坤李夕海牛超曾小牛杨晓芸. 一种基于Fisher投影的时间序列非线性检验[J]. 振动与冲击, 2015, 34(5): 179-185.
Lu shi-kun Li xi-hai Niu Chao Zeng xiao-niu Yang xiao-yun. A New Method of Detecting Nonlinearity for Time Series Based on Fisher Projection Transform. JOURNAL OF VIBRATION AND SHOCK, 2015, 34(5): 179-185.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2015/V34/I5/179

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