Interpretation of singular Spectrum Analysis as Complete eigenfilter Decomposition
Interpretation of singular Spectrum Analysis as Complete eigenfilter Decomposition
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DOI：
10.1142/s1793536912500239
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发表时间：
2012-10
期刊：
影响因子：
--
通讯作者：
K. Kume
中科院分区：
文献类型：
--
作者：
K. Kume
奇异谱分析是对时间序列进行非参数的自适应谱分解。该方法首先对原始时间序列的轨迹矩阵进行奇异值分解，然后对分解后的序列进行重构。在本文中，我们证明了这些过程可以简单地视为时间序列的完全特征滤波分解。特征滤波器是由轨迹矩阵的奇异向量构造的，奇异向量的完备性保证了特征滤波器的完备性。本文的解释为奇异谱分析提供了新的视角。
Singular spectrum analysis is a nonparametric and adaptive spectral decomposition of a time series. This method consists of the singular value decomposition for the trajectory matrix constructed from the original time series, followed with the subsequent reconstruction of the decomposed series. In the present paper, we show that these procedures can be viewed simply as complete eigenfilter decomposition of the time series. The eigenfilters are constructed from the singular vectors of the trajectory matrix and the completeness of the singular vectors ensure the completeness of the eigenfilters. The present interpretation gives new insight into the singular spectrum analysis.