Improved singular spectrum analysis for time series with missing data
Improved singular spectrum analysis for time series with missing data
复制标题
改进了缺失数据时间序列的奇异谱分析
DOI：
10.5194/npg-22-371-2015
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发表时间：
2015-01-01
影响因子：
2.2
通讯作者：
Li, B.
中科院分区：
文献类型：
--
作者：
Shen, Y.;Peng, F.;Li, B.
抽象的。奇异谱分析（SSA）是时间序列分析的一种有效方法。基于原始时间序列可以从其主成分中再生的性质，本文提出了一种改进的SSA（ISSA）来处理不完全时间序列，Schoellhamer（2001）的改进SSA（SSAM）是其特例。用旧金山弗朗西斯科湾悬浮泥沙浓度的合成和真实的不完全时间序列数据对该方法进行了评价。对含有缺失数据的合成时间序列的分析结果表明，ISSA重建的主成分相对误差远小于SSAM重建的主成分相对误差。当缺失数据占整个时间序列的比例达到60%时，前四个主成分的相对误差分别改善了19.64%、41.34%、23.27%和50.30%。ISSA重建的时间序列的平均绝对误差和均方根误差也小于SSAM。当缺失数据占60%时，分别提高了34.45%和33.91%.真实的不完全时间序列的结果也表明，ISSA得出的标准差（SD）为12.27 mg L−1，小于SSAM得出的13.48 mg L−1。
Abstract. Singular spectrum analysis (SSA) is a powerful technique for time series analysis. Based on the property that the original time series can be reproduced from its principal components, this contribution develops an improved SSA (ISSA) for processing the incomplete time series and the modified SSA (SSAM) of Schoellhamer (2001) is its special case. The approach is evaluated with the synthetic and real incomplete time series data of suspended-sediment concentration from San Francisco Bay. The result from the synthetic time series with missing data shows that the relative errors of the principal components reconstructed by ISSA are much smaller than those reconstructed by SSAM. Moreover, when the percentage of the missing data over the whole time series reaches 60 %, the improvements of relative errors are up to 19.64, 41.34, 23.27 and 50.30 % for the first four principal components, respectively. Both the mean absolute error and mean root mean squared error of the reconstructed time series by ISSA are also smaller than those by SSAM. The respective improvements are 34.45 and 33.91 % when the missing data accounts for 60 %. The results from real incomplete time series also show that the standard deviation (SD) derived by ISSA is 12.27 mg L−1, smaller than the 13.48 mg L−1 derived by SSAM.