Abstract
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.
Highlights
Singular spectrum analysis (SSA) introduced by Broomhead and King (1986) for studying dynamical systems is a powerful toolkit for extracting short, noisy and chaotic signals (Vautard et al, 1992)
We have pointed out that this scale factor can be derived from Eq (15), which is the simplified version of our improved SSA (ISSA) approach, by supposing the missing data points with the same eigenvector elements
In order to evaluate the accuracies of reconstructed principal component (PC) from the time series with different percentages of missing data, following the approach of Shen et al (2014), we compute the relative errors of the first four modes derived by ISSA and SSA for time series with missing data (SSAM) with the following expression: 1N p=
Summary
Singular spectrum analysis (SSA) introduced by Broomhead and King (1986) for studying dynamical systems is a powerful toolkit for extracting short, noisy and chaotic signals (Vautard et al, 1992). The original time series is reconstructed with the first several RCs. The SSAM approach developed by Schoellhamer (2001) computes the elements c(j ) of the lagged correlation matrix by c(j ). The main difference of our ISSA approach from the SSAM approach of Schoellhamer (2001) is in calculating the PCs. We produce the PCs from observed data with Eq (14) according to the power spectrum (eigenvalues) and eigenvectors of the PCs, while Schoellhamer (2001) calculates the PCs from observed data with Eq (6) only according to the eigenvectors and uses the scale factor L/Li to compensate the missing value. We have pointed out that this scale factor can be derived from Eq (15), which is the simplified version of our ISSA approach, by supposing the missing data points with the same eigenvector elements. The only disadvantage of our method is that it will cost more computational effort
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
