scholarly journals Comparative Assessment of Hierarchical Clustering Methods for Grouping in Singular Spectrum Analysis

AppliedMath ◽  
2021 ◽  
Vol 1 (1) ◽  
pp. 18-36
Author(s):  
Hossein Hassani ◽  
Mahdi Kalantari ◽  
Christina Beneki
Keyword(s):  
Time Series ◽  
Hierarchical Clustering ◽  
Spectrum Analysis ◽  
Visual Information ◽  
Singular Spectrum Analysis ◽  
Clustering Methods ◽  
Dissimilarity Matrix ◽  
Singular Spectrum ◽  
Wide Range ◽  
Hierarchical Clustering Methods

Singular spectrum analysis (SSA) is a popular filtering and forecasting method that is used in a wide range of fields such as time series analysis and signal processing. A commonly used approach to identify the meaningful components of a time series in the grouping step of SSA is the utilization of the visual information of eigentriples. Another supplementary approach is that of employing an algorithm that performs clustering based on the dissimilarity matrix defined by weighted correlation between the components of a time series. The SSA literature search revealed that no investigation has compared the various clustering methods. The aim of this paper was to compare the effectiveness of different hierarchical clustering linkages to identify the appropriate groups in the grouping step of SSA. The comparison was performed based on the corrected Rand (CR) index as a comparison criterion that utilizes various simulated series. It was also demonstrated via two real-world time series how one can proceed, step-by-step, to conduct grouping in SSA using a hierarchical clustering method. This paper is supplemented with accompanying R codes.

Application of singular spectrum analysis in reconstruction of the annual signal from GRACE

2020 ◽  
Vol 14 (3) ◽  
pp. 295-302
Author(s):  
Chuandong Zhu ◽  
Wei Zhan ◽  
Jinzhao Liu ◽  
Ming Chen
Keyword(s):  
Time Series ◽  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Mixture Effect ◽  
Singular Spectrum ◽  
Grace Data ◽  
Terrestrial Water ◽  
Annual Signal ◽  
Long Term Variations

AbstractThe mixture effect of the long-term variations is a main challenge in single channel singular spectrum analysis (SSA) for the reconstruction of the annual signal from GRACE data. In this paper, a nonlinear long-term variations deduction method is used to improve the accuracy of annual signal reconstructed from GRACE data using SSA. Our method can identify and eliminate the nonlinear long-term variations of the equivalent water height time series recovered from GRACE. Therefore the mixture effect of the long-term variations can be avoided in the annual modes of SSA. For the global terrestrial water recovered from GRACE, the peak to peak value of the annual signal is between 1.4 cm and 126.9 cm, with an average of 11.7 cm. After the long-term and the annual term have been deducted, the standard deviation of residual time series is between 0.9 cm and 9.9 cm, with an average of 2.1 cm. Compared with the traditional least squares fitting method, our method can reflect the dynamic change of the annual signal in global terrestrial water, more accurately with an uncertainty of between 0.3 cm and 2.9 cm.

scholarly journals Time Series Imputation via L1 Norm-Based Singular Spectrum Analysis

2018 ◽  
Vol 17 (02) ◽  
pp. 1850017 ◽  
Author(s):  
Mahdi Kalantari ◽  
Masoud Yarmohammadi ◽  
Hossein Hassani ◽  
Emmanuel Sirimal Silva
Keyword(s):  
Time Series ◽  
Spectrum Analysis ◽  
Missing Values ◽  
Time Series Data ◽  
Singular Spectrum Analysis ◽  
Series Data ◽  
L1 Norm ◽  
Nonparametric Approach ◽  
Singular Spectrum ◽  
Simulated Time

Missing values in time series data is a well-known and important problem which many researchers have studied extensively in various fields. In this paper, a new nonparametric approach for missing value imputation in time series is proposed. The main novelty of this research is applying the [Formula: see text] norm-based version of Singular Spectrum Analysis (SSA), namely [Formula: see text]-SSA which is robust against outliers. The performance of the new imputation method has been compared with many other established methods. The comparison is done by applying them to various real and simulated time series. The obtained results confirm that the SSA-based methods, especially [Formula: see text]-SSA can provide better imputation in comparison to other methods.

scholarly journals Evidence of structured Brownian dynamics from temperature time series analysis

1997 ◽  
Vol 4 (4) ◽  
pp. 251-254
Author(s):  
A. Pasini ◽  
V. Pelino ◽  
S. Potestà
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Spectrum Analysis ◽  
Brownian Dynamics ◽  
Singular Spectrum Analysis ◽  
Temperature Time Series ◽  
Singular Spectrum ◽  
The Usa ◽  
Temperature Time ◽  
Analysis Of Time Series

Abstract. An analysis of time series of monthly mean temperatures ranging from 1895 to 1989 is performed through application of Singular Spectrum Analysis (SSA) to data of several places in the USA. A common dynamics in the reconstructed spaces is obtained, with the evidence of a non-trivial and structured coupling of two Brownian motions, resembling the so-called Lévy flights. The idea that these two correlated functions are related to the zonal and eddy components of the atmospheric motions is suggested.

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