INTERPRETATION OF SINGULAR SPECTRUM ANALYSIS AS COMPLETE EIGENFILTER DECOMPOSITION

2012 ◽  
Vol 04 (04) ◽  
pp. 1250023 ◽  
Author(s):  
KENJI KUME
Keyword(s):  
Time Series ◽  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Singular Value ◽  
Original Time Series ◽  
Singular Vectors ◽  
Singular Spectrum ◽  
Original Time ◽  
Value Decomposition ◽  
Insight Into

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.

scholarly journals PERAMALAN JUMLAH KUNJUNGAN WISATAWAN MANCANEGARA KE BALI MENGGUNAKAN METODE SINGULAR SPECTRUM ANALYSIS

2019 ◽  
Vol 8 (4) ◽  
pp. 303
Author(s):  
MIRA AYU NOVITA SARI ◽  
I WAYAN SUMARJAYA ◽  
MADE SUSILAWATI
Keyword(s):  
Time Series ◽  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Window Length ◽  
Original Time Series ◽  
Number Of Components ◽  
Singular Spectrum ◽  
Original Time

Singular spectrum analysis (SSA) is a method to decompose the original time series into a summation of a small number of components that can be interpreted as varied trends, oscillatory, and noise components. The purpose of this research is to model and to find out the results of forecasting the number of foreign tourists arrival to Bali using SSA method. In this research, the accuracy of forecasting results will be calculated using the SSA model with reccurent singular spectrum analysis (RSSA) method. The best SSA model was obtained with a window length (L=94) and produces MAPE value of 7,65%.

Additive Decomposition of Power Spectrum Density in Singular Spectrum Analysis

2016 ◽  
Vol 08 (01) ◽  
pp. 1650003
Author(s):  
Kenji Kume ◽  
Naoko Nose-Togawa
Keyword(s):  
Time Series ◽  
Power Spectrum ◽  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Power Spectrum Density ◽  
Spectral Structure ◽  
Additive Decomposition ◽  
Singular Spectrum ◽  
Spectrum Density ◽  
Value Decomposition

Singular spectrum analysis (SSA) is a nonparametric and adaptive spectral decomposition of a time series. The singular value decomposition of the trajectory matrix and the anti-diagonal averaging lead to a time-series decomposition. In this paper, we propose an novel algorithm for the additive decomposition of the power spectrum density of a time series based on the filtering interpretation of SSA. This can be used to examine the spectral overlap or the admixture of the SSA decomposition. We can obtain insights into the spectral structure of the SSA decomposition which helps us for the proper choice of the window length in the practical application. The relationship to the conventional SSA decomposition of a time series is also discussed.

MULTIDIMENSIONAL EXTENSION OF SINGULAR SPECTRUM ANALYSIS BASED ON FILTERING INTERPRETATION

2014 ◽  
Vol 06 (01) ◽  
pp. 1450005 ◽  
Author(s):  
KENJI KUME ◽  
NAOKO NOSE-TOGAWA
Keyword(s):  
Time Series ◽  
Spectrum Analysis ◽  
Arbitrary Dimension ◽  
Singular Spectrum Analysis ◽  
Simple Algorithm ◽  
Image Data ◽  
Multidimensional Data ◽  
Data Series ◽  
Singular Spectrum ◽  
Original Time

Singular spectrum analysis is a nonparametric spectral decomposition of a time series. The singular spectrum analysis can be viewed as the two-step filtering with the complete set of eigenfilter adaptively constructed from the original time series. Based on this viewpoint, we present a flexible and quite simple algorithm for the singular spectrum analysis which can be applied to the multidimensional data series with arbitrary dimension. We have carried out the decomposition of two-dimensional image data, and the optimally constructed filters are found to be the smoothing or the edge enhancement filters of various type. We have also examined a simple example for the decomposition of 3D data.

Non-Negative Time Series Reconstruction via Singular Spectrum Analysis: A Case Study of Precipitation Dynamics in Nigeria

2020 ◽  
Vol 19 (04) ◽  
pp. 2050045
Author(s):  
Olushina Olawale Awe ◽  
Rahim Mahmoudvand ◽  
Paulo Canas Rodrigues
Keyword(s):  
Time Series ◽  
Spectrum Analysis ◽  
Time Series Data ◽  
Singular Spectrum Analysis ◽  
Real Data ◽  
Series Data ◽  
Monthly Precipitation ◽  
Singular Spectrum ◽  
Value Decomposition ◽  
Negative Time

A proper understanding and analysis of the processes involved in seasonal precipitation variability and dynamics is essential to provide reliable information about climate change and how it can affect matters of critical importance such as water availability and agricultural productivity in urban cities. Precipitation data, as many other time series data present only non-negative observations, are is not constrained by standard time series methods. In this paper, we propose a modified singular spectrum analysis (SSA) algorithm for decomposition and reconstruction of time series with non-negative values. Our approach uses a non-negative matrix factorization (NMF) instead of the singular value decomposition in the SSA algorithm. The new algorithm is compared with the classic SSA algorithm by considering a simulation study and observed data of monthly precipitation of four major cities in Nigeria (Lagos, Kano, Ibadan and Kaduna). Although in terms of mean stared errors both methods give similar results, the percentage of negative fitted values for reconstructions with the classical SSA algorithm reached more than [Formula: see text] in our real data application, which is inappropriate for non-negative time series. The proposed adaptation of the SSA algorithm for non-negative time series data provides an important development with applications in many fields where time series data has non-negative constraints.

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.

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