scholarly journals Modified singular spectrum analysis in identifying rainfall trend over peninsular Malaysia

2019 ◽  
Vol 15 (1) ◽  
pp. 283
Author(s):  
S.M. Shaharudin ◽  
N. Ahmad ◽  
N.H. Zainuddin
Keyword(s):  
Time Series ◽  
Spectrum Analysis ◽  
Time Series Data ◽  
Singular Spectrum Analysis ◽  
Singular Values ◽  
Peninsular Malaysia ◽  
Series Data ◽  
Rainfall Time Series ◽  
Singular Spectrum ◽  
Torrential Rainfall

<p>Identifying the local time scale of the torrential rainfall pattern through Singular Spectrum Analysis (SSA) is useful to separate the trend and noise components. However, SSA poses two main issues which are torrential rainfall time series data have coinciding singular values and the leading components from eigenvector obtained from the decomposing time series matrix are usually assesed by graphical inference lacking in a specific statistical measure. In consequences to both issues, the extracted trend from SSA tended to flatten out and did not show any distinct pattern.  This problem was approached in two ways. First, an Iterative Oblique SSA (Iterative O-SSA) was presented to make adjustment to the singular values data. Second, a measure was introduced to group the decomposed eigenvector based on Robust Sparse K-means (RSK-Means). As the results, the extracted trend using modification of SSA appeared to fit the original time series and looked more flexible compared to SSA.</p>

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 Improved singular spectrum analysis for time series with missing data

2014 ◽  
Vol 1 (2) ◽  
pp. 1947-1966
Author(s):  
Y. Shen ◽  
F. Peng ◽  
B. Li
Keyword(s):  
Time Series ◽  
Missing Data ◽  
San Francisco ◽  
Principal Components ◽  
Spectrum Analysis ◽  
Time Series Data ◽  
Singular Spectrum Analysis ◽  
Series Data ◽  
Singular Spectrum ◽  
Relative Errors

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 will develop an improved SSA (ISSA) for processing the incomplete time series and the modified SSA (SSAM) of Schoellhamer (2001) is its special case. The approach was 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. Besides, both the mean absolute errors and mean root mean squared errors of the reconstructed time series by ISSA are also much 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 SD derived by ISSA is 12.27 mg L−1, smaller than 13.48 mg L−1 derived by SSAM.

Multiple-channel Singular Spectrum Analysis-based noise reduction for MT data observed in Boso Peninsula, Japan

2021 ◽  
Author(s):  
Shu Kaneko ◽  
Katsumi Hattori ◽  
Toru Mogi ◽  
Chie Yoshino
Keyword(s):  
Time Series ◽  
Noise Reduction ◽  
Spectrum Analysis ◽  
Reduction Method ◽  
Time Series Data ◽  
Singular Spectrum Analysis ◽  
Series Data ◽  
Boso Peninsula ◽  
Singular Spectrum ◽  
Kanto Earthquake

&lt;p&gt;Off the coast of the Boso Peninsula, there is a triple junction of the Pacific Plate, the Philippine Sea Plate, and the North American Plate and the Boso Peninsula is one of the seismically active areas in Japan. There are also epicenter areas such as the 1703 Genroku Kanto Earthquake (M8.2), the 1923 Taisho Kanto Earthquake (M7.9), and the Boso Slow Slip which occurs every 6 years, which are geologically interesting places. To estimate the subsurface resistivity structure of the whole Boso area, Magnetotelluric (MT) survey with 41 sites (inter-sites distance of 7 km) has been conducted in 2014-2016, using U43 (12 sites, 1 Hz sampling ; Tierra Technica) and MTU-5, 5A, net (41 sites, 15, 150, and 2400 Hz sampling; Phoenix Geophysics). However, the Boso area is greatly affected by leak current from DC-driven trains, factories, and power lines, so the observed data are contaminated by artificial noises. When we tried to apply the conventional noise reduction method (e.g., remote reference (Gamble et al., 1979) and BIRRP (Chave and Thomson, 2004)) in frequency domain, the obtained MT sounding curve was not ideal. In particular, the phase between the periods of 20 and 400 sec was close to 0 degrees. It suggests that the method used is insufficient to reduce the near-field effect for the Boso data. Thus, we developed a new noise reduction method using MSSA (Multi-channel Singular Spectrum Analysis) as a pre-processing method in time domain.&lt;/p&gt;&lt;p&gt;The procedure is as follows;&lt;/p&gt;&lt;p&gt;(1) Decompose 6 component data (Hx, Hy, Ex, Ey, Hxr and Hyr: H and E means magnetic and electric field, respectively, x and y indicates NS and EW component, and r denotes the reference field observed at a quiet station) using MSSA into 6&amp;#215;M principal components (PCs). &amp;#160;Here, M shows the window length of MSSA.&lt;/p&gt;&lt;p&gt;(2) Check contribution and periods of each PC and eliminate the PCs which are corresponding to the longer periods of variation. That is &amp;#8220;detrend&amp;#8221; of the original data.&lt;/p&gt;&lt;p&gt;(3) Apply the second MSSA to the detrended time series data to separate signals and noises shorter than 400 sec.&lt;/p&gt;&lt;p&gt;(4) Calculating correlation coefficients between H and Hr and between E and Hr for each PC and select the PCs with higher correlation to reconstruct time series data to make MT analysis.&lt;/p&gt;&lt;p&gt;Then, we perform MT analysis by BIRRP to estimate apparent resistivity,&lt;/p&gt;&lt;p&gt;As a result, the coherences of H-Hr, and E-Hr were improved and the MT sounding curve became smoother than those results by the conventional noise reduction methods. This indicated that the effectiveness of the proposed noise reduction. However, further investigation in different periods and sites will be required.&lt;/p&gt;

scholarly journals Improved singular spectrum analysis for time series with missing data

2015 ◽  
Vol 22 (4) ◽  
pp. 371-376 ◽  
Author(s):  
Y. Shen ◽  
F. Peng ◽  
B. Li
Keyword(s):  
Time Series ◽  
Missing Data ◽  
San Francisco ◽  
Principal Components ◽  
Spectrum Analysis ◽  
Time Series Data ◽  
Singular Spectrum Analysis ◽  
Series Data ◽  
Singular Spectrum ◽  
Relative Errors

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.

scholarly journals The Decomposition and Forecasting of Mutual Investment Funds Using Singular Spectrum Analysis

Entropy ◽  
2020 ◽  
Vol 22 (1) ◽  
pp. 83 ◽  
Author(s):  
Paulo Canas Rodrigues ◽  
Jonatha Pimentel ◽  
Patrick Messala ◽  
Mohammad Kazemi
Keyword(s):  
Time Series ◽  
Spectrum Analysis ◽  
Time Series Data ◽  
Singular Spectrum Analysis ◽  
Model Fit ◽  
Series Data ◽  
Computational Time ◽  
Investment Funds ◽  
Singular Spectrum ◽  
Non Parametric

Singular spectrum analysis (SSA) is a non-parametric method that breaks down a time series into a set of components that can be interpreted and grouped as trend, periodicity, and noise, emphasizing the separability of the underlying components and separate periodicities that occur at different time scales. The original time series can be recovered by summing all components. However, only the components associated to the signal should be considered for the reconstruction of the noise-free time series and to conduct forecasts. When the time series data has the presence of outliers, SSA and other classic parametric and non-parametric methods might result in misleading conclusions and robust methodologies should be used. In this paper we consider the use of two robust SSA algorithms for model fit and one for model forecasting. The classic SSA model, the robust SSA alternatives, and the autoregressive integrated moving average (ARIMA) model are compared in terms of computational time and accuracy for model fit and model forecast, using a simulation example and time series data from the quotas and returns of six mutual investment funds. When outliers are present in the data, the simulation study shows that the robust SSA algorithms outperform the classical ARIMA and SSA models.

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.

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