A Preliminary Investigation into the Effect of Outlier(s) on Singular Spectrum Analysis

2014 ◽  
Vol 13 (04) ◽  
pp. 1450029 ◽  
Author(s):  
Hossein Hassani ◽  
Rahim Mahmoudvand ◽  
Hardi Nabe Omer ◽  
Emmanuel Sirimal Silva
Keyword(s):  
Spectrum Analysis ◽  
Preliminary Investigation ◽  
Singular Spectrum Analysis ◽  
Real Data ◽  
Data Sets ◽  
Singular Spectrum ◽  
The Matrix ◽  
Points Of View ◽  
Different Parts

The aim of this paper is to study the effect of outliers on different parts of singular spectrum analysis (SSA) from both theoretical and practical points of view. The rank of the trajectory matrix, the magnitude of eigenvalues, reconstruction, and forecasting results are evaluated using simulated and real data sets. The performance of both recurrent and vector forecasting procedures are assessed in the presence of outliers. We find that the existence of outliers affect the rank of the matrix and increases the linear recurrent dimensions whilst also having a significant impact on SSA reconstruction and forecasting processes. There is also evidence to suggest that in the presence of outliers, the vector SSA forecasts are more robust in comparison to the recurrent SSA forecasts. These results indicate that the identification and removal of the outliers are mandatory to achieve optimal SSA decomposition and forecasting results.

scholarly journals Predicting COVID-19 Pandemic in Saudi Arabia Using Modified Singular Spectrum Analysis

2020 ◽  
Author(s):  
Nader Alharbi
Keyword(s):  
Saudi Arabia ◽  
Noise Reduction ◽  
Spectrum Analysis ◽  
Signal To Noise Ratio ◽  
Singular Spectrum Analysis ◽  
Real Data ◽  
Signal Extraction ◽  
Signal To Noise ◽  
Singular Spectrum ◽  
Data Points

Abstract This research presents a modified Singular Spectrum Analysis (SSA) approach for the analysis of COVID-19 in Saudi Arabia. We have proposed this approach and developed it in [1–3] for separability and grouping step in SSA, which plays an important role for reconstruction and forecasting in the SSA. The modified SSA mainly enables us to identify the number of the interpretable components required for separability, signal extraction and noise reduction. The approach was examined using different number of simulated and real data with different structures and signal to noise ratio. In this study we examine its capability in analysing COVID-19 data. Then, we use Vector SSA for predicting new data points and the peak of this pandemic. The results shows that the approach can be used as a promising one in decomposing and forecasting the daily cases of COVID-19 in Saudi Arabia.

Adaptive singular spectrum analysis for seismic denoising and interpolation

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. V133-V142 ◽  
Author(s):  
Hojjat Haghshenas Lari ◽  
Mostafa Naghizadeh ◽  
Mauricio D. Sacchi ◽  
Ali Gholami
Keyword(s):  
Spectrum Analysis ◽  
Seismic Data ◽  
Singular Spectrum Analysis ◽  
Computational Cost ◽  
Hankel Matrix ◽  
Real Data ◽  
Singular Spectrum ◽  
Value Decomposition ◽  
Spatially Varying ◽  
Spatial Patches

We have developed an adaptive singular spectrum analysis (ASSA) method for seismic data denoising and interpolation purposes. Our algorithm iteratively updates the singular-value decomposition (SVD) of current spatial patches using the most recently added spatial sample. The method reduces the computational cost of classic singular spectrum analysis (SSA) by requiring QR decompositions on smaller matrices rather than the factorization of the entire Hankel matrix of the data. A comparison between results obtained by the ASSA and SSA methods, in which the SVD applies to all of the traces at once, proves that the ASSA method is a valid way to cope with spatially varying dips. In addition, a comparison of the ASSA method with the windowed SSA method indicates gains in efficiency and accuracy. Synthetic and real data examples illustrate the effectiveness of our method.

Signal extraction using randomized-order multichannel singular spectrum analysis

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. V69-V84 ◽  
Author(s):  
Weilin Huang ◽  
Runqiu Wang ◽  
Yimin Yuan ◽  
Shuwei Gan ◽  
Yangkang Chen
Keyword(s):  
Spectrum Analysis ◽  
Random Noise ◽  
Singular Spectrum Analysis ◽  
Data Sets ◽  
Noise Attenuation ◽  
Coherent Noise ◽  
Singular Spectrum ◽  
3D Data ◽  
Time Space ◽  
Ground Roll

Multichannel singular spectrum analysis (MSSA) is an effective algorithm for random noise attenuation; however, it cannot be used to suppress coherent noise. This limitation results from the fact that the conventional MSSA method cannot distinguish between useful signals and coherent noise in the singular spectrum. We have developed a randomization operator to disperse the energy of the coherent noise in the time-space domain. Furthermore, we have developed a novel algorithm for the extraction of useful signals, i.e., for simultaneous random and coherent noise attenuation, by introducing a randomization operator into the conventional MSSA algorithm. In this method, which we call randomized-order MSSA, the traces along the trajectory of each signal component are randomly rearranged. Two ways to extract the trajectories of different signal components are investigated. The first is based on picking the extrema of the upper envelopes, a method that is also constrained by local and global gradients. The second is based on dip scanning in local processing windows, also known as the Radon method. The proposed algorithm can be applied in 2D and 3D data sets to extract different coherent signal components or to attenuate ground roll and multiples. Different synthetic and field data examples demonstrate the successful performance of the proposed method.

scholarly journals Predicting COVID-19 Pandemic in Saudi Arabia Using Modified Singular Spectrum Analysis

2020 ◽  
Author(s):  
Nader Alharbi
Keyword(s):  
Saudi Arabia ◽  
Noise Reduction ◽  
Spectrum Analysis ◽  
Signal To Noise Ratio ◽  
Singular Spectrum Analysis ◽  
Real Data ◽  
Signal Extraction ◽  
Signal To Noise ◽  
Singular Spectrum ◽  
Data Points

AbstractThis research presents a modified Singular Spectrum Analysis (SSA) approach for the analysis of COVID-19 in Saudi Arabia. We have proposed this approach and developed it in [1–3] for separability and grouping step in SSA, which plays an important role for reconstruction and forecasting in the SSA. The modified SSA mainly enables us to identify the number of the interpretable components required for separability, signal extraction and noise reduction. The approach was examined using different number of simulated and real data with different structures and signal to noise ratio. In this study we examine its capability in analysing COVID-19 data. Then, we use Vector SSA for predicting new data points and the peak of this pandemic. The results shows that the approach can be used as a promising one in decomposing and forecasting the daily cases of COVID-19 in Saudi Arabia.

scholarly journals Predicting COVID-19 Pandemic in Saudi Arabia Using Modified Singular Spectrum Analysis

2020 ◽  
Author(s):  
Nader Alharbi
Keyword(s):  
Saudi Arabia ◽  
Noise Reduction ◽  
Spectrum Analysis ◽  
Signal To Noise Ratio ◽  
Singular Spectrum Analysis ◽  
Real Data ◽  
Signal Extraction ◽  
Signal To Noise ◽  
Singular Spectrum ◽  
Data Points

Abstract This research presents a modified Singular Spectrum Analysis (SSA) approach for the analysis of COVID-19 in Saudi Arabia. We have proposed this approach and developed it in [1–3] for separability and grouping step in SSA, which plays an important role for reconstruction and forecasting in the SSA. The modified SSA mainly enables us to identify the number of the interpretable components required for separability, signal extraction and noise reduction. The approach was examined using different number of simulated and real data with different structures and signal to noise ratio. In this study we examine its capability in analysing COVID-19 data. Then, we use Vector SSA for predicting new data points and the peak of this pandemic. The results shows that the approach can be used as a promising one in decomposing and forecasting the daily cases of COVID-19 in Saudi Arabia.

scholarly journals Forecasting the COVID-19 Pandemic in Saudi Arabia Using a Modified Singular Spectrum Analysis Approach: Model Development and Data Analysis

JMIRx Med ◽  
10.2196/21044 ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. e21044 ◽  
Author(s):  
Nader Alharbi
Keyword(s):  
Time Series ◽  
Saudi Arabia ◽  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Model Development ◽  
Real Data ◽  
Primary Objective ◽  
Infected People ◽  
Singular Spectrum ◽  
Global Pandemic

Background Infectious disease is one of the main issues that threatens human health worldwide. The 2019 outbreak of the new coronavirus SARS-CoV-2, which causes the disease COVID-19, has become a serious global pandemic. Many attempts have been made to forecast the spread of the disease using various methods, including time series models. Among the attempts to model the pandemic, to the best of our knowledge, no studies have used the singular spectrum analysis (SSA) technique to forecast confirmed cases. Objective The primary objective of this paper is to construct a reliable, robust, and interpretable model for describing, decomposing, and forecasting the number of confirmed cases of COVID-19 and predicting the peak of the pandemic in Saudi Arabia. Methods A modified singular spectrum analysis (SSA) approach was applied for the analysis of the COVID-19 pandemic in Saudi Arabia. We proposed this approach and developed it in our previous studies regarding the separability and grouping steps in SSA, which play important roles in reconstruction and forecasting. The modified SSA approach mainly enables us to identify the number of interpretable components required for separability, signal extraction, and noise reduction. The approach was examined using different levels of simulated and real data with different structures and signal-to-noise ratios. In this study, we examined the capability of the approach to analyze COVID-19 data. We then used vector SSA to predict new data points and the peak of the pandemic in Saudi Arabia. Results In the first stage, the confirmed daily cases on the first 42 days (March 02 to April 12, 2020) were used and analyzed to identify the value of the number of required eigenvalues (r) for separability between noise and signal. After obtaining the value of r, which was 2, and extracting the signals, vector SSA was used to predict and determine the pandemic peak. In the second stage, we updated the data and included 81 daily case values. We used the same window length and number of eigenvalues for reconstruction and forecasting of the points 90 days ahead. The results of both forecasting scenarios indicated that the peak would occur around the end of May or June 2020 and that the crisis would end between the end of June and the middle of August 2020, with a total number of infected people of approximately 330,000. Conclusions Our results confirm the impressive performance of modified SSA in analyzing COVID-19 data and selecting the value of r for identifying the signal subspace from a noisy time series and then making a reliable prediction of daily confirmed cases using the vector SSA method.

scholarly journals Weighted Linear Recurrent Forecasting in Singular Spectrum Analysis

2019 ◽  
Vol 19 (01) ◽  
pp. 2050010
Author(s):  
Mahdi Kalantari ◽  
Hossein Hassani ◽  
Emmanuel Sirimal Silva
Keyword(s):  
Time Series ◽  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Real Data ◽  
Recurrent Relation ◽  
Singular Spectrum ◽  
Viable Solution ◽  
Simulated Time ◽  
Simulated Time Series

Singular Spectrum Analysis (SSA) is an increasingly popular time series filtering and forecasting technique. Owing to its widespread applications in a variety of fields, there is a growing interest towards improving its forecasting capabilities. As such, this paper takes into consideration the Recurrent forecasting approach in SSA (SSA-R) and presents a new mechanism for improving the accuracy of forecasts attainable via this method. The proposed Recurrent SSA-R approach is referred to as Weighted SSA-R (W:SSA-R), and we propose using a weighting algorithm for weigthing the coefficients of the Linear Recurrent Relation (LRR). The performance of forecasts from the W:SSA-R approach are compared with forecasts from the established SSA-R approach. We exploit real data and various simulated time series for the comparison, so as to provide the reader with more conclusive findings. Our results confirm that the W:SSA-R approach can provide comparatively more accurate forecasts and is indeed a viable solution for improving forecasts by SSA.

ON THE SEPARABILITY BETWEEN SIGNAL AND NOISE IN SINGULAR SPECTRUM ANALYSIS

2012 ◽  
Vol 11 (02) ◽  
pp. 1250014 ◽  
Author(s):  
HOSSEIN HASSANI ◽  
RAHIM MAHMOUDVAND ◽  
MOHAMMAD ZOKAEI ◽  
MANSOUREH GHODSI
Keyword(s):  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Real Data ◽  
Point Of View ◽  
Window Length ◽  
Noise Component ◽  
Singular Spectrum ◽  
Optimal Value ◽  
Empirical Point ◽  
Theoretical Results

The optimal value of the window length in singular spectrum analysis (SSA) is considered with respect to the concept of separability between signal and noise component, from the theoretical and practical perspective. The theoretical results confirm that for a wide class of time series of length N, the suitable value of this parameter is median{1, …, N}. The results of both simulated and real data verify the effectiveness of the theoretical results. The theoretical results obtained here coincide with those obtained previously from the empirical point of view.

Computational efficient multidimensional singular spectrum analysis for prestack seismic data reconstruction

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. V111-V119 ◽  
Author(s):  
Jinkun Cheng ◽  
Mauricio Sacchi ◽  
Jianjun Gao
Keyword(s):  
Spectrum Analysis ◽  
Seismic Data ◽  
Singular Spectrum Analysis ◽  
Real Data ◽  
Data Reconstruction ◽  
Hankel Matrices ◽  
Computational Costs ◽  
Singular Spectrum ◽  
Seismic Data Reconstruction ◽  
Memory Efficient

We have evaluated a fast and memory efficient implementation of the multidimensional singular spectrum analysis (MSSA) method for seismic data reconstruction. The new algorithm makes use of random projections and the structure of Hankel matrices to avoid the construction of large Hankel trajectory matrices. Through tests with synthetic and real data examples, we find that the presented algorithm significantly decreases the computational costs of MSSA seismic data recovery without compromising its accuracy.

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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