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.

scholarly journals Window Length Selection of Singular Spectrum Analysis and Application to Precipitation Time Series

2017 ◽  
Vol 19 (2) ◽  
pp. 306-317 ◽  
Keyword(s):  
Time Series ◽  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Precipitation Data ◽  
Window Length ◽  
Analysis Method ◽  
Precipitation Time Series ◽  
Singular Spectrum ◽  
Periodogram Analysis ◽  
Selection Of

Window length is a very critical tuning parameter in Singular Spectrum Analysis (SSA) technique. For finding the optimal value of window length in SSA application, Periodogram analysis method with SSA for referencing on the selection of window length and confirm that the periodogram analysis can provide a good option for window length selection in the application of SSA. Several potential periods of Florida precipitation data are firstly obtained using periodogram analysis method. The SSA technique is applied to precipitation data with different window length as the period and experiential recommendation to extract the precipitation time series, which determines the leading components for reconstructing the precipitation and forecast respectively. A regressive model linear recurrent formula (LRF) model is used to discover physically evolution with the SSA modes of precipitation variability. Precipitation forecasts are deduced from SSA patterns and compared with observed precipitation. Comparison of forecasting results with observed precipitation indicates that the forecasts with window length of L=60 have the better performance among all. Our findings successfully confirm that the periodogram analysis can provide a good option for window length selection in the application of SSA and presents a detailed physical explanation on the varying conditions of precipitation variables.

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 PERAMALAN BEBAN LISTRIK DAERAH ISTIMEWA YOGYAKARTA DENGAN METODE SINGULAR SPECTRUM ANALYSIS (SSA)

2019 ◽  
Vol 12 (2) ◽  
pp. 214
Author(s):  
Herni Utami ◽  
Yunita Wulan Sari ◽  
Subanar Subanar ◽  
Abdurakhman Abdurakhman ◽  
Gunardi Gunardi
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Electricity Demand ◽  
Signal Extraction ◽  
Forecasting Model ◽  
Window Length ◽  
Singular Spectral Analysis ◽  
Singular Spectrum

This paper will study forecasting model for electricity demand in Yogyakarta and forecast it for 2019 until 2024. Usually, electricity demand data contain seasonal. We propose Singular Spectral Analysis-Linear Recurrent Formula (SSA-LRF) method. The SSA process consists of decomposing a time series for signal extraction and then reconstructing a less noisy series which is used for forecasting. The SSA-LRF method will be used to forecast h-step ahead. In this study, we use monthly electricity demand in Yogyakarta for 11 year (2008 to 2018). The forecasting results indicates that the forecast using window length of L=26 have good performance with MAPE of 1.9%.

Akurasi Peramalan Long Horizon dengan Singular Spectrum Analysis

2019 ◽  
Vol 3 (2) ◽  
pp. 93-99
Author(s):  
Awit Marwati Sakinah
Keyword(s):  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Window Length ◽  
Singular Spectrum

Perubahan iklim akhir-akhir ini tidak dapat dihindari. Salah satu penyebab perubahan iklim adalah perubahan suhu udara. Untuk itu, perlu dilakukan peramalan suhu agar penyimpangannya dapat diantisipasi. Dalam penelitian ini akan dibandingkan akurasi hasil peramalan dengan menggunakan model Singular Spectrum Analysis (SSA) dengan R-forecasting dan V-Forecasting. Peramalan dengan metode SSA R-forecasting dan V-Forecasting pada suhu Jakarta menggunakan window length L= 204 dan r=3 menghasilkan ramalan yang tidak jauh berbeda (aproksimasi kekontinuannya hampir sama). Berdasarkan hasil analisis, didapat MAPE untuk hasil permalan dengan SSA R-forecasting sebesar 5,0029 yang lebih besar dari MAPE SSA V-Forecasting sebesar 4,0067. Ini munjukkan bahwa peramalan suhu untuk long horizon lebih akurat dengan menggunakan V-Forecasting dibandingkan dengan R-Forecasting.

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.

Separability and window length in singular spectrum analysis

2011 ◽  
Vol 349 (17-18) ◽  
pp. 987-990 ◽  
Author(s):  
Hossein Hassani ◽  
Rahim Mahmoudvand ◽  
Mohammad Zokaei
Keyword(s):  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Window Length ◽  
Singular Spectrum

Selection of window length for singular spectrum analysis

2015 ◽  
Vol 352 (4) ◽  
pp. 1541-1560 ◽  
Author(s):  
Rui Wang ◽  
Hong-Guang Ma ◽  
Guo-Qing Liu ◽  
Dong-Guang Zuo
Keyword(s):  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Window Length ◽  
Singular Spectrum ◽  
Selection Of

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.

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