scholarly journals Automatic Grouping in Singular Spectrum Analysis

Forecasting ◽  
2019 ◽  
Vol 1 (1) ◽  
pp. 189-204 ◽  
Author(s):  
Mahdi Kalantari ◽  
Hossein Hassani
Keyword(s):  
Time Series ◽  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Filtering Method ◽  
Singular Spectrum ◽  
Validation Criterion ◽  
Matrix Norms ◽  
Automatic Grouping ◽  
Simulated Time ◽  
Simulated Time Series

Singular spectrum analysis (SSA) is a non-parametric forecasting and filtering method that has many applications in a variety of fields such as signal processing, economics and time series analysis. One of the four steps of the SSA, which is called the grouping step, plays a pivotal role in the SSA because reconstruction and forecasting of results are directly affected by the outputs of this step. Usually, the grouping step of SSA is time consuming as the interpretable components are manually selected. An alternative more optimized approach is to apply automatic grouping methods. In this paper, a new dissimilarity measure between two components of a time series that is based on various matrix norms is first proposed. Then, using the new dissimilarity matrices, the capabilities of different hierarchical clustering linkages are compared to identify appropriate groups in the SSA grouping step. The performance of the proposed approach is assessed using the corrected Rand index as validation criterion and utilizing various real-world and simulated time series.

Singular Spectrum Analysis Based on L1-Norm

2016 ◽  
Vol 15 (01) ◽  
pp. 1650009 ◽  
Author(s):  
Mahdi Kalantari ◽  
Masoud Yarmohammadi ◽  
Hossein Hassani
Keyword(s):  
Time Series ◽  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Frobenius Norm ◽  
L1 Norm ◽  
Empirical Results ◽  
Singular Spectrum ◽  
Simulated Time ◽  
Simulated Time Series ◽  
Basic Version

In recent years, the singular spectrum analysis (SSA) technique has been further developed and increasingly applied to solve many practical problems. The aim of this research is to introduce a new version of SSA based on [Formula: see text]-norm. The performance of the proposed approach is assessed by applying it to various real and simulated time series, especially with outliers. The results are compared with those obtained using the basic version of SSA which is based on the Frobenius norm or [Formula: see text]-norm. Different criteria are also examined including reconstruction errors and forecasting performances. The theoretical and empirical results confirm that SSA based on [Formula: see text]-norm can provide better reconstruction and forecasts in comparison to basic SSA when faced with time series which are polluted by outliers.

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.

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.

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.

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