Singular Spectrum Analysis Approach Research Articles

Evidence of short-term groundwater recharge signal propagation from the Andes to the central Atacama Desert: a singular spectrum analysis approach

ABSTRACTThe effect of pressure-driven groundwater recharge signal propagation in the Andean-Atacamenian environment is investigated by assessing a record of 15 years of water table fluctuations of an unconfined–confined aquifer system. Based on a singular spectrum analysis of water table time series, it is shown that, in the given case, groundwater levels in the central Atacama Desert are hydraulically controlled by two distant recharge areas associated with the Andes. The maximum observed range of the pressure signal propagation is ~50 km over an elevation difference of more than 3000 m at a lag of ~25 months. Several findings indicate that an often-cited study misinterpreted a water level rise at the same site as an in-situ alluvial fan recharge. Thus, the effect’s impact on groundwater dynamics in complex aquifer systems can easily be overlooked. Singular spectrum analysis could be of use to investigate pressure effects at hydrologically comparable sites.

Modeling European industrial production with multivariate singular spectrum analysis: A cross‐industry analysis

In this paper, an optimized multivariate singular spectrum analysis (MSSA) approach is proposed to find leading indicators of cross‐industry relations between 24 monthly, seasonally unadjusted industrial production (IP) series for German, French, and UK economies. Both recurrent and vector forecasting algorithms of horizontal MSSA (HMSSA) are considered. The results from the proposed multivariate approach are compared with those obtained via the optimized univariate singular spectrum analysis (SSA) forecasting algorithm to determine the statistical significance of each outcome. The data are rigorously tested for normality, seasonal unit root hypothesis, and structural breaks. The results are presented such that users can not only identify the most appropriate model based on the aim of the analysis, but also easily identify the leading indicators for each IP variable in each country. Our findings show that, for all three countries, forecasts from the proposed MSSA algorithm outperform the optimized SSA algorithm in over 70% of cases. Accordingly, this new approach succeeds in identifying leading indicators and is a viable option for selecting the SSA choices L and r, which minimizes a loss function.

River flow prediction using hybrid models of support vector regression with the wavelet transform, singular spectrum analysis and chaotic approach

Prediction of water amount that will enter the reservoirs in the following month is of vital importance especially for semi-arid countries like Turkey. Climate projections emphasize that water scarcity will be one of the serious problems in the future. This study presents a methodology for predicting river flow for the subsequent month based on the time series of observed monthly river flow with hybrid models of support vector regression (SVR). Monthly river flow over the period 1940–2012 observed for the Kizilirmak River in Turkey has been used for training the method, which then has been applied for predictions over a period of 3 years. SVR is a specific implementation of support vector machines (SVMs), which transforms the observed input data time series into a high-dimensional feature space (input matrix) by way of a kernel function and performs a linear regression in this space. SVR requires a special input matrix. The input matrix was produced by wavelet transforms (WT), singular spectrum analysis (SSA), and a chaotic approach (CA) applied to the input time series. WT convolutes the original time series into a series of wavelets, and SSA decomposes the time series into a trend, an oscillatory and a noise component by singular value decomposition. CA uses a phase space formed by trajectories, which represent the dynamics producing the time series. These three methods for producing the input matrix for the SVR proved successful, while the SVR-WT combination resulted in the highest coefficient of determination and the lowest mean absolute error.

A simple SSA-based de-noising technique to remove ECG interference in EMG signals

Abstract Electromyography (EMG) signals provide significant information of muscle activity that may be used, among others, to estimate the activation stages during a certain activity or to predict fatigue. Heart activity or electrocardiogram (ECG) is one of the main contamination sources, especially in trunk muscles. This paper proposes a novel method based on Singular Spectrum Analysis (SSA) and frequency analysis to separate both signals present in the raw data. The performance of the method has been compared in time and frequency domains with traditional high-pass filtering or novel techniques such as Complete Ensemble Empirical Mode Decomposition or Wavelets analysis. The results show that for both time and frequency domains the proposed approach outperforms the other methods. Thus, the proposed SSA approach is a valid method to remove the ECG artifact from the contaminated EMG signals without using an ECG reference signal.

Electricity consumption forecasting using singular spectrum analysis

Singular Spectrum Analysis (SSA) is a non-parametric technique that allows the decomposition of a time series into signal and noise. Thus, it is a useful technique to trend extraction, smooth and filter a time series. The effect on performance of both Box and Jenkins' and Holt-Winters models when applied to the time series filtered by SSA is investigated in this paper. Three different methodologies are evaluated in the SSA approach: Principal Component Analysis (PCA), Cluster Analysis and Graphical Analysis of Singular Vectors. In order to illustrate and compare the methodologies, in this paper, we also present the main results of a computational experiment with the monthly residential consumption of electricity in Brazil.

Investigation of the noise effect on fractal dimension of EEG in schizophrenia patients using wavelet and SSA-based approaches

ObjectivesComplexity measures have been enormously used in schizophrenia patients to estimate brain dynamics. However, the conflicting results in terms of both increased and reduced complexity values have been reported in these studies depending on the patients’ clinical status or symptom severity or medication and age status. The objective of this study is to investigate the nonlinear brain dynamics of chronic, medicated schizophrenia patients and healthy control subjects using Katz's fractal dimension (FD). Moreover, in order to determine noise effect on complexity of EEG data, a noise elimination method based on wavelet and singular spectrum analysis (SSA) were assessed. MethodsTwenty-two schizophrenia patients and twenty-two age- and gender-matched control subjects underwent a resting state EEG examination with 120s. The discrete wavelet transform (DWT) was applied for EEG decomposition. Using a SSA approach, noise was removed and EEG reconstructed by inverse wavelet transform. The brain complexity of participants was investigated and compared using Katz's FD obtained from original and preprocessed EEG data. ResultsLower complexity values were found in schizophrenia patients. However, this difference was only statistically significant for each channel in preprocessed, noiseless EEG data. The most significant complexity differences between patients and controls were obtained in left frontal and parietal regions of the brain. ConclusionOur findings demonstrate that the utilizing of complexity measures with preprocessing approaches on EEG data to analyze schizophrenics’ brain dynamics might be a useful and discriminative tool for diagnostic purposes. Therefore, we expect that nonlinear analysis will give us more valuable results for understanding of schizophrenics’ brain.

Singular Spectrum Analysis for Effective Feature Extraction in Hyperspectral Imaging

As a very recent technique for time-series analysis, singular spectrum analysis (SSA) has been applied in many diverse areas, where an original 1-D signal can be decomposed into a sum of components, including varying trends, oscillations, and noise. Considering pixel-based spectral profiles as 1-D signals, in this letter, SSA has been applied in hyperspectral imaging for effective feature extraction. By removing noisy components in extracting the features, the discriminating ability of the features has been much improved. Experiments show that this SSA approach supersedes the empirical mode decomposition technique from which our work was originally inspired, where improved results in effective data classification using support vector machine are also reported.

Forecasting U.S. Tourist arrivals using optimal Singular Spectrum Analysis

This study examines the potential advantages of using Singular Spectrum Analysis (SSA) for forecasting tourism demand. To do this it examines the performance of SSA forecasts using monthly data for tourist arrivals into the Unites States over the period 1996 to 2012. The SSA forecasts are compared to those from a range of other forecasting approaches previously used to forecast tourism demand. These include ARIMA, exponential smoothing and neural networks. The results presented show that the SSA approach produces forecasts which perform (statistically) significantly better than the alternative methods in forecasting total tourist arrivals into the U.S. Forecasts using the SSA approach are also shown to offer a significantly better forecasting performance for arrivals into the U.S. from individual source countries. Of the alternative forecasting approaches exponential smoothing and feed-forward neural networks in particular were found to perform poorly. The key conclusion is that Singular Spectrum Analysis (SSA) offers significant advantages in forecasting tourist arrivals into the US and is worthy of consideration for other forecasting studies of tourism demand.

Day‐ahead electricity price analysis and forecasting by singular spectrum analysis

This study proposes a model-free approach for day-ahead electricity price forecasting. The proposed approached is based on the singular spectrum analysis (SSA) technique. The SSA is a relatively new and powerful technique in time series analysis and forecasting thanks to its well-known capabilities in extracting the main structure of the broad classes of the time series. In this study, it is shown that SSA can be employed to decompose the original electricity price series into trend, periodic and noisy components. The main part of the price series, that is, the trend and harmonic components, is reconstructed by removing the noise component from the original series. The reconstructed price series is then used for forecasting the day-ahead electricity prices. The proposed approach is evaluated by analysing and forecasting of the day-ahead electricity prices in the Australian and Spanish electricity markets. The forecasting results confirm the superiority of the SSA approach compared with some of the recently published forecasting techniques.

Signal Extraction and Forecasting of the UK Tourism Income Time Series: A Singular Spectrum Analysis Approach

ABSTRACTWe present and apply singular spectrum analysis (SSA), a relatively new, non‐parametric and data‐driven method for signal extraction (trends, seasonal and business cycle components) and forecasting of UK tourism income. Our results show that SSA slightly outperforms SARIMA and time‐varying‐parameter state space models in terms of root mean square error, mean absolute error and mean absolute percentage error forecasting criteria. Copyright © 2011 John Wiley & Sons, Ltd.

Application of Singular Spectrum Analysis to the Noise Reduction of Intrusion Detection Alarms

Intrusion detection systems typically create a large volume of alarms and most of them are false alarms that can be seen as background noises caused by normal system behaviors. Manual analysis of a large number of alarms is both time consuming and labor intensive. This study focuses on the statistical analysis of the alarm flow. Using the Singular Spectrum Analysis (SSA) approach, we found that the alarm flow has a small intrinsic dimension, and the structure of alarm flow can be composed by leading components (normal components) and residual components (abnormal components). Only changes in abnormal components are worth of further study to confirm whether they are true or false alarm. To achieve this goal, an SSA-based anomalies detection algorithm was implemented and applied to catch anomalous changes in residua components, and thus interesting alarms were highlighted and noises were filtered out. Compared with detection approaches using stationary models, our SSA-based method can well deal with the non-stationary natures inherent in the alarm flow. Evaluation results from real network data show a significant increase in model accuracy, and more efficient filtering of alarm noise.

An adaptive singular spectrum analysis approach to murmur detection from heart sounds

Murmur is the result of various heart abnormalities. A new robust approach for separation of murmur from heart sound has been suggested in this article. Singular spectrum analysis (SSA) has been adapted to the changes in the statistical properties of the data and effectively used for detection of murmur from single-channel heart sound (HS) signals. Incorporating a cleverly selected a priori within the SSA reconstruction process, results in an accurate separation of normal HS from the murmur segment. Another contribution of this work is selection of the correct subspace of the desired signal component automatically. In addition, the subspace size can be identified iteratively. A number of HS signals with murmur have been processed using the proposed adaptive SSA (ASSA) technique and the results have been quantified both objectively and subjectively.

Trend forecasting based on Singular Spectrum Analysis of traffic workload in a large-scale wireless LAN

Network traffic load in an IEEE802.11 infrastructure arises from the superposition of traffic accessed by wireless clients associated with access points (APs). An accurate load characterization can be beneficial in modeling network traffic and addressing a variety of problems including coverage planning, resource reservation and network monitoring for anomaly detection. This study focuses on the statistical analysis of the traffic load measured in a campus-wide IEEE802.11 infrastructure at each AP. Using the Singular Spectrum Analysis approach, we found that the time-series of traffic load at a given AP has a small intrinsic dimension. In particular, these time-series can be accurately modeled using a small number of leading (principal) components. This proved to be critical for understanding the main features of the components forming the network traffic. Statistical analysis of leading components has demonstrated that even a few first components form the main part of the information. The residual components capture the small irregular variations, which do not fit in the basic part of the network traffic and can be interpreted as a stochastic noise. Based on these properties, we also studied contributions of the various components to the overall structure of the traffic load of an AP and its variation over time. Finally, we designed and evaluated the performance of a traffic predictor for the trend component, obtained by projecting the original time-series on the set of leading components.

Timescale effect estimation in time-series studies of air pollution and health: A Singular Spectrum Analysis approach

A wealth of epidemiological data suggests an association between mortality/morbidity from pulmonary and cardiovascular adverse events and air pollution, but uncertainty remains as to the extent implied by those associations although the abundance of the data. In this paper we describe an SSA (Singular Spectrum Analysis) based approach in order to decompose the time-series of particulate matter concentration into a set of exposure variables, each one representing a different timescale. We implement our methodology to investigate both acute and long-term effects of $PM_{10}$ exposure on morbidity from respiratory causes within the urban area of Bari, Italy.