Singular Spectrum Analysis: Methodology and Comparison

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.

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.

Singular spectrum analysis and forecasting of hydrological time series

SUMMARY The techniques of time series analysis are presented in this paper and are applied to certain non-stationary water pollution data, in a meaningful way, to obtain a more effective analysis of such data. The analysis results in models which may be used for forecasting and the sample spectra which describe the underlying processes which generated the data. The use of the results can be of great value in the understanding and in management aspects of our environmental problems. It is becoming ever more apparent that there must be more effective analysis and interpretation of water pollution data in order to be able to attain water quality. The development of more sophisticated measuring devices and techniques which will continuously record several variables of interest (for example, dissolved oxygen (DO), biochemical oxygen demand (BOD), sunlight intensity, and temperature), requires the use of dataanalysis techniques to obtain a more fundamental understanding of the processes which generated these data. By applying the techniques of time series analysis, maximum results are possible. The ultimate objective of time series analysis is the estimation and reconstruction of the underlying generating process from a given time series. From this analysis possible laws may be discovered or indicated that the variables may obey, and thus allow future values of the variables to be forecasted. Hence time series analysis affords us a way to gain maximum results from the pollution variables and thus can aid in the understanding and management of water quality. In this paper we shall make use of the techniques of time series analysis to analyze certain dissolved oxygen water quality data. The dissolved oxygen concentration which exists in a stream while it is receiving an organic waste load is the variable by which the waste assimilation capacity of a stream is measured. The dissolved oxygen data used in this analysis were originally presented by Thomann [1967] and were continuously recorded by monitoring stations situated along the Delaware Estuary. Thomann used the technique of Fourier analysis to analyze these DO data, but this approach requires the assumption of fixed amplitudes, frequencies, and phases, and breaks

Singular spectrum analysis (SSA) is a nonparametric method for separating time series data into a sum of small numbers of interpretable components (signal + noise). One of the steps of the SSA method, which is referenced to Embedding, is extremely sensitive to contamination of outliers which are often founded in time series analysis. To reduce the effect of outliers, SSA based on Singular Spectrum Decomposition (SSD) method is proposed. In this article, the ability of SSA based on SSD and basic SSA are compared in time series reconstruction in the presence of outliers. It is noteworthy that the matrix norm used in Basic SSA is the Frobenius norm or L 2-norm. There is a newer version of SSA that is based on L 1-norm and called L 1-SSA. It was confirmed that L 1-SSA is robust against outliers. In this regard, this research is also introduced a new version of SSD based on L 1-norm which is called L 1-SSD. A wide empirical study on both simulated and real data verifies the efficiency of basic SSA based on SSD and L 1-norm in reconstructing the time series where polluted by outliers.

Tissues exhibiting quasi-periodic structures are modeled as a collection of diffuse and coherent scatterers. Coherent components are quantified by mean scatterer spacing (MSS) and are closely related to tissue structure. MSS is a quantitative ultrasound parameter useful for characterizing quasi-periodic tissues and must be determined accurately. The study aims at determining the impact of correlation level (CL) of eigenvectors on MSS estimated by Singular Spectrum Analysis (SSA), compared to other spectral methods, of a periodic distribution of scatterers using backscattered ultrasound signals. Five transducers (1, 2.25, 3.5, 5 and 7.5 MHz) were used on a pulse-echo configuration. Transducers were moved parallel to the phantoms (matrix of cylindrical copper bars) to collect signals for processing with the spectral autocorrelation, SSA and quadratic transformation for MSS estimation. The sensitivity of the SSA was analyzed for CL values of 0.5, 0.6, 0.7 and 0.8. It was evidenced that as the level of correlation decreases, the sensitivity of the methods decreases. The extreme sensitivity values of the SSA technique are 0.05 (CL =0.8,7.5 MHz) and 5.5 (CL =0.5,1 MHz). For these extreme values, the MSS estimation error was 0.8% and 18% respectively, for the SSA technique.

A Novel approach for predicting monthly water demand by combining singular spectrum analysis with neural networks

Smart factories and big data are important factors in the Fourth Industrial Revolution. Smart factories aim for automation and integration; however, the most important part is the application of data. Despite extensive research on the maintenance and quality management of big data-based production equipment, industrial data gathered for analysis contain more normal data than abnormal data. In addition, a significant amount of energy is expended in the data pre-processing process to analyze the acquired data. Therefore, to maintain production equipment and quality management, data classification technology that allows easy data analysis by classifying abnormal data into normal data is required. In this paper, we propose an abnormal data classification architecture for cycle data sets gathered from production facilities through SSA-CAE along with data storage methods for each product unit. SSA-CAE is a hybrid technique that combines singular spectrum analysis (SSA) techniques that are effective in reducing noise in time series data with convolutional auto encoder (CAE) that have performed well in time series.

This article presents a comprehensive study of sales predictions using time series analysis, focusing on a case study of Walmart sales data. The aim of this study is to evaluate the effectiveness of various time series forecasting techniques in predicting weekly sales data for Walmart stores. Leveraging a dataset from Kaggle comprising weekly sales data from various Walmart stores around the United States, this study explores the effectiveness of time series analysis in forecasting future sales trends. Various time series analysis techniques, including Auto Regressive Integrated Moving Average (ARIMA), Seasonal Auto Regressive Integrated Moving Average (SARIMA), Prophet, Exponential Smoothing, and Gaussian Processes, are applied to model and forecast Walmart sales data. By comparing the performance of these models, the study seeks to identify the most accurate and reliable methods for forecasting retail sales, thereby providing valuable insights for improving sales predictions in the retail sector. The study includes an extensive exploratory data analysis (EDA) phase to preprocess the data, detect outliers, and visualize sales trends over time. Additionally, the article discusses the partitioning of data into training and testing sets for model evaluation. Performance metrics such as Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) are utilized to compare the accuracy of different time series models. The results indicate that Gaussian Processes outperform other models in terms of accuracy, with an RMSE of 34,116.09 and an MAE of 25,495.72, significantly lower than the other models evaluated. For comparison, ARIMA and SARIMA models both yielded an RMSE of 555,502.2 and an MAE of 462,767.3, while the Prophet model showed an RMSE of 567,509.2 and an MAE of 474,990.8. Exponential Smoothing also performed well with an RMSE of 555,081.7 and an MAE of 464,110.5. These findings suggest the potential of Gaussian Processes for accurate sales forecasting. However, the study also highlights the strengths and weaknesses of each forecasting methodology, emphasizing the need for further research to refine existing techniques and explore novel modeling approaches. Overall, this study contributes to the understanding of time series analysis in retail sales forecasting and provides insights for improving future forecasting endeavors.

Indonesia is a country with a population that still uses the agricultural sector as the highest livelihood. The Central Statistics Agency said 38.61% were in this sector. However, the issue of climate change caused by an increase in global temperature has begun to impact the agricultural sector in several regions. Therefore, this study aims to understand the effect of increasing surface temperature anomaly on the Oldeman climate pattern in Dumai City. The data used are in-situ observation rainfall data for 1981 - 2010, rainfall reanalysis data for 1991 - 2020, surface temperature anomaly data for 1991 - 2020. The data validation methods used are spearman correlation and Kendall-tau methods. The approach to explore changes in the Oldeman climate pattern uses time series analysis techniques such as ACF, PACF, and moving average of 1 year lag-time with a period of 10 years. The rainfall data validation test result show that the average spatial correlation value is 0.86. It can be used to explore time-series climate data in 3 locations in Dumai. As a result, time series analysis found a positive trend in rainfall data significantly along with the temperature anomaly but the Oldeman's climate pattern analysis in Dumai is monitored as stable in type B1. Overall, it is concluded that the change in the surface temperature anomaly variability and trend as a manifestation of climate change in Dumai has not impacted in the Oldeman agricultural climate patterns. Keywords: Climate Change, Oldeman, Time Series, Rainfall, Temperature

This study investigates radio signal propagation at 5.8 GHz in an underground parking garage for vehicle-to-infrastructure (V2I) communication, a widespread scenario present in urban centers.Broadband measurements were conducted using orthogonal frequencydivision multiplexing (OFDM), enabling the characterization of the radio channel in terms of path loss (PL) and temporal dispersion.The power delay profile (PDP) was obtained via inverse Fourier transform of the channel impulse response (CIR).Multipath components were identified and compared using the constant false alarm rate (CFAR) and singular spectrum analysis (SSA) techniques.The results showed that the SSA technique is effective for multipath component identification.

In the paper the algorithm of singular structural analysis and forecasting of a multidimensional series by the MSSA method is used. The program was developed, in which the steps of the method for the selection of singular decomposition components were implemented, the analysis and forecast of real time series was carried out. Singular spectrum analysis (SSA) is increasingly used in the study of time series. Unlike other methods of statistical research of time series, this method is used to study the structure, selection of individual components and forecast of both stationary and non-stationary time series. It does not require an analytical model of the series. In fact, this approach is based on the method of principal components. It is based on the transformation of a series into a matrix and its singular decomposition. After identifying the components of the singular decomposition, their grouping takes place, which leads to the decomposition of the original series into additive components, such as trend, oscillations (periodics), and noise. The SSA method allows you to continue the structure of the time series, thus building a forecast (continuation). An important direction of the development of the SSA method as a method of time series analysis is its generalization for the analysis of multidimensional time series. The method is known as MSSA (Multi-Channel SSA) or E-EOFs (Extended Empirical Orthogonal Functions). In this case, the expected result is the simultaneous decomposition of several series into interpreted components. However, a sufficiently complete theory for MSSA does not exist.

On statistical inference in time series analysis of the evolution of road safety

Singular spectrum analysis (SSA) is a nonparametric spectral estimation method that decomposes time series signals into interpretable components. With the rise of big time series, the demand for effective and scalable SSA techniques has become increasingly urgent. In this paper, we propose a novel multiway extension of SSA, called higher-order multivariate SSA (HO-MSSA), specifically designed for multivariate and multichannel time series signal analysis via tensor decomposition. HO-MSSA utilizes time-delay embedding and tensor singular value decomposition to transform multichannel time series signals into trajectory tensors, which are then decomposed into elementary components in the Fourier domain, rather than the time domain as in traditional SSA methods. These components are grouped into disjoint subsets using spectral clustering, enabling the reconstruction of the underlying source signals. Experimental results demonstrate that HO-MSSA outperforms state-of-the-art SSA methods in various biomedical applications, including electromyography (EMG), electrocardiography (ECG), and electroencephalogram (EEG) signals. • A novel tensor-based multivariate singular spectrum analysis is introduced. • A new time embedding technique embeds time series into a higher dimension. • Tensor SVD is used to factorize the trajectory tensor of time series. • Spectral clustering detects and groups the underlying time series components.

Time series analysis of lava flux