SINGULAR SPECTRAL ANALYSIS OF TEMPERATURE MULTIDIMENSIONAL TIME SERIES

Singular spectrum analysis (SSA) is relatively new method for analysis of non-stationary time series. The weakness of SSA is lack of analytical model representation of time series, e.g., as a sum of simple functions, which could be clearer and easier for interpretation than a large number of components in form of time series. In this paper we propose to use variative modeling, based on joint use of SSA and method of modeleteka, for obtaining of analytical model of time series, providing necessary level of adequacy, compactness and interpretability. First, time series are decomposed into components using SSA, significant components are selected using formal indicators (e.g. variance contributed by component, etc.). Second, each significant component is identified according to the purpose of identification with simple and interpretable model from preformed modeleteka. The result is final model of time series in additive or additive-multiplicative form. Applicability of the method is shown on synthetic data and time series of daily changes of water turbidity in the river in the city of Chelyabinsk in 2005.

Singular spectrum analysis and forecasting of hydrological time series

Multivariate correlation analysis - a method for the analysis of multidimensional time series in environmental studies

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.

An application of Singular Spectrum Analysis(SSA) Method, based on a new elaborated tensorial approach of computation of singular values and left and right singular vectors of arbitrary non-square matrices, for time series is presented. All necessary calculations of singular values and both types (left and right) singular vectors are performed on the base of elaborated tensorial approach. It is showed that non parametric SSA can be efficiently used as a universal filter to separate Low and High frequencies components in long signals and time series.

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.

The availability of continuous spatiotemporal land surface temperature (LST) with high resolution is critical for many disciplines including hydrology, meteorology, ecology, and geology. Like other remote sensing data, satellite–based LST is also encountered with the cloud issue. In this research, over 5000 daytime and nighttime MODIS–LST images are utilized during 2014–2020 for Yazd–Ardakan plain in Yazd, Iran. The multi–channel singular spectrum analysis (MSSA) model is employed to reconstruct missing values due to dusts, clouds, and sensor defect. The selection of eigenvalues is based on the Monte Carlo test and the spectral analysis of eigenvalues. It is found that enlarging the window size has no effect on the number of significant components of the signal which account for the most variance of the data. However, data variance changes for all the three components. Employing two images per day, window sizes 60, 180, 360, and 720 are examined for reconstructing one year LST, where these selections are based on monthly, seasonal, semi-annual, and annual LST cycles, respectively. The results show that window size 60 had the least computational cost and the highest accuracy with RMSE (root mean square error) of 2.6 °C for the entire study region and 1.4 °C for a selected pixel. The gap–filling performance of MSSA is also compared with the one by the harmonic analysis of time series (HANTS) model, showing the superiority of MSSA with an improved RMSE of about 2.7 °C for the study region. In addition, daytime and nighttime LST series for different land covers are compared. Lastly, the maximum, minimum, and average LST for each day and night as well as average and standard deviation of LST images in the seven-year-long time series are also computed.

Singular Spectrum Analysis (SSA) is a non-parametric and rapidly developing method of time series analysis. Recently, this technique receives much attention in a variety of fields. In SSA, a special matrix that is called lag-covariance matrix plays a pivotal role in analyzing stationary time series. The objective of this paper is to examine whether the Empirical Spectral Distribution (ESD) of lag-covariance matrix converges to Marˇcenko{Pastur distribution or not. Such limiting distribution can help us to provide more reliable statistical inference when encountering with high-dimensional data. Moreover, a simulation study is performed and some tools of Random Matrix Theory (RMT) are used

The article will present the methodology for holistic time series analysis, based on time series transformation model REFII (REFII is an acronym for Raise-Equal-Fall and the model version is II or 2) Patel et al. (Mining motifs in massive time series databases, 2002) [1], Perng and Parker (SQL/LPP: a time series extension of SQL based on limited patience patterns, 1999) [2], Popivanov and Miller (Similarity search over time series data using wavelets, 2002) [3]. The main purpose of REFII model is to automate time series analysis through a unique transformation model of time series. The advantage of this approach to a time series analysis is the linkage of different methods for time series analysis linking traditional data mining tools in time series, and constructing new algorithms for analyzing time series. REFII model is not a closed system, which means that there is a finite set of methods. This is primarily a model used for transformation of values of time series, which prepares data used by different sets of methods based on the same model of transformation in the domain of problem space. REFII model gives a new approach in time series analysis based on a unique model of transformation, which is a base for all kind of time series analyses. In combination with elements of other methods, such as self-organizing maps or frequent-pattern trees, REFII models can make new hybrid methods for efficient time temporal data mining. Similar principle of hybridization could be used as a tool for time series temporal pattern recognition. The article describes real case study illustrating practical application of described methodology.

This study introduces singular spectrum decomposition (SSD), a new adaptive method for decomposing nonlinear and nonstationary time series in narrow-banded components. The method takes its origin from singular spectrum analysis (SSA), a nonparametric spectral estimation method used for analysis and prediction of time series. Unlike SSA, SSD is a decomposition method in which the choice of fundamental parameters has been completely automated. This is achieved by focusing on the frequency content of the signal. In particular, this holds for the choice of the window length used to generate the trajectory matrix of the data and for the selection of its principal components for the reconstruction of a specific component series. Moreover, a new definition of the trajectory matrix with respect to the standard SSA allows the oscillatory content in the data to be enhanced and guarantees decrease of energy of the residual. Through the numerical examples and simulations, the SSD method is shown to be able to accurately retrieve different components concealed in the data, minimizing at the same time the generation of spurious components. Applications on time series from both the biological and the physical domain are also presented highlighting the capability of SSD to yield physically meaningful components.

As a maritime country strategically located along the world's leading transportation routes, Indonesia often faces increased ship accidents. Based on the Basarnas Statistics Book, ship accidents handled by Basarnas from 2021 to 2023 increased by 3%. This condition requires an effective forecasting method to carry out SAR operations to predict ship accidents in the Indonesian region in the future and assess the readiness and needs of Basarnas resources. This study compares the forecasting results obtained using the Singular Spectrum Analysis (SSA) and the Local Linear methods. Both methods do not require parametric assumptions. The data used in this study are divided into training data and test data. This data is secondary data obtained from the Basarnas Statistics Book. The training data in this study is the number of SAR operations from January 2021 to December 2022, while the testing data is from January 2023 to December 2023. From the analysis results, it is known that the method with the smallest MAPE is the Local Linear method with a MAPE of test data of 18.67% (good forecasting category), optimal bandwidth (h) = 4.299, and CV (h) = 231.39 where bandwidth is used to determine the level of smoothness of the estimate, while the CV (h) value is used to select the optimal bandwidth that minimizes the estimation error. At the same time, the SSA method has a MAPE of 40.27% (fair forecasting category). This shows that the Local Linear method provides a more accurate forecast of the number of SAR operations related to ship accidents in Indonesia. This research contributes to the SDGs to make Basarnas an effective and accountable institution and improve the planning and decision-making process in SAR operations through accurate forecasting research is relevant to accurate forecasting.

Indonesia is an archipelagic country where 2/3 of its territory is ocean. The vastness of Indonesia's oceans is expected to produce abundant sea products that can meet the needs of Indonesian consumers, especially fish. Adequacy of the amount of fish consumption can be assessed through the number of fish catch. Based on data at the Ministry of Marine Affairs and Fisheries in 2015, West Java has a low growth of fish consumption, 6.05% in 2010-2014. Therefore, it is necessary to forecast the results of fish catch for several years ahead so it can be known whether the provision of fish consumption will be fulfilled or not. One method that can be used is Singular Spectrum Analysis (SSA). The SSA method is a flexible method because it uses a nonparametric approach. That is, in its application, this method does not require the model specification of time series data, as well as parametric assumptions. Forecasting accuracy of a method is said to be good if it has a MAPE value less than 20%. MAPE of SSA method forecast is 6.19% so that SSA method is suitable for forecasting of capture fishery production in West Java Province. The forecast for fishery production in West Java Province in 2015 for the first, second, third, and fourth quarter were 53,978.49 Ton, 54,406.91 Ton, 50,889.11 Ton, and 56,896.96 Ton, respectively.

Time series analysis methods have been applied to a large number of practical problems, including modeling and forecasting economic time series and process and quality control. One aspect of time series analysis is the use of discrete linear transfer functions to model the interrelationships between input and output time series. This paper is an introduction to the identification, estimation, and diagnostic checking of these models. Some aspects of forecasting with transfer function models are also discussed. A survey of intervention analysis models in which the input series is an indicator variable corresponding to an isolated event thought to influence the output is also given. Familiarity with univariate autoregressive integrated moving average modeling is assumed. Extensions to more general multiple time series analysis methods are also briefly discussed.

Non-stationary time series plays a prominent role in the analysis of performance time series of many real-world systems. Recently, fuzzy time series models have been extended to forecast non-stationary time series. Over different phases of time, performance time series may show drastic changes. Therefore, a non-stationary time series is partitioned according to different phases of time. These phases may be taken as weeks, months, or years. Over different phases of time, the universe of discourse, knowledge base, and rule base may vary. A common constraint in the modelling of time-variant fuzzy time series is their incapability to address the phase change of time in the model and accordingly incorporate the necessary changes in the universe of discourse, knowledge base, and rule base over different time phases. To address this issue, a Phase-cum-Time Variant Fuzzy Time Series Model (PTVFTS) is presented in this paper. The PTVFTS model is developed so that it will address the problem of phase change as well as the time variations within each phase simultaneously. The concept of the model rebuilding process is applied to handle changes over each phase and the modified parameter adaptation technique is used for the time variations within each phase. The developed model is applied to the daily closing price time series for the years 2017, 2018, 2019, 2020, 2021, and 2022 separately of stock market indices, NASDAQ, S&P 500, Dow Jones, and TAIEX. The comparison of the developed model is made with the time-variant fuzzy time series model known as the non-stationary fuzzy time series model (NSFTS), Dynamic Evolving Neural-Fuzzy Inference System (DENFIS) model, Long Short-Term Memory (LSTM) model, and the classical Auto-Regressive Integrated Moving Average (ARIMA) model. The efficiency of the developed PTVFTS model is tested using forecasting metrics and statistical tests. The comparison shows that the developed model is more efficient in forecasting phase-cum-time variant non-stationary time series.

Microseismic (MS) monitoring technology has been widely used to monitor ground pressure disasters. However, the underground mining environment is complex and contains many types of noise sources. Furthermore, the traditional recognition method entails a complex process with low recognition accuracy for MS signals, so it is difficult to serve for the safe production of mines. Therefore, this study established a hybrid model combining the singular spectrum analysis (SSA) method, convolutional neural networks (CNN), and long short-term memory networks (LSTM). First, the principal components of monitoring signals were extracted with the SSA method, and then spatial and temporal features of monitoring signals were separately extracted with the CNN and LSTM. Based on actual field data collected from Xiadian Gold Mine, the hybrid model was compared with the CNN, LSTM, and back-propagation networks (BP), as well as commonly used recognition methods including the support vector machine (SVM), decision tree (DT), K-nearest neighbor (KNN), and linear discriminant analysis (LDA). The results show that the proposed hybrid model can accurately extract data features of monitoring signals and further improve MS signals' recognition performance. Furthermore, the recognition accuracy of mechanical signals in monitoring signals is particularly increased using the hybrid model, which avoids confusion with MS signals.