Singular spectrum analysis and forecasting of hydrological time series

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.

Improving forecasting accuracy of medium and long-term runoff using artificial neural network based on EEMD decomposition

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.

This paper presents the technique of Singular Spectrum Analysis (SSA) and its application for electric load forecasting purposes. SSA is a relatively new non-parametric data-driven technique developed to model non-linear and/or non-stationary, noisy time series. SSA is able to decompose the original time series into the sum of independent components, which represent the trend, oscillatory behavior (periodic or quasi- periodic components) and noise. One of the main advantages of SSA compared to other non-parametric approaches is that only two parameters are required to model the time series under analysis. An example of application is given, with regards to forecasting the monthly electric load demand in a Venezuelan region served by wind power generators. In this case, careful demand estimation is required since the wind generation output could be highly variable and additional conventional generation or transmission links would be required to satisfy the load demand. A comparison with other classical time-series approaches (like exponential smoothing and Auto Regressive Integrated Moving Average models) is presented. The results show that SSA is a powerful approach to model time series, capable of identifying sub-time series (trends along with seasonal periodic components).

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.

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.

Singular spectrum analysis (SSA) has recently been applied to various geodetic time series studies. As a data-adaptive method, SSA is capable of extracting signals with non-constant phase and amplitudes. Although SSA is a competent method in the presence of white noise, the contribution of colored noise, having semi-periodic behavior, degrades its performance. Parts of colored noise can be absorbed in the SSA eigenmodes, which specifies signals and hence resulting in spurious modulation or losing significant signals. Signals and colored noise are thus to be discriminated in the signal identification procedure. Monte Carlo SSA (MCSSA) in its original formulation, providing a significance test against the AR(1) noise null hypothesis, can be misinterpreted when other colored noise structures contribute to the series. We propose an algorithm for MCSSA that is not limited to the AR(1) noise hypothesis. It estimates the noise model parameters using LS-VCE and generates the surrogate data using the Cholesky decomposition. The algorithm is adapted to GPS position time series where the underlying noise is a combination of white noise and flicker noise. GPS position time series, postulated real situation, are first simulated to include annual and semiannual signals plus white and flicker noise. The results indicate that MCSSA can extract the annual and semiannual signals with 2.11 and 1.25 mm amplitudes (the global mean values) from 20-year-long time series, with 95% confidence level, if flicker noise is less than 17 and 13 $$ {\text{mm/year}}^{1/4} $$ , respectively. The longer the time series or the stronger the signals are, the higher these thresholds will be. This conclusion is also verified when applying MCSSA to the up component of GPS position time series of 347 JPL stations.

Accurate hydrological prediction faces challenges due to diverse datasets and the absence of universally applicable models. This study investigates meta-learning's role in identifying optimal models for hydrological time series forecasting in specific contexts. We explore limitations in model identification and introduce meta-learning as a solution. The proposed methodology formalizes the model selection process by using meta-features from a dataset that includes time series, geology, and the experimental configuration and results of predictions . These features are crucial for empowering the meta-learner to make informed model selections. The study encompasses localized and national analyses, offering insights into the meta-learner's performance across distinct geographic regions. In this initial phase of the experiment, we present the results of the Meta-Learners within the context of a localized evaluation in Ireland, we evaluated the Neagh Bann River Basin District ( NB RBD) which covers an area of around 5740 km2. It includes all of County Armagh, large parts of Counties Antrim, Londonderry, Down and Tyrone and a small area County Fermanagh in Ireland.  Using the NB RBD dataset which comprises 16 monitoring stations, we constructed the details of 12  prediction models.  The second phase of the experiment widens its scope by encompassing data from multiple locations across Ireland. This broader approach allows us to draw upon a more extensive and diverse dataset, comprehensively evaluating meta-learner performance within a national context. By incorporating data from various regions in Ireland, we aim to capture a more holistic understanding of the meta-learners' adaptability and effectiveness in a nationally diverse landscape.  We used data from 249 hydrometric stations in Ireland, each corresponding to a distinct geographical location. This comprehensive dataset encompasses various locations across the country, offering a rich and diverse perspective for our analysis. Evaluation results demonstrate the performance of 12 models. Models like Random Forest and K-Nearest Neighbors show promise, while Support Vector Machine struggles consistently. Addressing class imbalance through resampling techniques proves effective, underscoring the importance of tailored model selection strategies. Key findings highlight model performance variability, concerns about overfitting, and the significance of appropriate resampling strategies. The meta-learner's application showcases its value in leveraging strengths across classifiers and mitigating weaknesses. In conclusion, this study contributes to advancing adaptive model selection methodologies in hydrological time series forecasting.  Keywords: Meta-learning, model selection, hydrologic time-series prediction.

The failure of cutting tools significantly decreases machining productivity and product quality; thus, tool condition monitoring is significant in modern manufacturing processes. A new method that is based on singular spectrum analysis and Mahalanobis distance are combined to extract the crucial characteristics from spindle motor current to monitor the tool's condition. The singular spectrum analysis is a novel nonparametric technique for extracting the properties of nonlinear and nonstationary signals. However, because the components are not completely independent, the original singular spectrum analysis eventually leads to misinterpretation of the final results. The proposed method is used to overcome the weakness of the original singular spectrum analysis. The singular spectrum analysis algorithm is adopted to decompose the original signal and the useful singular values that correspond to the tool condition can be extracted. The Mahalanobis distance of the singular values is proposed as a feature that can effectively express the tool condition. The experiments on a CNC Vertical Machining Center demonstrate that this method is effective and can accurately detect the tool breakage in mill process.

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

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.

The spectral characteristics of the delta /sup 18/O isotopic ratio time series of the Quelccaya ice cap summit core are investigated with the multi taper method (MTM), the singular spectrum analysis (SSA) and the wavelet transform (WT) techniques for the 500 y long 1485-1984 period. The most significant (at the 99.8% level) cycle according to the MTM F-test has a period centered at 14.4 y while the largest variance explaining oscillation according to the SSA technique has a period centered at 12.9 y. The stability over time of these periods is investigated by performing evolutive MTM and SSA on the 500 y long delta /sup 18/O series with a 100 y wide moving window. It is shown that the cycles with largest amplitude and that the oscillations with largest extracting variance have corresponding periods aggregated around 13.5 y that are very stable over the period between 1485 and 1984. The WT of the same isotopic time series reveals the existence of a main oscillation around 12 y which are also very stable in time. The relation between the isotopic data at Quelccaya and the annual sea surface temperature (SST) field anomalies is then evaluated for the overlapping 1919-1984 period. Significant global correlation and significant coherency at 12.1 y are found between the isotopic series and the annual global sea surface temperature (GSST) series. Moreover, the correlation between the low (over 8 y) frequency component of the isotopic time series and the annual SST field point out significant values in the tropical North Atlantic. This region is characterized by a main SST variability at 12.8 y.

Singular Spectrum Analysis (SSA) is a novel non-parametric technique based on principle of multivariate statistics. The original time series is decomposed into a number of additive time series, each of which can be easily identified as being part of the modulated signals, or as being part of the random noise. It shows that the embedding dimension m of a dynamical time series can be conducted by the Singular Value Decomposition (SVD) experiments. This SVD scheme was used to detect low-dimensionally dynamic signals and the residuals. It provides trend extraction involves a decomposition of a time series into low-frequency trends and high-frequency variability. In this study, first, SSA is used to decompose the nonlinear seismic responses of reinforced concrete frames and to elucidate permanent deformation. Then, damage feature extraction is conducted using the high-frequency variability of SSA to identify the occurrence of damage. Comparison the results with the Holder exponent and the Level-1 detail of the discrete wavelet component to detect the damage occurrence was made. Finally, using SSA to estimate the permanent deformation using recorded acceleration data was also discussed. In this study, four reinforced concrete frame test data collected in response to various degrees of seismic excitation are used to demonstrate the application of SSA in damage detection.

In recent years Singular Spectrum Analysis (SSA), used as a powerful technique in time series analysis, has been developed and applied to many practical problems. In this paper, the performance of the SSA tech- nique has been considered by applying it to a well-known time series data set, namely, monthly accidental deaths in the USA. The results are com- pared with those obtained using Box-Jenkins SARIMA models, the ARAR algorithm and the Holt-Winter algorithm (as described in Brockwell and Davis (2002)). The results show that the SSA technique gives a much more accurate forecast than the other methods indicated above.

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.