Ozone density at cold-point mesopause (O3-CPM) can provide information on long-term atmospheric trends. Compared to ground-level ozone, O3-CPM is not only adversely affected by chemical substances emitted from human activities but is also regulated by solar radiation. Therefore, an accurate prediction of O3-CPM is necessary. However, it is difficult for traditional forecasting methods to predict the main trends and seasonal characteristics of ozone time series while capturing the random components and noise of O3-CPM. In order to improve the prediction accuracy of O3-CPM, this paper proposes a hybrid SSA-SARIMA-GSVR model based on the Singular Spectrum Analysis (SSA) method, which combines the Seasonal Autoregressive Integrated Moving Average Model (SARIMA) and the Gray Wolf Algorithm Optimized Support Vector Regression Algorithm (GSVR). First, the O3-CPM sequence is decomposed using SSA, and the concept of reconstruction threshold (RT) is introduced to categorize the decomposed singular values into two classes. The categorized RT reconstructed sequences containing periodic features and major trends are fed into the SARIMA model for prediction, and the N-RT reconstructed sequences (original sequence N minus RT reconstructed sequence) containing stochastic components and nonlinear features are fed into the GSVR model for prediction. The final prediction results are obtained by superimposing the outputs of these two models. The results confirm that, compared to various commonly used time series forecasting models such as Long Short-Term Memory (LSTM), Informer, SVR, SARIMA, GSVR, SSA-GSVR, and SSA-SARIMA models, the proposed SSA-SARIMA-GSVR hybrid prediction model has the lowest error evaluation metrics, enabling accurate and efficient prediction of the O3-CPM time series. Specifically, the proposed model achieved an RMSE of 0.26, MAE of 0.212, and R2 of 0.987 on the test set, outperforming the best baseline model (SARIMA) by 45.8%, 42.1%, and 3.1%, respectively.

Surface roughness is a critical parameter used to describe the microscopic geometric deviations of a part, and serves as an essential indicator for assessing the quality of surface processing in various mechanical components. This study evaluates Singular Spectrum Analysis (SSA) for surface roughness profile separation, comparing its effectiveness with the ISO standard Gaussian filter. Using NIST roughness measurement data, this study investigates how SSA’s window length and grouping method affect roughness parameters. The findings indicate that with an appropriately chosen window length, the SSA technique can effectively separate roughness signals and yield roughness parameter values comparable to those obtained using the Gaussian filter, such as the arithmetical mean deviation of the assessed profile (Ra), the root mean square deviation of the assessed profile (Rq), and the kurtosis of the assessed profile (Rku). These findings establish SSA as a viable alternative for surface roughness profile separation, with broad applications in surface metrology.

ABSTRACT Global Navigation Satellite System (GNSS) coordinate time series exhibit significant periodic characteristics. The existing studies mainly focus on obtaining accurate amplitude and phase of periodic signals, while the period lengths are commonly set as constant empirical values. Nevertheless, due to geophysical signals and technical-related systematic errors, the actual period length may have Period Errors (PE), including Period Offset (PO) or Period Variation (PV). Using empirical period length would lead to incorrect periodic modeling and overestimation of velocity uncertainty. This paper establishes a rigorous theoretical harmonic model considering the impact of PE, then uses the Nonlinear Least Squares (NLS) and Unscented Kalman Filter (UKF) to estimate periodic signals in GNSS coordinate time series. Our simulation results show that the NLS model considering PO (NLS_Period) significantly outperforms the traditional harmonic model estimated by Weighted Least Squares (WLS) in modeling period signals. Especially for long time series and large amplitudes, NLS_Period reduces the period amplitude fitting error by up to 8 times compared to the traditional harmonic model when the annual amplitude is 8.2 mm over a 28‑year span. When the period length varies, the UKF model, UKF_Amp_Period, considering PV, PO, and Period Amplitude Variations (PAV) together achieve the best fitting results, with accuracies of 61%, 40.6%, and 40.2% higher than WLS, Singular Spectrum Analysis (SSA), and the model considering only PAV (UKF_Amp), respectively. When applied to modeling periodic signals in real GNSS coordinate time series, the UKF_Amp_Period method improves fitting accuracy by about 9–10% compared to WLS, while the spectral index decreases by 5.6–8.4%. Our work confirms the importance of accurate period length in the harmonic modeling of GNSS coordinate time series. Considering the actual period length of signals not only achieves more accurate periodic modeling results but could also potentially explain the period signals from the perspective of period length variations.

Heart rate tracking using Photoplethysmography (PPG) suffers from motion artifacts, which can change signal structure in a way that the spectral peak due to motion artifacts (MAs) can mask the actual peak related to the heart rate. To handle the problem just mentioned, a novel mathematical model for heart rate (HR) tracking is introduced. Our technique is based on a mathematical model for a multichannel PPG. The model uses a fixed-resolution spectrum of Fast Fourier Transform (FFT), Chirplet Z Transform (CZT) spectra at various resolutions, confinement of spectral space, previous heart rate, range of the signal, and a golden seed (GS) algorithm to generate the next heart rate. GS algorithm is a novel technique which is introduced to handle the masking of spectral peaks related to HRs. The GS algorithm utilizes intensity profiling, the Singular Spectrum Analysis (SSA) algorithm, spectral multiplication and subtraction, and proximity clustering to enhance the masked peak. The average time taken by our technique is 21.21ms and a mean average error of 2.12 on the IEEE signal processing Cup 2015 makes it fit for the real-time applications.

Spectral decomposition and temporal dynamics of CO and O₃ in Campo Grande, Brazil: a singular spectrum analysis approach

Abstract Electroencephalography (EEG) contains multiple rhythmic components, but few studies have focused on the non-rhythmic component of EEG, which may be associated with multiple brain states and background activities, and there is still no effective method to separate these two components. In this study, we propose a method to separate the rhythmic and non-rhythmic components of EEG by combining Singular Spectrum Analysis (SSA) and clustering. The repetitive pattern components of EEG were extracted by SSA decomposition, and clustered according to their time-frequency characteristics. The analysis of simulation data shows that this method can effectively extract EEG rhythmic components and maintain their spectral and phase characteristics; the rhythmic and non-rhythmic components separated from real EEG can effectively distinguish multiple brain states. The proposed method is expected to advance the understanding of how both rhythmic and non-rhythmic EEG analyses relate to brain states and functions.

Locating Water Supply Pipeline Leaks Using Multivariate Variational Mode Decomposition and Multichannel Singular Spectrum Analysis

Abstract The Korea Pathfinder Lunar Orbiter (KPLO) spacecraft utilizes the KPLO Magnetometer (KMAG) payload, a three‐fluxgate magnetometer array mounted on a 1.2 m boom, to measure crustal and induced lunar magnetic fields. The short boom length exposes the magnetometers to intricate, multi‐source stray magnetic fields. These interference signals include a low‐frequency, 20 nT peak‐to‐peak signal from the solar panels and batteries as the spacecraft transitions between sunlight and darkness during certain orbital phases. These stray magnetic fields impede the analysis of lunar magnetic anomalies with magnitudes up to 3 nT at a 100 km altitude. Additionally, downlink issues during the mission's initial stages occasionally resulted in data gaps of up to 12 min (approximately 13% of the orbit) in several orbits. To overcome these data quality challenges, we present a comprehensive three‐component method: (a) the Recurrent Forecasting Multichannel Singular Spectrum Analysis (M‐SSA) algorithm interpolates data gaps, (b) Wavelet‐Adaptive Interference Cancellation for Underdetermined Platforms (WAIC‐UP) removes stray magnetic fields from the continuous magnetometer measurements, and (c) the Removal Algorithm for Magnetometer Environmental Noise (RAMEN) gradiometry algorithm corrects low‐frequency trends not observed by WAIC‐UP. We demonstrate the efficacy of our approach by comparing the results with contemporaneous magnetic field measurements from the lunar‐orbiting ARTEMIS‐P1 spacecraft and lunar crustal magnetic field maps from the Lunar Prospector and Kaguya missions. This integrated application of M‐SSA, WAIC‐UP, and RAMEN enables KMAG to reliably investigate lunar magnetic fields despite non‐dipolar spacecraft interference and intermittent data gaps.

Abstract Time series analysis is fundamental to characterizing the variability inherent in multi-wavelength emissions from blazars. However, a major observational challenge lies in the need for well-sampled, temporally uniform data, which is often hindered by irregular sampling and data gaps. These gaps can significantly affect the reliability and accuracy of methods used to probe source variability. This paper investigates the impact of such observational gaps on time series analysis of blazar emissions. To do so, we systematically evaluate how these gaps alter observed variability patterns, mask genuine periodic signals, and introduce false periodicity detections. This evaluation is conducted using both simulated and real observational data. We assess a range of widely used time series analysis methods, including the Lomb-Scargle periodogram, Phase Dispersion Minimization, and the recently proposed Singular Spectrum Analysis (SSA). Our results demonstrate a clear and significant degradation in period detection reliability when the percentage of gaps exceeds 50 %. In such cases, the period-significance relationship becomes increasingly distorted, often leading to misleading results. Among the tested methods, SSA stands out for its ability to yield consistent and robust detections despite high data incompleteness. Additionally, the analyzed methods tend to identify artificial periodicities of around one year, likely due to seasonal sampling effects, which can result in false positives if not carefully recognized. Finally, the periods detected with ≥3σ confidence are unlikely to result from stochastic processes or from the presence of gaps in the analyzed time series.

Time series forecasting is essential for analyzing past data to predict future trends, supporting planning, and decision-making. The SARIMA model is widely used for seasonal data but may be less effective for highly fluctuating or non-stationary data, which can impact forecast accuracy. As an alternative, Singular Spectrum Analysis (SSA) offers a flexible approach, decomposing time series into trend, seasonal, and noise components without strict parametric assumptions, making it effective for complex data patterns. This study compares SARIMA and SSA models in forecasting daily passenger counts on the Jakarta-Bandung high-speed rail, using data from November 1, 2023, to September 30, 2024. The results show that the performance of SSA is more stable compared to SARIMA in the term of MAPE, where SSA provides lower MAPE then SARIMA in all three scenarios of data splits. These results are expected due to the non-linear pattern that appears in the data. Moreover, the predictions on both methods show that slight increment of passengers in the end of 2024 to the beginning of 2025. This finding suggests that the government needs to consider implementing interventions if they wish to change the current trend, such as offering discounts or year-end holiday promotions.

Abstract The occurrence of sea surface temperature (SST) extremes may provoke profound impacts on ocean health. In the last decade, much effort has been dedicated to understanding and systematically describing marine heatwaves (MHWs) and cold spells (MCSs), defined as prolonged periods of anomalously warm or cold SSTs at a given location, respectively. However, an objective and agreed detection criterion for such extremes, applicable to past and future climates alike and separating the effects of climate variability and change, is still missing. Analysis of four decades of global daily satellite‐based SST data show that the identification of extremes is strongly dependent on the chosen data set and algorithmic choices that are difficult to set objectively. Sensitivity to the reference period (baseline) occurs because the warming trend shifts SST anomalies away from the baseline, resulting in a global increase in MHWs (moderate and strong) and a decrease in MCSs (strong and extreme). Here we show that the contributions from climate change can be effectively isolated by applying a data‐driven approach based on the singular spectrum analysis, which, unlike linear detrending, does not assume a prescribed behavior for the trend. Detrending removes long‐term changes in the occurrence of SST extremes, and also affects the metrics (such as intensity and duration) widely used to characterize these events. Data set intercomparison reveals possibly spurious MHW events in the early 1980s and quantitative discrepancies in the representation of long‐term variability.

Paying attention to returns: Forecasting returns as nonlinear AR time-varying drifts using multihead attention and Singular Spectrum Analysis

This study presents a forensic diagnostic framework aimed at enhancing the early detection, fault classification and remaining useful life (RUL) prediction of rolling bearing failures. The proposed network integrates a novel three-stage machine learning formulation – (1) identification of health state using voting ensemble, (2) prognostic analysis via a hybrid convolutional neural network and gated recurrent unit (CNN-GRU), and (3) fault type identification through the segment anything model (SAM) based on time-frequency representations. The ensemble and CNN-GRU models are trained on both time- and frequency-domain features from vibration signals, while SAM leverages this data in visual sense through iterative masking for zero-shot spatial-temporal fault segmentation. Pre-processing techniques, including piecewise aggregate approximation and singular spectrum analysis, are used to denoise and compress the vibration response without impacting key statistical traits. The proposed e-CNN-GRU-SAM network demonstrates better accuracy in diagnosing fault types, predicting RUL and identifying root causes under different operational conditions. This is established using diverse operating benchmark datasets that simulate induced and real-world degradation scenarios for generalization. Thus, the proposed framework offers a comprehensive forensic analysis toolkit for diagnosis and prognosis of bearings.

This study proposes a novel SSA-EMS framework that integrates Singular Spectrum Analysis (SSA) with Effect-Matched Spatial Filtering (EMS), combining the noise-reduction capability of SSA with the dynamic feature extraction advantages of EMS to optimize cross-subject EEG-based emotion feature extraction. Experiments were conducted using the SEED dataset under two evaluation paradigms: "cross-subject sample combination" and "subject-independent" assessment. Random Forest (RF) and SVM classifiers were employed to perform pairwise classification of three emotional states-positive, neutral, and negative. Results demonstrate that the SSA-EMS framework achieves RF classification accuracies exceeding 98% across the full frequency band, significantly outperforming single frequency bands. Notably, in the subject-independent evaluation, model accuracy remains above 96%, confirming the algorithm's strong cross-subject generalization capability. Experimental results validate that the SSA-EMS framework effectively captures dynamic neural differences associated with emotions. Nevertheless, limitations in binary classification and the potential for multimodal extension remain important directions for future research.

A hyperspectral imaging dataset and Grassmann manifold method for intraoperative pixel-wise classification of metastatic colon cancer in the liver.

Estimating the output gap and potential output presents a perpetual challenge for policymakers. Model-based estimations can yield inconsistent results if the underlying assumptions fail to capture the economy’s true dynamics. Conversely, while statistical filters offer a rapid estimate of potential output, they can be susceptible to spurious cycles and end-of-sample bias. In this study, we employ both univariate and multivariate singular spectrum analysis (SSA) as statistical filters to estimate the potential output and output gap for the Indian economy. The output gaps estimated using both univariate and multivariate SSA methods show a strong correlation and demonstrate high co-movements in terms of directional changes with ‘capacity utilization’, the Reserve Bank of India’s survey-based measures of the sentiment of the manufacturing sector. Counterfactual potential GDP was compiled to gauge the impact of the COVID-19 pandemic and subsequent disruptions in the global supply chain. Our findings indicate that the pandemic has led to a decline in India’s potential output and potential losses as measured by the difference between estimated counterfactual potential growth and potential growth are 4.6 per cent, 3.8 per cent, 2.9 per cent and 1.8 per cent, respectively, during the financial years 2020–2021 to 2023–2024. AMS Subject Classification: 62G05, 62H25, 62M10, 65C05, 62P20, 91B62

Time series of Global Positioning System (GPS) station positions include signals whose characteristics vary over time. Therefore, in detailed analyses, methods dedicated to nonstationary time series should be used. In this study, the Complementary Ensemble Empirical Mode Decomposition (CEEMD) method was used to model trends in time series of GPS station positions and to verify their nonlinearity. As the CEEMD method does not provide equations for assessing the uncertainty of the determined trend, we propose to use the bootstrap method for this purpose. In this study, daily time series of the Up components of 25 GPS stations from seismic regions in Europe and from the Nevada Geodetic Laboratory (NGL) service were used. The determined trends were compared with the trends calculated using the Singular Spectrum Analysis (SSA) method and then interpreted in the context of earthquakes occurring in the vicinity of the station. In turn, the bootstrap method was used to estimate the mean standard deviations of trends determined by the CEEMD as well as SSA method. The conducted studies showed the usefulness of the CEEMD method for modeling trends in time series of GPS station positions, especially for stations where changes may occur on short time scales, visible as the local nonlinearity of the trend, mainly due to earthquake events. The bootstrap-estimated mean standard deviation values for the modeled nonlinear trends are at the level of 1–3 mm, depending on the station. In turn, the root mean square error (RMSE) estimated between the nonlinear trend determined by the CEEMD method and the linear trend fitted to it by the least squares method does not exceed 3 mm. The conducted research indicates that the CEEMD method can be successfully used to model locally nonlinear trends resulting from earthquakes, and the mean standard deviation of the estimated trends is relatively low.

Partial Discharge Denoising of High-Voltage Cables for High-Speed Trains Based on Singular Spectrum Analysis and ICEEMDAN Decomposition

Abstract Understanding the fundamental motions of molecules, particularly vibrational motions, is essential for elucidating chemical reaction mechanisms. Time‐resolved X‐ray scattering (TRXS) has emerged as a powerful technique for investigating molecular vibrations, as it simultaneously provides both temporal and spatial information on vibrational modes. However, visualizing these vibrations via TRXS remains challenging due to technical limitations in achieving a high signal‐to‐noise ratio (SNR) and temporal resolution, making it difficult to resolve subtle oscillatory signals arising from molecular vibrations. Here, we present an integrative analysis framework developed to efficiently extract oscillatory signals from TRXS data and verify their association with molecular vibrations. The framework comprises two key steps: the extraction of oscillatory signals using singular spectrum analysis (SSA) and posterior structural analysis to assess the physical relevance of the extracted signals. By applying this scheme to simulated TRXS datasets, we demonstrate that it identifies oscillatory signals embedded in the data more effectively than conventional Fourier transform analysis, even under low SNR conditions. Furthermore, the structural analysis step effectively discriminates physically irrelevant components, such as harmonic and combination frequencies, and high‐frequency artifacts from signals corresponding to the fundamental frequencies of molecular vibrations. The proposed data analysis framework is expected to advance studies of molecular vibrations and wavepacket dynamics using TRXS, ultimately providing deeper insights into the ultrafast reaction dynamics.

Battery capacity degradation prediction based on singular spectrum analysis and improved deep learning