A state‐dependent linear recurrent formula with application to time series with structural breaks

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.

Brexit: Tracking and disentangling the sentiment towards leaving the EU

Groth and Ghil [Phys. Rev. E 84, 036206 (2011)PLEEE81539-375510.1103/PhysRevE.84.036206] developed a modified varimax rotation aimed at enhancing the ability of the multivariate singular spectrum analysis (M-SSA) to characterize phase synchronization in systems of coupled chaotic oscillators. Due to the special structure of the M-SSA eigenvectors, the modification proposed by Groth and Ghil imposes a constraint in the rotation of blocks of components associated with the different subsystems. Accordingly, here we call it a structured varimax rotation (SVR). The SVR was presented as successive pairwise rotations of the eigenvectors. The aim of this paper is threefold. First, we develop a closed matrix formulation for the entire family of structured orthomax rotation criteria, for which the SVR is a special case. Second, this matrix approach is used to enable the use of known singular value algorithms for fast computation, allowing a simultaneous rotation of the M-SSA eigenvectors (a Python code is provided in the Appendix). This could be critical in the characterization of phase synchronization phenomena in large real systems of coupled oscillators. Furthermore, the closed algebraic matrix formulation could be used in theoretical studies of the (modified) M-SSA approach. Third, we illustrate the use of the proposed singular value algorithm for the SVR in the context of the two benchmark examples of Groth and Ghil: the Rössler system in the chaotic (i) phase-coherent and (ii) funnel regimes. Comparison with the results obtained with Kaiser's original (unstructured) varimax rotation (UVR) reveals that both SVR and UVR give the same result for the phase-coherent scenario, but for the more complex behavior (ii) only the SVR improves on the M-SSA.

We show that multivariate singular spectrum analysis (M-SSA) greatly helps study phase synchronization in a large system of coupled oscillators and in the presence of high observational noise levels. With no need for detailed knowledge of individual subsystems nor any a priori phase definition for each of them, we demonstrate that M-SSA can automatically identify multiple oscillatory modes and detect whether these modes are shared by clusters of phase- and frequency-locked oscillators. As an essential modification of M-SSA, here we introduce variance-maximization (varimax) rotation of the M-SSA eigenvectors to optimally identify synchronized-oscillator clustering.

ABSTRACTKohli P, Siver PA, Marsicano LJ, Hamer JS, Coffin AM. 2017. Assessment of long-term trends for management of Candlewood Lake, Connecticut, USA. Lake Reserve Manage. 00:00–00.Candlewood Lake, the largest lake in Connecticut, is a pumped-storage reservoir formed in the 1920s for hydropower generation. Since its inception, the lake has experienced shifts in water quality coupled with watershed development and, in the 1980s, the introduction and spread of the invasive macrophyte, Myriophyllum spicatum. In response, a monitoring program to track water quality and a winter drawdown program to mitigate growth of M. spicatum were initiated in 1985. Recently it was suggested that the drawdown program exacerbated eutrophication of the lake. To test this hypothesis, statistical analyses of the long-term (1985 to 2012) database was conducted with a focus on trophic-related variables. We examined the database using principal component analysis (PCA) and multivariate singular spectrum analysis (MSSA). MSSA is an extension of PCA for multivariate time series data that accounts for both temporal and cross-sectional dependencies. We found no evidence that the trophic condition declined, or that the drawdowns have deteriorated the water quality. Instead, we found that lower TS, TSIChl, and TSSD values corresponding with improved trophic conditions occurred in summers following deep drawdowns, while significantly higher values correlated with shallow and less effective drawdowns. Overall, there has been a modest improvement in the trophic condition over time, attributed to a combination of the winter drawdowns and management efforts. In contrast, a steady and significant increase in dissolved salts, likely due to enhanced use of road deicing treatments, was documented.

Predicting daily exchange rate with singular spectrum analysis

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.

Spatially uneven illuminations are the dominant interference of video-based heart rate (HR) screening for cooperated subjects in a telehealth service. In this letter, a remote photoplethysmography (rPPG) method is introduced to stably extract pulsatile signals against uneven facial illuminations based on the multivariate singular spectrum analysis (MSSA). This method first divides the facial skins into multiple patches, where the hue channels resistant to light intensity variations are prepared from selected optimal patches. Considering the spatial correlations of heartbeats, the hue signals are then decomposed using the MSSA to reconstruct pulses. Finally, the HR is determined as the one with the highest ratio of energy around the dominant frequency from the first group of MSSA reconstructed signals. Experimental results demonstrate the effectiveness of the proposed method on the in-house BSIPL-rPPG database and the public COHFACE database, where the correlation coefficients of the estimated HRs achieve 0.95 and 0.98, respectively, outperforming those of the comparison methods.

This paper compares the out‐of‐sample forecasting accuracy of a wide class of structural, BVAR and VAR models for major sterling exchange rates over different forecast horizons. As representative structural models we employ a portfolio balance model and a modified uncovered interest parity model, with the latter producing the more accurate forecasts. Proper attention to the long‐run properties and the short‐run dynamics of structural models can improve on the forecasting performance of the random walk model. The structural model shows substantial improvement in medium‐term forecasting accuracy, whereas the BVAR model is the more accurate in the short term. BVAR and VAR models in levels strongly out predict these models formulated in difference form at all forecast horizons.

SummaryWe use univariate and multivariate singular spectrum analyses to predict the rate of inflation as well as changes in the direction of inflation time series for the USA. We use consumer price indices and realtime chain-weighted gross domestic product price index series in these prediction exercises. Moreover, we compare our out-of-sample, h-step-ahead moving prediction results with other prediction results based on methods such as the activity-based non-accelerating inflation rate of unemployment Phillips curve, auto-regressive AR(p) model, the dynamic factors model and random-walk models with the last as a naive forecasting method. We use short-run (quarterly) and long-run (1–6 years) time windows for predictions and find that multivariate singular spectrum analysis outperforms all other competing prediction methods. Also, we confirm the results of earlier studies that prediction of the rate of inflation in the USA during the period of the ‘Great Moderation’ is less challenging compared with the more volatile inflationary period of 1970–1985.

Infrared (IR) images are essential to improve the visibility of dark or camouflaged objects. Object recognition and segmentation based on a neural network using IR images provide more accuracy and insight than color visible images. But the bottleneck is the amount of relevant IR images for training. It is difficult to collect real-world IR images for special purposes, including space exploration, military and fire-fighting applications. To solve this problem, we created color visible and IR images using a Unity-based 3D game editor. These synthetically generated color visible and IR images were used to train cycle consistent adversarial networks (CycleGAN) to convert visible images to IR images. CycleGAN has the advantage that it does not require precisely matching visible and IR pairs for transformation training. In this study, we discovered that additional synthetic data can help improve CycleGAN performance. Neural network training using real data (N = 20) performed more accurate transformations than training using real (N = 10) and synthetic (N = 10) data combinations. The result indicates that the synthetic data cannot exceed the quality of the real data. Neural network training using real (N = 10) and synthetic (N = 100) data combinations showed almost the same performance as training using real data (N = 20). At least 10 times more synthetic data than real data is required to achieve the same performance. In summary, CycleGAN is used with synthetic data to improve the IR image conversion performance of visible images.

Time series models are widely used to examine temporal dynamics and uncover patterns across diverse fields. A commonly employed approach for modeling such data is the (Vector) Autoregressive (AR/VAR) model, in which each variable is represented as a linear combination of its own and others’ lagged values. However, the traditional (V)AR framework relies on the key assumption of stationarity, that autoregressive coefficients remain constant over time, which is often violated in practice, especially in systems affected by structural breaks, seasonal fluctuations, or evolving causal mechanisms. To overcome this limitation, Time-Varying (Vector) Autoregressive (TV-AR/TV-VAR) models have been developed, enabling model parameters to evolve over time and thus better capturing non-stationary behavior. Conventional approaches to estimating such models, including generalized additive modeling and kernel smoothing techniques, often require strong assumptions about basis functions, which can restrict their flexibility and applicability. To address these challenges, we introduce a novel framework that leverages physics-informed neural networks (PINN) to model TV-AR/TV-VAR processes. The proposed method extends the PINN framework to time series analysis by reducing reliance on explicitly defined physical structures, thereby broadening its applicability. Its effectiveness is validated through simulations on synthetic data and an empirical study of real-world health-related time series.

Although coal reserves are abundant in Pakistan, still share of gas and oil is about 65% in the energy mix. Pakistan, despite being a mineral-enriched country, is facing an alarming situation as its power generation is based on foreign exchange. The mineral sector of Pakistan is dominated by four principal minerals which are gas, oil, gypsum, and coal, while gypsum being a source of reclamation and poverty reduction. There is a strong need to analyze and forecast the production of these four principal minerals to cope up with emerging challenges. Data contains 114 observations from the period of July 2005 to December 2014, measured in terms of metric tonnes (MT). In parametric models, Box-Jenkins (B-J) methodology, a regression model with auto-regressive errors (ARAR), and Holt-Winter (HW) method are used to model. In nonparametric models, univariate singular spectrum analysis (SSA) and multivariate SSA (MSSA) modeling approach are applied. Data is split into train and test data in order to specify a suitable model for forecasting. Root Mean Square Error (RMSE), Mean Absolute Percentage Error, and Theil’s U statistic are utilized as the measure of accuracy. For gas and coal, HW model is a suitable model to forecast. For gypsum and oil, Auto-regressive Integrated Moving Average (Box Jenkins ARIMA) and MSSA provide more accurate predictions, respectively. The forecasts for gas and gypsum as compared to 2014 are expected to be approximately 11 % and 45 %, respectively, more in 2020. In 2020, the forecasts of oil are expected to be eight times more than in 2014. The production of coal in 2020 is expected to decrease 12 % than in 2014. There is a strong need to optimize the production of coal by providing incentives for exploration and mining. The stakeholders should make serious efforts to bring the production of coal at an optimum level such as by providing modern equipment and high incentives to promote coal mining and exploration.

Non-contact human respiratory rate measurement based on two-level fusions of video and FMCW radar information

Impacts of Natural Disasters on a Dynamic Economy