Search Results (1,245)

Noise contamination is a common challenge in the analysis of time series data, where stochastic perturbations can obscure deterministic dynamics and complicate the interpretation of signals from chaotic and physiological systems. Reliable identification of noise regimes and their intensity is therefore essential for robust analysis of dynamical and biomedical signals, where incorrect attribution of stochastic perturbations can lead to misleading interpretations of system behavior. For this reason, the present study examines the role of complexity-based descriptors for identifying stochastic perturbations in time series and analyzes how these metrics respond to different noise regimes across heterogeneous dynamical systems. A supervised learning approach based on complexity descriptors was developed to analyze controlled perturbations in multiple signal types. Gaussian, pink, and low-frequency noise disturbances were injected at predefined intensity levels into the Rössler and Lorenz chaotic systems, the Hénon map, and synthetic electrocardiogram signals, while AR(1) processes were used for validation on inherently stochastic signals. From these systems, eighteen entropy-based, fractal, statistical, and singular value decomposition-based complexity metrics were extracted from either raw signals or reconstructed phase spaces. These features were used to perform three classification tasks that capture different aspects of noise characterization, including detecting the presence of noise, identifying the perturbation type, and discriminating between different noise intensities. In addition to predictive modeling, the study evaluates the complexity profiles and feature relevance of the metrics under varying perturbation regimes. The results show that no single complexity metric consistently discriminates noise regimes across all systems. Instead, system-specific relevance patterns emerge. Under given experimental constraints (data partitioning, machine learning algorithm, etc.), Approximate Entropy provides the strongest discrimination for the Lorenz system and the Hénon map, the Coefficient of Variation, Sample and Permutation Entropy dominate classification for ECG signals, and the Condition Number and Variance of first derivative together with Fisher Information are most informative for the Rössler system. Across all datasets, the proposed framework achieves an average accuracy of 99% for noise presence detection, 98.4% for noise type classification, and 98.5% for noise intensity classification. These findings demonstrate that complexity metrics capture structural and statistical signatures of stochastic perturbations across a diverse set of dynamic systems. Full article

Forecasting crop pest outbreaks under conditions of increasing agroclimatic variability is a critical task for intelligent decision support systems in agriculture. Traditional statistical and empirical models typically have limited transferability and insufficient accuracy when describing nonlinear and multiscale relationships between climatic factors and pest population dynamics. This paper proposes a hybrid algorithm combining wavelet analysis and deep learning methods for forecasting agroclimatic pest infestation levels. The algorithm is based on multiscale decomposition of time series using a discrete wavelet transform, after which the extracted components are used as input features for a deep neural network implementing a nonlinear mapping between climatic parameters and infestation indicators. The developed computational framework includes the stages of data preprocessing, feature space formation, model training, and forecast generation in a single, reproducible pipeline. An experimental evaluation using long-term agroclimatic and phytosanitary data showed that the proposed algorithm outperforms classical regression and individual neural network models in terms of RMSE, MAE, and the coefficient of determination. The results confirm the effectiveness of integrating wavelet analysis and deep learning for developing phytosanitary risk forecasting algorithms and demonstrate the potential of the proposed approach for implementation in intelligent precision farming systems. Full article

Accurate time-series simulation of carbon emissions for both the whole society and the electricity industry is pivotal for realizing China’s “Dual Carbon” goals. This research constructs a hybrid simulation architecture integrating factor decomposition with deep learning to quantify emission trajectories for both the whole society and the electricity industry in Anhui Province. First, the extended Kaya identity and Logarithmic Mean Divisia Index (LMDI) are employed to analyze socioeconomic drivers. The decomposition analysis indicates that per capita income is the primary driver of carbon emissions, whereas energy intensity exerts the strongest inhibitory effect. Subsequently, Variational Mode Decomposition (VMD) is applied to the nonstationary emission series to produce multi-scale sub-signals, which are then fed into a predictive model comprising a Bayesian-optimized (BO) Transformer coupled with Long Short-Term Memory (LSTM) networks. The study establishes three distinct evolution scenarios: Moderate Sustainability (MS), Business as Usual (BAU), and Strong Economic Growth (SEG). Simulation results indicate that under MS, carbon emissions from the whole society and the electricity industry peak in 2029 at 435.2 Mt and 2030 at 281.2 Mt, respectively. Conversely, the SEG scenario delays the peak of the whole society to 2034, while the electricity industry fails to peak before 2035. These findings reveal significant risks of temporal asynchrony between the whole society and the electricity industry peaks, providing robust methodological support for regional decarbonization planning. Full article

With the widespread adoption of electric vehicles, predicting user charging consumption can enhance the operational efficiency of charging infrastructure. However, differences in user charging habits result in charging station operators obtaining data that is non-continuous and event-driven, lacking internal battery state information. This makes traditional methods difficult to apply directly. This paper explores how to accurately predict user charging consumption based on non-continuous observation data from charging stations. To this end, we propose a three-stage solution: (1) Design a method for segmenting the temporal sequence of users’ internal charging behavior based on statistical significance testing, enabling unsupervised recognition of homogeneous sequences of user behavior patterns; (2) establish a continuous-time reconstruction mechanism based on a physics-inspired power decay model to convert discrete homogenous sequences into equidistant daily sequences of charging consumption; (3) utilize seasonal and trend decomposition using Loess (STL) time-series decomposition to extract the component from the reconstructed sequence and input it as a feature into the Long Short-Term Memory (LSTM) prediction model. Through experimental validation using real charging data, the proposed method significantly enhances prediction performance, providing an effective solution for forecasting user charging consumption in actual charging stations. Full article

Accurate forecasting of equity returns remains fundamentally constrained by weak short-horizon predictability, pronounced noise, and structural non-stationarity. While deep learning models have been widely applied to financial time series, most studies prioritize point prediction and provide limited guidance on reliable uncertainty quantification, particularly in emerging markets. This study developed an uncertainty-aware forecasting framework for the South African equity market by integrating variational mode decomposition (VMD), gated recurrent units (GRUs), and temporal conformal prediction (TCP) to construct distribution-free prediction intervals with finite-sample coverage guarantees. Using daily returns from the FTSE/JSE All Share Index, we first confirmed that baseline recurrent models applied directly to raw returns exhibited negligible out-of-sample explanatory power, consistent with weak-form market efficiency. Incorporating VMD enhanced representation learning and improved point forecast accuracy by isolating latent frequency components. However, model-based predictive variance alone proved insufficient for reliable calibration. Embedding the models within a rolling conformal prediction framework restored near-nominal coverage across multiple confidence levels while allowing interval widths to adapt dynamically to changing volatility regimes. Robustness analyses, including walk-forward validation, stress-regime evaluation, and block permutation negative control experiments, indicated that the observed performance was not driven by temporal leakage or alignment artifacts. The results further highlight a trade-off between interval sharpness and tail-risk protection, particularly during extreme market events. Overall, the findings support a shift from return-level prediction toward calibrated uncertainty estimation as a more stable and economically meaningful objective in non-stationary financial environments. Full article

In real-world data, the structural symmetry of time series across temporal scales is often disrupted by the entanglement of trend, seasonal, and high-frequency components. This poses significant challenges to reliable time-series forecasting (TSF) in applications like power dispatch and meteorological analysis. Transformer-based methods typically model mixed signals without explicit inductive bias, while current decomposition-based approaches often rely on linear approximations for trend evolution, leading to unstable extrapolation in long-term forecasting. To overcome these challenges, this paper proposes the Decomposition Patch Time Series Transformer (DecompPatchTST), a hybrid forecasting framework integrating decomposition, trend extrapolation, and patch-based representation. A moving-average operator first decomposes the sequence into trend and residual parts. The trend is extrapolated via a learnable polynomial basis, which adaptively models complex nonlinear trends to ensure smooth long-range dynamics, whereas the residual is divided into temporal patches and modeled by a shared transformer encoder to capture seasonal and high-frequency variations. The final forecast aggregates both components through an additive structure. Experiments on ETT datasets show that DecompPatchTST is more stable with relatively smoother error growth from 96 to 720 forecasting steps. Its practical performance is further demonstrated on real-world Australian electricity data. Full article

The nature of nonlinear dynamics of financial markets results in fractal geometry and chaotic behavior that can be viewed on a variety of scales in time. This paper conducts research on the fractal characteristics of the stock network and its contribution to the price of assets based on the Fractal Market Hypothesis (FMH). A multiscale network centrality measure is built based on high-frequency return dependencies to measure the self-similar, scale-invariant nature of inter-stock dependencies. The network factor and portfolio returns are then broken down with the wavelet packet decomposition (WPD) to obtain frequency-domain profiles, which characterize the variability of risk transmission in relation to investment horizons. The profiles are consistent with scaling properties of fractal, but the decomposition does not identify causal pathways on its own. Estimation of fractal dimension by use of the box-counting technique aided by the Hurst exponent analysis reveals that the A-share of China market exhibited long-range dependence and multifractal scaling. Network factor has the largest explanatory power in mid-frequency between the D5 and D6 bands of 32 to 128 days. This intermediary frequency concentration is consistent with the hypothesis of heterogeneous markets, in which the groups of investors with varying time horizons generate scale-related price dynamics. The addition of the network factor to a 6-factor specification lowers the GRS under the 5-factor specification by 31.45 to 17.82 on the same test-asset universe, indicating better cross-sectional coverage in the sample. The estimates of the Lyapunov exponents (0.039) as well as the correlation dimension ($D_2=4.7$) confirm the presence of low-dimensional chaotic processes of the network factor series, but these values are specific to the Chinese A-share market over the 2005–2023 sample period. These results provide a frequency-disaggregated use of network-based factor modeling and suggest that it can be applicable in multiscale portfolio risk management where the investor horizon is not uniform. Full article

The Bayan Obo Mining District, recognized as the largest rare-earth resource base worldwide, has experienced significant surface instability due to intensive mining and large-scale dumping activities. To address the challenges posed by complex geological conditions and mining-induced disturbances, this study employs dual-ascending Sentinel-1A C-band Synthetic Aperture Radar (SAR) datasets (Path 11 and Path 113) and applies the Small Baseline Subset Interferometric Synthetic Aperture Radar (SBAS-InSAR) technique to retrieve time-series deformation along the line-of-sight (LOS) direction for each track. Through temporal normalization and spatial matching, paired LOS observations from the two tracks were established. Based on the SAR observation geometry and under the assumption that the north–south component is negligible, a LOS projection model was constructed and a geometric decomposition was performed to derive the east–west and vertical two-dimensional deformation fields. The results indicate that the study area is generally stable, while significant subsidence occurs in the northern pit and adjacent waste-dump zones, with local maximum rates approaching 50 mm/year, predominantly controlled by the vertical component. The two-dimensional deformation analysis reveals that vertical displacement dominates surface motion, whereas east–west movement shows smaller amplitudes but clear directional concentration. In particular, the east–west slopes exhibit slightly higher velocities, suggesting a lateral adjustment tendency along this direction, likely related to the overall east–west geometric configuration of the open-pit and waste-dump areas. Time-series observations further reveal that precipitation-related surface deformation occurs with an approximate two-month delay, reflecting the hydrological–mechanical coupling processes of rainfall infiltration, pore-water pressure propagation, and dump-material consolidation. Overall, this study reveals the multi-dimensional deformation characteristics and precipitation-driven stage-wise response of the mining area, demonstrating the effectiveness of the dual-ascending SBAS-InSAR for two-dimensional deformation monitoring in highly disturbed environments, and providing a scientific basis for surface stability assessment and geohazard prevention. Full article

Groundwater is a critical natural and strategic economic resource, and the accurate prediction of groundwater depth dynamics is essential for the rational development and utilization of water resources. However, under the combined influence of climate variability, human activities, and complex hydrogeological conditions, groundwater level time series exhibit strong nonlinear and non-stationary characteristics, posing great challenges to the accurate prediction of groundwater level dynamics. Most existing prediction models rely on sufficient hydro-meteorological and exploitation data that are difficult to obtain in water-scarce regions, or fail to effectively decouple the multi-scale features of non-stationary groundwater level signals, resulting in limited prediction accuracy and insufficient generalization ability. To address these research gaps, this study takes Zhengzhou, a typical water-deficient city in the Yellow River Basin, as the study area, and proposes a hybrid deep learning framework combining Variational Mode Decomposition (VMD) and Long Short-Term Memory (LSTM) neural network for predicting shallow and intermediate-deep groundwater level changes. Kolmogorov–Arnold Networks (KANs) and Gated Recurrent Units (GRUs) are selected as benchmark models to verify the superior performance of the proposed framework. In this framework, the non-stationary groundwater level signal is adaptively decomposed into Intrinsic Mode Functions (IMFs) with distinct frequency characteristics via VMD. An independent LSTM model is constructed for each IMF to capture its unique temporal variation pattern, and the final groundwater level prediction is obtained by linearly reconstructing the predicted results of all IMFs. The results show that the coefficient of determination (R²) of the VMD-LSTM model exceeds 0.90 for all monitoring datasets, with low Mean Absolute Error (MAE) and Mean Squared Error (MSE). It significantly outperforms the benchmark models in handling nonlinear and non-stationary time series features. Using only historical groundwater level data as input, the proposed framework effectively overcomes the limitation of insufficient driving variables in data-scarce regions and fully explores the multi-scale evolution of groundwater dynamics through the synergistic effect of multi-scale decomposition and deep learning. The method presented in this study provides a novel and reliable technical approach for groundwater level prediction in water-deficient and data-limited areas, and also offers scientific support for the rational management and sustainable utilization of regional groundwater resources. Future research will incorporate driving factors such as meteorology and exploitation to further improve the model’s ability to capture abrupt changes in groundwater level dynamics. Full article

Here, we develop a digital community management application (APP) and an energy prediction and analysis system for smart communities. The system integrates the internet of things (IoT) technology and multiple prediction models to improve the intelligence and automation of community energy management. The developed APP has the following functions: user classification, announcement notification, express delivery management, GPS positioning navigation, calendar, and energy forecast. The hardware architecture of the system consists of a voltage/current sensing module, a Wireless Fidelity (Wi-Fi) module, and an Arduino platform, allowing real-time feedback and display of power consumption data. The energy forecasting part proposes a two-layer hybrid model architecture. This architecture combines Seasonal Trend decomposition using Loess (STL) time series decomposition, extreme gradient boosting (XGBoost), and Seasonal Autoregressive Integrated Moving Average (SARIMA) models to predict residential electricity consumption trends over the next 3 years. The results of the model prediction are verified using the data on Taiwan’s electricity consumption. The model accurately predicts the average monthly residential electricity consumption with a relative error of 5.8%, an acceptable energy management accuracy. This system integrates APP applications and efficient prediction models, demonstrating its great potential in smart community energy management and enhanced resident interaction. Full article

Accurate prediction of shipping freight indices, represented by the Baltic Dry Index (BDI), is crucial for operational decision-making and risk management in the shipping industry. Existing models mainly rely on historical time-series data and often overlook the influence of unstructured information such as market sentiment. To address this limitation, this study proposes a dynamic freight rate prediction framework integrating a shipping text sentiment index. First, a shipping news sentiment index is constructed using a RoBERTa-based pre-trained model to quantify the impact of market sentiment on freight rate fluctuations. Second, the BDI series is decomposed and reconstructed through Variational Mode Decomposition (VMD) and Fuzzy C-Means (FCM) clustering to extract multiscale features. Finally, a deep learning based multi-step prediction model is developed by incorporating the sentiment index into the forecasting process. Empirical results show that the proposed model significantly outperforms benchmark models without sentiment information in terms of MAE, RMSE, and R², and demonstrates greater robustness under extreme market conditions. These findings provide a novel methodological framework for improving freight rate forecasting accuracy and offer practical decision support for shipping enterprises. Full article

Accurate forecasting of copper futures prices is crucial for risk management and investment decisions. However, existing approaches primarily rely on historical prices and incorporate behavioral signals without a unified modeling framework. To address this limitation, we propose MBTI-Net (Multi-source Behavior-Triggered Interaction Network), a behavior-aware forecasting framework for heterogeneous copper market data. We first construct a compact behavioral factor from Baidu search indices via a multi-view projection strategy that preserves structural and predictive information. We then develop a complexity-aware reconstruction mechanism that aggregates intrinsic mode functions into multi-frequency components based on fuzzy entropy and energy. To accommodate distributional and volatility differences between behavioral and market variables, we introduce VB-ReVIN (Volatility- and Behavior-aware Reversible Instance Normalization). Building upon these representations, MBTI-Net models dynamic multi-source interactions triggered by behavioral intensity and market conditions, enabling adaptive cross-source information fusion. Experiments on LME and SHFE copper futures datasets demonstrate consistent improvements over state-of-the-art benchmarks, highlighting the importance of explicitly modeling behavior-driven dependencies in financial forecasting. Full article

Modeling nonstationary time series in financial and energy markets remains challenging due to nonlinear dynamics, volatility clustering, and frequent regime shifts that distort the underlying probabilistic structure of the data. This study introduces a novel probabilistic–statistical decomposition framework, termed Robust Adaptive Decomposition (RAD), designed to preserve probabilistic symmetry between deterministic and stochastic components. In this context, symmetry refers to maintaining statistical balance—particularly in the means, variances, and distributional structures—between the extracted modes and the residual series, thereby preventing artificial bias or variance distortion during decomposition. The RAD framework adaptively determines the optimal number of modes needed to effectively separate short-term fluctuations from long-term structural movements. Unlike conventional techniques, such as Empirical Mode Decomposition (EMD), Ensemble EMD (EEMD), and CEEMDAN, the proposed method incorporates a robustness mechanism that mitigates mode mixing and reduces distortions induced by extreme shocks and regime transitions. The empirical evaluation is conducted on six oil-related energy commodities—Brent crude oil, kerosene, propane, sulfur diesel, heating oil, and gasoline—whose price dynamics exhibit pronounced nonlinearity and structural volatility. When integrated with ARIMA forecasting models, the RAD-based framework consistently outperforms benchmark decomposition approaches. Across all datasets, RAD–ARIMA achieves reductions of approximately 65–90% in MAE, 60–85% in RMSE, and up to 95% in MAPE relative to CEEMDAN-based models. These results demonstrate that RAD provides a mathematically rigorous and computationally efficient preprocessing mechanism that preserves statistical equilibrium while effectively disentangling deterministic structures from stochastic noise. Beyond oil markets, the framework offers broad applicability in econometric modeling, financial forecasting, and risk management, contributing to probability- and statistics-driven symmetry analysis in complex dynamic systems. Full article

The frequency of extreme weather events has become higher, and electricity consumption has also become more complex. These changes increase the risk of overload in distribution transformers (DTs), and this risk threatens the stability and reliability of the power grid. Existing methods have significant limitations. Traditional static threshold methods (based on DGA gas ratios and electrical signal thresholds) fail to consider temporal changes and complex links between factors, while modern machine learning models lack cause–effect relationships over time and clear ways to describe uncertainty. With such motivations, this paper proposes a causal-enhanced hybrid framework, which combines Long Short-Term Memory (LSTM) networks and Random Forest (RF) algorithms. The framework uses causal Seasonal Trend decomposition using Loess (STL) to reveal load patterns at different time scales. The mutual information index and spatiotemporal graph convolutional network (ST-GCN) are used to explore nonlinear relations and reveal how temperature affects load changes. The LSTM model captures time dependence in load series, and the Bayesian optimized Random Forest is used to solve the problem of data imbalance and quantify uncertainty. In addition, the framework constructs an early warning system that combines data from many sources in real time. Test results show that the proposed algorithm exhibits excellent performance in multi-source data environments. Full article

Self-supervised contrastive learning has recently shown promise for time-series representation learning, yet most existing methods treat sequences holistically and leave trend and seasonal components entangled, limiting their effectiveness for long-horizon multivariate forecasting. We study decomposition-aware representation learning for time-series forecasting without negative pairs. We propose the Trend-Season Contrastive Learner (TSCL), a Siamese framework that decomposes each series into trend, seasonality, and residual components, encodes trend and seasonality with dedicated encoders and a learnable Fourier layer, and optimizes a positive-pair contrastive objective over component-wise representations. Experiments on five public benchmarks (ETTh1, ETTh2, ETTm1, ETTm2, and Weather) show that TSCL consistently improves downstream forecasting across prediction horizons. Averaged over all datasets and horizons, TSCL achieves 0.489 MSE and 0.488 MAE, yielding an about 20–30% lower error than representative contrastive baselines (e.g., SimTS and CoST). Paired t-tests further confirm that the improvements are statistically significant in most settings. These results indicate that decomposition-aware contrastive learning yields robust and generalizable representations for long-horizon forecasting across diverse temporal resolutions. Full article