Crude oil prices exhibit significant nonlinearity, nonstationarity, and multi-scale fluctuation characteristics, making decomposition-ensemble methods widely adopted to improve forecasting accuracy. However, existing decomposition-ensemble studies largely rely on a bottom-up aggregation strategy, where final forecasts are primarily derived from the direct summation of single-level components, thereby overlooking the trend and structural information embedded in the original series and other hierarchical levels. To address this issue, this paper proposes a decomposition-ensemble crude oil price forecasting method based on forecast reconciliation to systematically evaluate the impact of multi-level information coordination on predictive performance. Empirical results based on WTI and Brent crude oil prices demonstrate that most reconciliation methods achieve superior performance compared to the traditional bottom-up aggregation approach across various scenarios, indicating that multi-level information coordination significantly enhances the accuracy of crude oil price forecasts. Furthermore, this study shows that conventional decomposition-ensemble forecasting can be extended to a hierarchical reconciliation forecasting problem, and that hierarchical reconciliation need not be confined to natural hierarchies such as regions, industries, or products, but can also be extended to artificial multi-scale hierarchies constructed through decomposition and ensemble, thereby offering a new research paradigm for energy price forecasting.

Water quality index (WQI) forecasting is essential for safeguarding aquatic ecosystems and supporting effective environmental decision-making. However, owing to the influence of complex hydrodynamics and external disturbances, traditional forecasting approaches based on point estimates often fail to capture predictive uncertainty, limiting their effectiveness in real-world management scenarios. This study proposes a spatiotemporal interval prediction framework that explicitly models the dynamic propagation of uncertainty across time and space. By decomposing interval-valued WQI series using bivariate ensemble empirical mode decomposition (BEEMD) and modelling the spatiotemporal evolution of interval uncertainty through multiscale temporal learning and graph-based spatial dependency modelling, the method predicts structured fluctuation ranges, delivering uncertainty-aware forecasts that go beyond conventional point-based methods. Experiments on Chaohu Lake demonstrate improved predictive accuracy and early warning capability, underscoring the potential of uncertainty-aware water quality modelling.

Large language model (LLM)-based time series forecasting (TSF) has demonstrated strong performance by separately modeling time series and textual information. However, prior text-related research has primarily focused on prompt design and text converted from time series, while the utilization of exogenous textual signals, such as event information, remains insufficient. Moreover, we observed that existing LLM-based solutions often struggle to achieve stable and structure-aware cross-modal representations when exogenous textual signals are incorporated. To address these issues, we introduce TRDA-TS, a LLM multimodal time series forecasting framework based on a regularized diffusion cooperative fusion and text-enhanced mechanism. Specifically, we introduce multi-scale and multi-frequency modeling into the transformer architecture, reorganize fragmented textual data into causally filtered trend descriptions, and encode the resulting compact textual records using a frozen GPT-2 backbone to obtain contextualized textual representations for downstream cross-modal fusion. The extracted representations are subsequently passed through a multimodal fusion layer, which consists of a bidirectional contextual graph diffusion module and a target-aware cross-modal alignment loss for stabilizing cross-modal interaction. Finally, a downstream prediction head generates the final forecasts. Extensive experiments conducted on nine datasets across diverse domains, compared against eight state-of-the-art TSF baselines, demonstrate the effectiveness and accuracy of the proposed TRDA-TS model. Compared with state-of-the-art (SOTA) baselines, TRDA-TS achieves an average improvement of 18.22% in MSE and 12.55% in MAE across all datasets.

With the advancement of modern information technology, the collection and analysis of multi-source time series data play an important role in decision-making and process management. However, due to the complexity of capturing the dynamic features for spatio-temporal information, multi-source time series forecasting remains a challenging problem. Previous spatio-temporal models usually overlook the integration of physical and spatial dependencies between multivariable data features, as well as the effects of dynamic diffusion. To address these challenges, the authors propose a Spatio-Temporal Information Dual-layer Diffusion Network (STIDDN) for multi-source time series collaborative forecasting. STIDDN employs residual LSTM networks for temporal dependency modeling of internal features at each station, while the Dual-layer Diffusion Graph Convolutional Network (Dual-DGCN) focuses on capturing both physical and spatial dual-layer dependencies between stations, along with the dynamic diffusion process. By integrating spatio-temporal information through a skip-connection and multi-head attention mechanism, STIDDN achieves effective collaborative forecasting across multiple stations. Extensive experimental results demonstrate that the proposed model consistently outperforms advanced baseline models on two different spatio-temporal prediction task datasets.

Accurate predictions of air quality enable governments and relevant authorities to take promptly measures for protecting public health. With the increasing time-varying nature of air pollutants, predicting daily average concentrations alone is no longer sufficient for environmental management and risk warning. Hence, this paper proposes a multi-resolution interval-valued PM2.5 concentration combination prediction model, which based on interval decomposition and attention mechanism reconstruction. Firstly, the interval-valued time series (ITS) was decomposed and adaptively reconstructed using the binary empirical mode decomposition (BEMD) algorithm and attention-based reconstruction. Subsequently, multi-resolution linear projection layers were applied to extract temporal features from the time series. Finally, a hybrid prediction module was implemented that combines CNN and LSTM to predict each subsequence and integrate them to derive the final interval prediction values for PM2.5. In the proposed framework, the reconstruction technique effectively resolved the issue of inconsistent numbers of different feature decomposition subsequences, while the linear projection layer fully captured the multi-resolution characteristics of the time series. Empirical studies conducted in three districts of Beijing showed that, compared to state-of-the-art baseline models, the framework reduced the average values of five interval evaluation metrics by 11.2%, 17.4%, 11.7%, 10.5%, and 14.8%, respectively. This interval-valued prediction framework can effectively assist urban air quality management and warning.

Water quality is vital for both human health and the ecological environment, and accurate predictions of the Water Quality Index (WQI) playa key role in timely monitoring of water conditions, providing essential support for environmental protection and management efforts. However, most existing studies focus on single monitoring sites, overlooking the interactions between neighboring locations. To address this limitation, this paper proposes a comprehensive water quality prediction framework that integrates spatial feature extraction, ordinary differential equations, and physical-informed constraints, called PI-GCN-SRLSTM. This framework enables WQI predictions across multiple sites and future time steps. First, a two-layer Graph Convolutional Network (GCN) is employed to capture the spatial features of WQI. Next, an enhanced Long Short-Term Memory network (LSTM), based on a second-order residual network (SRLSTM), is designed to capture complex temporal dynamics. Finally, to ensure predictions remain realistic, a gradient constraint is incorporated into the model's loss function, improving the stability and reliability of the results. Experimental results based on the Chaohu lake dataset demonstrate that the proposed framework outperforms state-of-the-art benchmark models across six evaluation metrics: RMSE, MSE, MAE, MAPE, m1, and m2, with improvements of 30.47%, 43.04%, 29.57%, 29.92%, 0.83%, and 1.63%, respectively.

Accurate natural gas price forecasts play a critical role in mitigating market volatility, guiding commodity trading, and enhancing regulatory decision-making. However, the existing natural gas price prediction studies predominantly rely on data with a limited lag period as the forecast input, ignoring historical information, and considering less the complex information embedded in historical data. Therefore, we propose a novel probabilistic connectivity network (PCnet) link prediction model for natural gas prices, comprising four key components: data decomposition, node influence measurement, probabilistic network construction, and combination forecasting. First, the Aquila Optimizer is employed to optimize the parameters of Variational Mode Decomposition to decompose the original data and extract its intrinsic mode functions, providing a better feature. Second, a K-shell method positioned with neighbor and Shell-diversity (KPNS) is proposed to comprehensively and effectively measure the contained information between nodes and extract structural features basis for subsequent modeling. Third, a probabilistic connectivity network (PCnet) is constructed based on the KPNS, effectively preserving the uncertainty information of the nodes. Finally, a Local Random Walk with Restart is used to locate similar nodes in the network, and the prediction results are obtained with a combination of Support Vector Regression, CatBoost, and Extra Trees according to the link prediction idea. The empirical results validate the outstanding predictive accuracy of the model, highlighting its potential applicability in natural gas price forecasting.

Group decision-making refers to the collective decision-making of multiple decision-makers to solve a common problem. However, decision-makers typically exhibit different psychological attitudes and behaviors in the decision-making process, which leads to actual decisions deviating from the solution recommendations obtained by traditional quantitative methods. More importantly, most existing studies on consensus fail to simultaneously consider the internal process of consensus building and psychological behaviors of decision-makers. To address this gap, this paper proposes a novel group decision-making method using a minimum deviation distribution ranking model and fairness concern-based consensus building. First, a fairness utility function is established to compare evaluation information from different decision-makers capturing fairness concern between individuals. Then, an optimization model is developed to determine decision-makers’ weights. Additionally, a fairness-based consensus model is proposed, which considers decision-makers’ acceptable adjustment range to avoid excessive information loss. To derive the priority vector, we develop a ranking model based on minimum deviation distribution by controlling the deviation in the minimum range. Finally, we provide a numerical example and comparative analysis to evaluate the effectiveness and superiority of our method, and conduct a robustness test to verify the stability and reliability of the ranking model.

Efficient prediction of air pollutant concentration is of great significance to air pollution prevention, human health protection, and cleaner production. Previous air quality studies mainly focused on point-based and interval-based forecasts, and a potential problem with these methods is that some important information may be lost. Therefore, this paper puts forward a novel ternary interval decomposition ensemble paradigm for air pollutant concentration forecasting, which is capable of capturing the daily minimum, daily average, and daily maximum of air pollutant concentration concurrently. In this paradigm, the ternary interval-valued air pollutant concentration time series (TIAPCTS) is innovatively constructed. Multivariate empirical mode decomposition is first applied to decompose the TIAPCTS into multiple ternary intrinsic mode functions (TIMFs) and one ternary residue (TR). Then, the lower, middle, and upper bounds of each TIMF and TR are simultaneously fitted and predicted by the three-output multivariate relevance vector machine. To obtain better final outputs, an optimal variable weight ensemble approach is suggested to integrate the forecasting results of TIMFs and TR. The novelty of this study comes from the ternary interval forecasting perspective, multivariate modeling techniques, and weighted ensemble strategy, which not only fully take possible associations among the lower, middle, and upper bounds into account but also improve the modeling efficiency while generating multiple correlated outputs. The proposed paradigm is justified with six kinds of real-world air pollutant concentration data from Beijing and Shanghai, China, indicating it is a promising alternative for air pollution concentration analysis and forecast.

Accurate multi-energy load prediction is essential for effective energy management and ensuring grid reliability. Existing methods often struggle to fully capture the intricate temporal complexities and inter-variable dependencies present in multivariate time-series data. To address this, we propose a multi-scale temporal channel features fusion-based method for multi-energy load prediction. Firstly, we introduce a Dynamic Channel Weighted Strategy, which adaptively reconstructs intrinsic mode functions derived from Variational Mode Decomposition, reducing the number of channels and computational costs while retaining essential features. Secondly, we develop an Adaptive Channel Fusion LSTM (ACF-LSTM) by integrating learnable graph neural networks and graph convolution operations into traditional LSTM cells, enabling effective modeling of channel correlations in multivariate time series. By modeling multi-energy load data from dual perspectives using the ACF-LSTM, we construct a Temporal-Channel Feature Fusion (TCFF) block that combines both time and frequency domains for comprehensive feature extraction. A learnable frequency selection mechanism within the TCFF block adaptively identifies relevant frequency components, enhancing the model's ability to capture periodic patterns and long-term dependencies. Experiments on the Power Consumption dataset show that our model achieves a significant improvement in accuracy, reducing MAE by 38.60% and RMSE by 32.56%, highlighting its reliability and generalization for multi-energy load prediction.

The accuracy of economic forecasting directly influences the formulation of economic policies and profoundly impacts the stable operation of the economy. As a pivotal indicator of economic activity, predicting the producer price index (PPI) is crucial. Although most existing research is focused on the overall PPI, economic and financial institutions are increasingly interested in its partially disaggregated components. Therefore, this paper proposes a hybrid hierarchical deep network prediction framework called Attention-HRNN-GRU (AHG) with parameter adaptive transfer, which integrates algorithms such as the attention mechanism, the Hierarchical Recurrent Neural Network (HRNN) and the Gated Recurrent Unit (GRU). First, an independent GRU network is designed and trained separately for each PPI level to perform preliminary predictions. The internal parameters of each level’s network are preserved to facilitate interlevel information transfer, forming an initial HRNN framework. An attention mechanism is then introduced to adaptively adjust the parameters of the upper-level prediction model that are used as the prediction parameters for the lower-level model. This process enables effective information transfer across multiple levels, producing high-accuracy prediction outcomes. This method effectively addresses a common issue in traditional hierarchical data prediction, where the direct application of upper-level parameters to lower-level data often overlooks variations between sequences. Experimental results show that the proposed AHG model markedly reduces prediction errors compared with those of the current advanced HRNN model. For example, the root mean square error (RMSE) of the producing materials index improved by 13.11

Transformer-based models have significantly advanced long-term time series forecasting by leveraging self-attention mechanisms to capture long-term dependencies. However, these models face high computational costs, slow inference speeds, and limitations in utilizing information from longer lookback windows. Additionally, existing methods often neglect implicit spatial dependencies between variables, and struggle with semantic misalignment and insufficient diffusion of spatial information. To address these challenges, we propose DTSFormer, a Decoupled Temporal-Spatial Diffusion Transformer designed specifically for long-term time series forecasting: (1) DTSFormer effectively integrates temporal features with implicit spatial attributes, ensuring comprehensive utilization of both temporal and spatial information. (2) DTSFormer introduce a Mix-hop Diffusion layer to effectively propagate and aggregate spatial information while preserving the original graph structure, significantly improving the accuracy of spatial information dissemination. (3) we develop a cross-diffusion attention mechanism based on the Expectation-Maximization algorithm, which integrates graph structure information with varying semantics under a seasonal trend decomposition framework. This approach enhances the fusion of semantic information from different graph structures and reduces computational complexity. Our extensive experiments on multiple benchmark datasets across different domains demonstrate that DTSFormer consistently achieves state-of-the-art performance in both accuracy and efficiency. These results validate DTSFormer as a robust and scalable solution for advanced long-term time series forecasting tasks.

The intermittency and variability of photovoltaic (PV) power generation make accurate forecasting essential for reliable grid integration. While advanced PV plant sensors now provide rich meteorological data, fully leveraging this complex information remains a significant challenge. This paper proposes an enhanced PV load forecasting framework that captures dynamic interdependencies and multiscale periodicities among meteorological factors. The framework consists of three key modules: (1) fine granularity-aware feature aggregation, which integrates fine-grained data into coarse-grained prediction tasks to uncover latent behavioral patterns; (2) dual temporal sampling strategies that combine a multiscale frequency approach with a multi-stride sampling method to enhance the ability of LSTM to learn periodic patterns across different time scales; and (3) multiscale channel correlation modeling, which employs a trainable channel correlation graph with graph convolution operations to model dynamic intervariable dependencies across multiple scales while also reducing noise sensitivity compared with conventional CNN-based approaches. The experimental results on the Alice Springs meteorological dataset demonstrate that the proposed model significantly outperforms state-of-the-art methods, achieving a 23.87% reduction in the RMSE for PV power forecasting.

The increasing demand for electricity underscores the need for accurate power load forecasting to optimize grid management and resource allocation. With the emergence of more complex multi-energy hybrid systems, the resulting multivariate power load data pose significant challenges for precise forecasting. To address this, we propose a novel framework that integrates Variational Mode Decomposition (VMD) with an Encoder-Decoder architecture featuring customized Gaussian Implicit Spatio-Temporal (GIST) blocks to uncover implicit spatial dependencies across temporal and multi-feature dimensions. Initially, VMD decomposes the original time series into multiple resolution components, effectively reducing noise and extracting intrinsic temporal patterns. These components are then processed by an Encoder-Decoder network for prediction. Within each GIST block, token embedding is applied to the input before being fed into a Gaussian Mixture Model (GMM)-based implicit spatio-temporal representation module. Unlike conventional expectation-maximization (EM) algorithms, our learned Gaussian modeling approach provides a more adaptive and computationally efficient alternative for residential power load forecasting. Temporal dependencies are further captured through Long Short-Term Memory (LSTM) units and attention mechanisms across subsequent blocks, enhancing the model's predictive capability. Experimental validation demonstrates the superior performance of our proposed model, achieving reductions of 7.98% and 9.32% in Mean Absolute Error (MAE) and Root Mean Square Error (RMSE), respectively, compared to existing forecasting models. Notably, our GMM-based approach outperforms traditional two-dimensional convolution-based methods, yielding improvements of 11.3% and 5.72% in MAE and RMSE, highlighting the efficacy of our framework in handling complex multivariate power load data.

Accurately predicting new energy vehicle (NEV) sales not only contributes to promoting sustainable mobility but also provides support for resource allocation and infrastructure planning. To address the limitations of existing methods in integrating market sentiment and capturing multiscale data characteristics, this paper proposes a hybrid forecasting model that incorporates complexity self-awareness and sentiment score correction. First, a comprehensive time series dataset is constructed using historical sales data and the corresponding online reviews. Second, the market-oriented sentiment score self-correction (MSSC) algorithm is applied to dynamically optimize sentiment variables. Then, ensemble empirical mode decomposition (EEMD) is used to extract multifrequency components, which are evaluated and classified via the self-aware complexity-driven intelligent quantification (SCIQ) method for refined modelling. An empirical analysis based on BYD Tang NEV sales data demonstrates that the proposed model outperforms state-of-the-art benchmark models across four evaluation metrics. Moreover, after incorporating SCIQ and MSSC, the prediction accuracy improved by 30.04% and 22.34%, respectively, in terms of the RMSE, and by 2.04% and 1.39%, respectively, in terms of the first-order effectiveness. Furthermore, SHAP analysis is employed to interpret key influencing factors, enabling the formulation of consumer-oriented policy recommendations that support high-quality NEV industry development.

Robotic grasp is one of crucial visual tasks for service robots as well as industrial robots. The existing deep vision learning approaches for robotic grasp most utilize RGB-D as single modality or indiscriminating usage of them, which often overlook the valuable depth information in RGB-D images. To address this limitation, this paper proposes a smart dual-modal aligned transformer deep network (SATNet), which is not only very lightweight but also well performed for robotic grasping tasks using RGB-D images. Specifically, a novel ATFormer module with the two parallel aligned transformer encoder blocks are elaborated to fuse global feature maps efficiently. The experiments on Cornell dataset demonstrate that the proposed model outperforms existing methods, which not only enjoys impressively lightweight framework with only 0.27M parameters, but also achieves accuracy of 97.8% and inference time of 16.3ms.

Aiming at the impact of financing structure and cash holdings on enterprise innovation, this article uses the system GMM model. The empirical findings show that the higher the proportion of equity financing, the more cash companies hold, and the more R&D expenses companies put on. Mediation effect model and GMM method are used here. The total effect of financing structure on enterprise innovation c = 0.028, the direct effect of financing structure on enterprise innovation c’ = 0.025, and the indirect effect of financing structure on enterprise innovation a × b = 0.121 × 0.020, these effects are statistically significant. Cash holdings is an intermediary channel between financing structure and enterprise innovation. In addition, using quantile grouping and interaction items of financial marketization degree, this paper finds that, when financial marketization degree is low, the effect of equity financing in external financing through cash holding channels to promote the growth of R&D expenses is more significant than when financial marketization degree is high. With the help of the placebo test, it is of great significance to develop the stock market and raise the degree of financial marketization for promoting enterprise innovation.