Traditional heterogeneous autoregressive models of realized volatility (HAR-RV) often fail because of the invalidity of residual randomness assumptions, and limitations arise since their reliance on specific data features for volatility characterization. To address these issues, this study constructs uncertain HAR-RV models based on uncertainty theory. Building on this foundation, this study further introduces uncertain quantiles into the modeling framework, develops uncertain quantile HAR-RV models, and provides parameter estimation along with rigorous mathematical proofs. Finally, this study applies the constructed models to volatility forecasting in China's crude oil futures market. Through randomness tests, out-of-sample evaluations, and robustness tests, the limitations of traditional models that lead to failure are systematically validated, and the superior predictive performance of the proposed models across different quantiles is demonstrated. Furthermore, leveraging the unique perspective of uncertainty theory in handling imprecise data, a new perspective for volatility forecasting that uses uncertainty distributions to characterize the daily realized volatility is provided.

In the context of highly digitalized and complex financial markets, financial forecasting and risk monitoring face challenges such as strong data nonlinearity, frequent fluctuations, and high real-time requirements. To address the difficulty of traditional forecasting models in balancing accuracy and stability, this paper constructs an intelligent analysis algorithm for financial forecasting data and designs a financial risk monitoring system integrating forecasting, identification, and early warning based on this algorithm. By introducing a multi-model fusion mechanism and a dynamic risk threshold method, the synergistic linkage between forecasting results and risk monitoring is achieved. Experimental results show that, compared with traditional time series models, the mean squared error of the multi-model fusion forecasting algorithm decreases from 0.0218 to 0.0093, and the goodness of fit improves to 0.938; the risk monitoring module achieves an identification accuracy of 94.1% under high-risk conditions, with an average response time of less than 2 seconds; the system maintains a task success rate of over 99.2% for 168 hours of continuous operation. The research results verify the comprehensive advantages of the proposed method in terms of financial forecasting accuracy, timeliness of risk identification, and system stability, providing effective technical support for intelligent financial risk control and regulatory decision-making.

Accurate prediction of high-dimensional macroeconomic indicators is crucial for evidence-based policy formulation and market decision-making. However, such data exhibit inherent signal characteristics including non-stationarity, noise contamination, multicollinearity, and complex nonlinear dependencies, which are key challenges in signal processing. To address these issues from a signal processing perspective, this paper proposes a deep learning-enhanced factor model named 3PRF-SAM-Transformer, which formulates macroeconomic time series as a superposition of common signal factors, residual signal factors, and additive noise. The model employs the Three-Pass Regression Filter (3PRF) to extract low-frequency common signal factors from high-dimensional datasets, and utilizes the self-attention mechanism within the Transformer architecture to capture residual nonlinear dependencies relevant to the target variable. Furthermore, by integrating the Sharpness-Aware Minimization (SAM) optimizer, the Transformer model is guided to converge toward flatter minima of the loss landscape, thereby effectively mitigating overfitting issues associated with its large parameter capacity. We conducted comparative experiments against multiple hybrid models, including artificial neural networks (ANN), recurrent neural networks (RNN), long short-term memory networks (LSTM), and gated recurrent units (GRU) combined with 3PRF. Experimental results demonstrate that 3PRF-SAM-Transformer consistently outperforms all baseline models in out-of-sample prediction, achieving not only higher prediction accuracy but also stronger generalization capabilities.

The Vector AutoRegressive (VAR) model is widely used in macroeconomic modeling but struggles with the curse of dimensionality. The Factor-Augmented VAR (FAVAR) model addresses this by extracting latent factors, typically via Principal Component Analysis (PCA), yet remains constrained by linear structures and limited adaptability to high-dimensional, nonlinear macroeconomic relationships. To overcome these challenges, this study proposes a Gromov-Wasserstein Autoencoder (GWAE)-FAVAR framework, integrating optimal transport theory to improve factor extraction while preserving intrinsic economic structures. Empirical analysis on U.S. macroeconomic data-including energy, inflation, national accounts, labor markets, and government finance-demonstrates that GWAE-FAVAR enhances factor interpretability and predictive accuracy. Additionally, we introduce a Transformer-Enhanced VAR, leveraging self-attention mechanisms to capture long-term dependencies and nonlinear interactions in macro-financial data. Results indicate that our approach significantly improves forecasting performance, particularly during economic shocks and structural shifts. This study bridges econometrics and machine learning, advancing macroeconomic modeling through geometric deep learning. The proposed framework offers a robust and interpretable alternative to traditional factor models, enhancing macroeconomic inference and forecasting.

Temperature is an important factor affecting daily life, and accurate multi-step temperature prediction can provide essential support for weather prediction, energy management, agricultural planning, and disaster mitigation. However, as the prediction horizon extends, the nonlinear nature of temperature data becomes more prominent, making it increasingly difficult to accurately model temporal variation patterns. Regarding this issue, this paper proposes a multi-step temperature prediction system which comprises a multi-frequency information extraction subsystem and a high-precision prediction subsystem. The multi-frequency information extraction subsystem employs a decomposition-clustering-reconstruction strategy to obtain high, medium, and low-frequency data from the original temperature data. In the high-precision prediction subsystem, we employ an encoders-decoder architecture with an adaptive weighting mechanism to extract features from multi-frequency data and produce prediction results. In addition, to further enhance prediction accuracy, time-frequency domain fusion is applied during training to capture differences between predictions and actual values from multiple angles. To evaluate the performance of the prediction system, three sets of comparative experiments are conducted on four datasets, demonstrating that the proposed system outperforms other benchmark models.

This paper enhances gold futures volatility forecasting by integrating a novel growth rate changepoint correction (GRCPC) filter into the traditional time-varying parameter stochastic volatility in mean (TVP-SVM) model. The GRCPC filter adaptively corrects data using the Prophet model's trend term growth rate to adjust changepoints, significantly filters noise and aligns corrected values with the overall trend. Out-of-sample results show that the TVP-SVM-GRCPC model markedly improves gold futures volatility forecasting accuracy. Further study evaluates the model's efficacy in forecasting volatility during various risk periods and examines the impact of selectively applying the filter strategy in large sample.

This study introduces a novel aligned technical index, derived from multiple technical indicators, that encompasses a broader spectrum of technical measurement strategies than those obtained from previous 3PRF (Three-Pass Regression Filter) research. Our empirical results demonstrate that this index exhibits significant predictive power for new energy price returns in both in-sample and out-of-sample tests. This index is extracted using the 3PRF method and yields significantly better results than those obtained with traditional methods. Considering that the market typically operates in two states, we incorporate a regime-switching model with time-varying transition probabilities into our forecasting framework. The findings indicate that the technical index influences the probability of regime transitions between states and that the inclusion of a regime-switching model further enhances predictive performance. The incorporation of the regime-switching mechanism further improves the predictive performance of the model. Moreover, from an asset allocation perspective, both the technical index and regime-switching models deliver considerable economic value to mean-variance investors.

Crude oil plays a critical role in the global energy system, and fluctuations in its price have far-reaching implications for economic stability and energy policy. This study develops a novel Multi-Graph Deep Forecasting Model (MGDF) framework to enhance the accuracy of crude oil price forecasting. The proposed model integrates thirteen influential variables across six dimensions: macroeconomic policy, market sentiment, geopolitical risk, supply and demand, cross-market influence, and economic activity as embedded features. A central innovation of MGDF is the construction of multi-layer graphs that capture both quantitative and semantic dependencies: (i) mutual information graphs characterize evolving linear and nonlinear interrelations among predictors, while (ii) LLM-based text graphs extract semantic linkages from unstructured news data using large language models. These graph embeddings are combined with Temporal Convolutional Networks (TCNs) to capture time-series patterns and integrated with a Long Short-Term Memory (LSTM) architecture for sequential forecasting. Empirical results demonstrate that MGDF consistently outperforms benchmark models across multiple evaluation metrics, including MSE, MAE, RMSE, and R-squared. Robustness is further confirmed through Model Confidence Set (MCS) and Diebold-Mariano (DM) tests, underscoring the model’s statistical reliability. The findings provide both a methodological contribution to the energy forecasting literature and practical insights for policymakers and market participants in mitigating risks associated with oil price volatility. JEL classification: C22; C53; Q43

In a complex and volatile macroeconomic environment, precious metals, which have the functions of preservation, appreciation, and hedging, play an important role in investment risk management. Therefore, this study adopts the extended GARCH-MIDAS model to investigate the underlying connection between gold price volatility and different uncertain shocks. In this paper, we consider five uncertainty indicators and then decompose them into different states to capture their shock sizes. Next, we introduce uncertainty shocks into the MIDAS structure to test whether they contain relevant and valid information about gold price volatility forecasts. Specifically, parameter significance suggests a positive association between uncertain indicators and gold price volatility, but variability in the influence of their shock sizes on gold price volatility. Out-of-sample results present that the extended model that includes asymmetric shock sizes outperforms other competitive models. Besides, the model that includes large shock sizes exhibits better predictive performance than the model that includes small shocks. Finally, based on the empirical analyses, this paper provides new insights for the gold industry, futures exchanges, government regulators, and investors engaged in futures hedging to achieve risk control and financial stability in response to uncertain shocks.

This paper utilizes a hybrid model to analyze the impression of information from the GECON indicator on the volatility prediction of the clean energy market. The model architecture is constructed by embedding a recurrent neural network (RNN) into the GARCH-MIDAS model. The results show that RNN-GARCH-MIDAS-GECON achieves optimal ranking in volatility prediction. This work confirms the advantages of embedded hybrid integrated models in capturing nonlinear information in financial markets and achieving significant progress in volatility forecasts. Notably, this research will help to promote the construction of clean energy development and energy transition pathways.

Exchange rate changes affect economic activities and reflect the country's financial strength. In the current critical energy transition period, are exchange rate changes affected by the global energy transition? This paper focuses on three major exchange rates: USD/EUR, USD/CNY, and USD/JPY. Besides, we use total energy consumption, renewable energy consumption, and CO2 emissions in the residential, commercial, and industrial sectors to capture the energy transition progress. We have the following findings. On average, total energy consumption, renewable energy consumption, and CO2 emissions in different sectors will not affect USD/EUR and USD/JYP but USD/CNY. However, further research shows that industrial total energy consumption will have a long-term impact on USD/JYP. USD/JYP will react to residential renewable energy consumption in the short term while the industrial sector in the middle-long term. Residential and commercial total energy consumption have a short-lived impact on USD/CNY. Residential and commercial renewable energy consumption can affect USD/CNY in the long term while the impact of the industrial sector on USD/CNY is transient. In addition, all sectors' CO2 emissions have a significant short-term impact on USD/CNY. Therefore, countries should formulate more flexible exchange rate policies based on energy transition needs in different end-use sectors.

This paper aims to explore the impact of war attention on stock volatility predictability by constructing a new war attention index and employing an extended GARCH-MIDAS-ES model. The war attention index is developed by incorporating the Google search volume data for 56 warrelated keywords using natural language processing methods and dimensionality reduction techniques. Since war attention is considered an exogenous shock, we modify the new extended MIDAS model by incorporating the extreme effects caused by war attention into the GARCHMIDAS-ES framework. Compelling evidence demonstrates that our proposed war attention index is a statistically significant driver of S&P 500 volatility, and our extended model exhibits higher out -of -sample predictive accuracy as it captures both the normal and extreme effects of war attention on stock volatility within the MIDAS framework. By examining how war attention affects stock volatility predictability during the ongoing Russia-Ukraine war, we observe that the extended model's forecasting performance deteriorates as the forecasting horizon increases to a relatively large extent, which is in line with the findings of Andrei and Hasler (2015).

By constructing a novel index, the oil security attention index, this paper uses the heterogeneous autoregressi (HAR)-type and its extended models to study whether oil security attention can predict oil volatility. Based on the definition of the different dimensions of oil security and three-pass regression filter (TPRF) dimension reduction technology, combined with Google search volume data of 23 keywords related to oil security, the oil security attention index is constructed. Considering the potential nonlinear relationship between attention and oil volatility, we incorporate asymmetric effects in the new extended HAR-type models. The research findings show that the oil security attention index we propose can capture the volatility of West Texas Intermediate. The out-of-sample results indicate that the extended models have better predictive power, which confirms the asymmetric relationship between oil security attention and oil volatility. In the robustness analysis, we compare TPRF with traditional principal component analysis (PCA) and partial least squares (PLS), and show that the oil security attention index constructed using TPRF has more favourable information than PCA and PLS to capture the oil security attention of the public.

Despite widespread employment of digital technologies in renewable energy generating, transmitting, distribution, storage, and pricing, there is a lack of empirical investigation into the effects of digital technologies on renewable energy development. In this context, this paper estimates the influence of digital technologies on renewable energy market integration in China. This study conducts a series of regressions based on provincial data from 2003 to 2020 and an index of digital technologies measured with the entropy weight method, and finds that digital technologies have significantly bolstered renewable energy development in China. To analyze how to overcome specific barriers to renewable energy expansion, this paper also examines the case study of Qinghai province, which has the potential to power itself with 100% renewable energy. These findings provide valuable policy guidance for ASEAN countries regarding achieving carbon–neutral energy transitions.

The impact between time series may differ at different frequencies and time periods, and certain external events may cause sharp fluctuations in new financial markets. It is essential to conduct additional analyses on the extreme relationships in the time-frequency domain. However, extreme causal relationships and time-varying characteristics under various shocks usually cannot be detected simultaneously. Therefore, we reveal the extreme impacts and dynamic changes in global economic conditions on renewable energy by extending a fresh extreme wavelet-based method. Our results reveal significant extreme asymmetric impacts of economic conditions on renewable energy. Moreover, this effect was reinforced by extreme events such as the outbreak of the global financial crisis and the Russia–Ukraine conflict. This paper provides a deep analysis of economic conditions and renewable energy from a time-frequency domain perspective, which can aid investors and policy-makers in making relevant decisions under extreme conditions.

This study investigated whether a renewable energy attention (REA) index, based on natural language processing, Google search volume data, and dimensionality reduction methodology, can predict crude oil volatility. Considering the possible non-linear and time-varying effects, we adopted the time-varying transition probability Markov switching heterogeneous autoregressive-realized volatility (TVTP-MS-HAR-realized volatility (RV)) model. To further represent the impacts of REA, we developed an asymmetric TVTP-MS-HAR-RV model based on this model framework, i.e., the ASTVTP-MS-HAR-RV model. According to the results, the in-sample estimates indicated that West Texas Intermediate (WTI) volatility is more affected by negative REA shocks than by positive ones. Moreover, REA predicted WTI volatility better during low-volatility periods than in high ones. According to the out-of-sample findings, the ASTVTP-MS-HAR-RV-F model outperformed other competing models, indicating that time-varying transition probabilities and REA information can significantly improve volatility forecasting performance.

This article investigates the crude oil volatility index (OVX) forecasting from the perspective of cross-market asymmetric effects of Chinese stock market jumps. We calculate six kinds of positive and negative jumps based on the high-frequency data of stock returns which are used to represent the asymmetric shocks of stock markets. Principal component analysis (PCA) and momentum of predictability (MoP) strategy are employed separately to synthesize the information of asymmetric jumps. Our empirical results find that considering the positive and negative jumps in Chinese stock market helps to improve the forecasting ability of OVX, especially under the MoP strategy. The out-of-sample model confidence set (MCS) tests and Diebold-Mariano (DM) tests, the evaluation of economic significance and the robustness tests further verify our results.

Stationary GARCH-MIDAS models encounter challenges in effectively capturing the dynamic impact of realized volatility on crude oil price volatility. This study introduces a novel time-varying parameter GARCH-MIDAS (TVP-GARCH-MIDAS) model to address these challenges and intricately capture the evolving dynamics between variables. The empirical results underscore the superior precision of the TVP-GARCH-MIDAS model in reflecting the influence of realized volatility on crude oil price volatility over time. In comparison to the stationary GARCH-MIDAS and MS-GARCH-MIDAS models, the proposed model exhibits outstanding out-of-sample forecasting performance and has excellent economic significance. This study provides valuable insights for investors and policy-makers, supporting better risk management and more effective investment strategy formulation.

This paper focuses on the factor-augmented panel regression models with missing data and individual-varying factors. A so-called CCEM estimator for the slope coefficient is proposed and its asymptotic properties are investigated under some regularity conditions. Furthermore, a joint test statistic is constructed for serial correlation and heteroscedasticity in the idiosyncratic errors. Under the null hypothesis, the test statistic can be shown to be asymptotically chi-square distributed. Monte Carlo simulation results show that the proposed estimator and test statistic have desired performance in finite samples.