At present, chat generative pre-trained transformer (ChatGPT) as a representative of the rapid development of large language models, is widely used in stock market investment, algorithmic trading, risk management and other fields. This provides financial investors with new decision-making tools and investment paths. In this paper, we construct an investment trading model based on the bidirectional encoder representation from transformers (BERT) model and chat generative pre-trained transformer (ChatGPT) for the Chinese stock market, and realize the trading signals from financial news text data and traditional financial data. For the text data, the daily financial news is captured and matched with the corresponding stock codes. Secondly, we input the news text data into the trained fine-tuning BERT (FTBERT) model to get the sentiment tendency of each news item, and select the positive financial news as the positive investment trading signals. For the traditional financial data, we use the advanced parsing capability of chat generative pre-trained transformer (ChatGPT) to analyze the historical data of Chinese stock market. By adjusting the prompt to read the data, the key factors for stock investment are constructed, and the daily scores of each stock are output. Finally, the daily investment signals of each stock are obtained based on different data types, which are used as the basis for constructing investment portfolios and building effective investment strategies. The empirical results show that chat generative pre-trained transformer (ChatGPT) effectively determine the sentiment tendency of text. The fine-tuned model can effectively assist quantitative investment and bring investors excessive returns. This study attempts to apply big language modeling to financial investment and shows its potential value in generating stock investment signals. With the continuous development of technology and changes in the market environment, this artificial intelligence-based investment strategy will continue to evolve and create more value for investors.

Large models, exemplified by ChatGPT, represent a significant breakthrough in general generative artificial intelligence technology. Their far-reaching implications extend into diverse facets of human production, lifestyle, and cognitive processes, prompting a transformative paradigm shift in the realm of economic research. Originating from the convergence of big data and artificial intelligence, these large models introduce a novel approach to systemic analysis, particularly adept at scrutinizing intricate human economic and social systems. We first discuss the fundamental characteristics and development paradigms of ChatGPT and large models, focusing on how these models effectively tackle the methodological challenges posed by the "curse of dimensionality". We then delve into how ChatGPT and large models will influence the paradigm of economic research. This includes a shift from the assumption of the rational economic man to an AI-driven "human-machine hybrid" economic agent, from the isolated economic individual to the socio-economic individual whose behaviors are measurable, from the separation of macroeconomics and microeconomics to their integration, from the separation of qualitative and quantitative analysis to their unification, and from the long-dominant "small-model" paradigm to a "large-model" paradigm in economic research. We also cover the increasing significance of computer algorithms as a prominent research paradigm and method in economics. Finally, we point out the limitations inherent in artificial intelligence technologies, including large models, when employed as a research method in economics and the broader social sciences.

Bilevel Optimization recently became a very active research area. This is mainly due to its important applications from machine learning. In this paper, we give a gentle introduction to algorithms, theory, and applications of bilevel optimization. In particular, we will discuss the history of bilevel optimization, its applications in power grid, hyper-parameter optimization, meta learning, as well as algorithms for solving bilevel optimization and their convergence properties. We will mainly discuss algorithms for solving two types of bilevel optimization problems: lower-level problem is strongly convex and lower-level problem is convex. We will discuss gradient methods and value-function-based methods. Decentralized and federated bilevel optimization will also be discussed.

Commodity is an important part of industrial production and financial investment, and accurate commodity price forecasting is of great significance to safeguard industrial production and help investors avoid risks. However, most of the existing commodity price forecasting models are point-value models based on closing prices, which ignores the volatility information. Therefore we propose a heteroskedasticity threshold autoregressive interval model with exogenous variables (HTARIX) and apply it to the commodity markets. We also construct a test statistic based on interval-valued data to test whether there is conditional heteroskedasticity in the model, and propose a generalized minimum $D_K$ distance estimation. The advantage of our model is that it can capture the conditional heteroskedasticity and nonlinear features of interval-valued time series models. Compared with the point-valued models, our method contains more information of the data. The empirical results imply that HTARIX model performs better than other comparative models in interval-valued commodity price forecasting.

Existing research has shown that political crisis events can directly impact the tourism industry. However, the current methods suffer from potential changes of unobserved variables, which poses challenges for a reliable evaluation of the political crisis impacts. This paper proposes a panel counterfactual approach with Internet search index, which can quantitatively capture the change of crisis impacts across time and disentangle the effect of the event of interest from the rest. It also provides a tool to examine potential channels through which the crisis may affect tourist outflows. This research empirically applies the framework to analyze the THAAD event on tourist flows from the Chinese Mainland to South Korea. Findings highlight the strong and negative short-term impact of the political crisis on the tourists' intentions to visit a place. This paper provides essential evidence to help decision-makers improve the management of the tourism crisis.

It is with great pleasure and admiration that we celebrate the 60th birthday of Professor Lihua Xie, a distinguished researcher and visionary leader in the field of robust control and estimation. Prof. Xie’s remarkable journey, marked by outstanding achievements and groundbreaking contributions, has left an indelible mark on the world of engineering and academia.
Prof. Xie’s academic odyssey began at Nanjing University of Science and Technology, where he earned his bachelor’s and master’s degrees in 1983 and 1986, respectively. His pursuit of knowledge led him to the University of Newcastle, Australia, where he obtained his PhD in 1992. Since 1992, he has been a cornerstone of Nanyang Technological University (NTU), Singapore, currently serving as a distinguished professor in the School of Electrical and Electronic Engineering and as the Director of the Centre for Advanced Robotics Technology Innovation (CARTIN), NTU.
One of Prof. Xie’s pivotal contributions lies in the realm of robust control and estimation. His early work in the early 1990s addressed robust solutions for systems with parametric uncertainties, providing a profound understanding of how uncertainty influences control system performance. His pioneering research not only illuminated the impact of uncertainty but also offered effective strategies, particularly for parametric uncertainty, ensuring the robustness of control systems. Prof. Xie was among the first to develop robust estimation techniques for systems grappling with parametric uncertainties, influencing researchers globally since the 1990s.
In the past two decades, Prof. Xie, alongside his co-author, established a groundbreaking equivalence between quantized feedback and robust control. This breakthrough extended the applicability of existing robust control theory to the analysis and design of control systems operating under quantized feedback. His work also unraveled the intricate interplay among data rate, network topology, and agent dynamics in multi-agent consensus - a fundamental challenge in cooperative control. Prof. Xie’s research provided answers to crucial questions, such as determining the minimal data rate and network topology for multi-agent consensus, along with corresponding coding and decoding schemes.
The spectrum of Prof. Xie’s impact extends to compressive sensing, where he and his student established a phase transition relationship between sparsity and recoverability for complex signals. Their continuous compressive sensing algorithms and Vandermonde decomposition theory for multi-level Toeplitz matrices have found applications in array signal processing, marking another significant milestone in his illustrious career.
Beyond theoretical endeavors, Prof. Xie’s practical innovations have revolutionized localization and unmanned systems. His research group’s developments include a WiFi-based indoor positioning system, multi-modality sensor fusion technology, and a fully integrated navigation solution for UAVs. These innovations have found applications in diverse fields, from structure inspection and delivery using UAVs to a low-cost universal navigation system for AGVs in logistics and manufacturing.
In the realm of research and development leadership, Prof. Xie’s impact is equally profound. He is the founding Director of the Delta-NTU Corporate Laboratory for Cyber-physical Systems, which focuses on the development of smart manufacturing and smart learning technologies for industry. Additionally, Prof. Xie established the Centre for Advanced Robotics Technology Innovation, where he currently serves as the Director. The center’s mission is to pioneer advanced sensing and perception technologies, as well as collaborative robotics technologies, with applications in logistics, manufacturing, and elderly care.
As an accomplished researcher, Prof. Xie has demonstrated unparalleled dedication to serving the research community. His extensive editorial roles, including a founding Editor-inChief for Unmanned Systems and Associate Editor for Sciences China - Information Science, showcase his commitment to advancing scientific knowledge. He has played pivotal roles in various editorial boards, such as IET Book Series in Control and esteemed journals like IEEE Transactions on Automatic Control and Automatica.
Prof. Xie’s impact extends beyond editorial responsibilities; he has been a distinguished IEEE Distinguished Lecturer, a Board of Governors member for the IEEE Control System Society, and Vice President since January 2024. His leadership roles also include serving as General Chair of significant conferences, including the 62nd IEEE Conference on Decision and Control in December 2023.
His professional achievements, recognized by peers worldwide, include fellowships in the Academy of Engineering Singapore, the Institute of Electrical and Electronics Engineers (IEEE), International Federation of Automatic Control (IFAC), and the Chinese Automation Association (CAA).
In celebration of Prof. Xie’s 60th birthday, we invited 17 papers from friends and colleagues for this special issue. As editors, we extend our deepest gratitude to all the authors for their invaluable contributions. Special thanks to the Journal of Systems Science & Complexity editorial office, including Prof. Xiao-Shan Gao (Editor-in-Chief), Prof. Yanlong Zhao (Managing Editor), and Ms. Guoyun Wu (Editorial Director), for their steadfast support from the conception to the publication of this special issue.
On this momentous occasion, we express our profound appreciation for Prof. Lihua Xie for his unwavering commitment to advancing knowledge and look forward to the continued brilliance and innovation in the next chapters of his illustrious career.
Happy Birthday, Prof. Lihua Xie!

In the context of the "double carbon" target, promoting the green and low-carbon transformation of economic and social development is a major systemic project. Developing renewable energy and improving energy efficiency will help to build a more efficient green energy system. Analyzing the effect of energy transformation has important reference value for formulating a reasonable carbon emission policy and achieving medium and long-term emission reduction targets. This study takes this as a starting point. Firstly, static panel and dynamic panel system generalized method of moments (GMM) are used to estimate the impact of energy transformation, renewable energy efficiency and non-renewable energy efficiency on major macroeconomic variables. Secondly, the intermediate production sector is subdivided into renewable energy production sector and non-renewable energy production sector. The dynamic stochastic general equilibrium (DSGE) model is constructed to analyze the short-term impact of energy transformation impact, renewable energy efficiency impact and non-renewable energy efficiency impact on major macroeconomic variables. The analysis shows that: 1) energy transformation promotes the transfer of resources between sectors, the output of renewable energy production sector will increase, while the output of non-renewable energy production sector and carbon emissions will decrease; 2) The improvement of two kinds of energy efficiency will produce economic expansion effect, but it will also produce energy rebound effect and increase carbon emissions; 3) At the end of the simulation period, the implementation of the carbon emission intensity policy will promote the growth effect of three shocks on output, but will also hinder the emission reduction effect and aggravate the rebound effect in the process of energy transformation. The implementation of the carbon tax policy will inhibit the rebound effect of two types of energy efficiency shocks on carbon emissions. In the process of energy transformation, we should rely on a reasonable carbon emission policy and formulate medium and long-term emission reduction targets. This study has important reference value for China to analyze the effect of energy transformation.

This paper proposes the real-time Realized EGARCH-MIDAS (RT-REGARCH-MIDAS) model which adequately captures the information content of high-frequency data, the current return information and the long memory of volatility to model and forecast Chinese stock market volatility. An empirical analysis based on the 5-minute high-frequency data of the Shanghai Stock Exchange Composite Index (SSEC) and the Shenzhen Stock Exchange Component Index (SZSEC) shows that the RT-REGARCH-MIDAS model outperforms a variety of competitor models in fitting the return data and can describe the stock market volatility better. Using robust loss functions and the model confidence set (MCS) test, the paper compares the out-of-sample forecasting ability of the model and other competitor models for Chinese stock market volatility. Our empirical results show that accounting for the information content of high-frequency data, the current return information and the long memory of volatility plays an important role in forecasting stock market volatility. As a consequence, the proposed RT-REGARCH-MIDAS model performs the best in forecasting Chinese stock market volatility. Further, according to the robustness checks, the superior volatility forecasting ability of the model is robust to alternative realized measure, alternative forecast windows, alternative MIDAS lags, alternative forecasting horizons and out-of-sample R² test. Finally, a volatility timing strategy shows that the proposed model yields more significant economic value of portfolio compared to the other models.

It is conjectured by Professor Zhi-Wei Sun that for each given odd prime $p>100, $ there always exists an solution $(x,y,z)\in[1,p]^3$ to the Pythagoras equation $x^2+y^2=z^2$ such that $x,y,z$ are quadratic residues or non-residues modulo $p$ respectively (eight cases in total). In this paper, we are able to prove the above assertion for all sufficiently large primes $p$, and the method is based on the recent Burgess bound for character sums of forms in many variables due to Lillian B. Pierce and Junyan Xu.

With the explosive growth of investable assets and asset information, portfolio selection faces the dual challenges of high dimensionality in both assets and characteristics. This paper proposes a portfolio selection framework based on machine learning and asset characteristics. Leveraging the inherent advantages of machine learning, the framework utilizes asset characteristics to directly predict portfolio weights, bypassing return distribution prediction in the conventional two-step portfolio management paradigm. The framework is applied to asset allocation research in the Chinese stock market. The research results show that: 1) The proposed investment strategies capture incremental information within high-dimensional characteristics and uncover both linear and non-linear relationships between asset characteristics and portfolio weights, resulting in a significant enhancement of investment performance. 2) Trading friction-related characteristics are the most important indicators for predicting portfolio weights. 3) These strategies yield higher returns on stocks with stricter arbitrage restrictions while exhibiting lower sensitivity to changes in macroeconomic conditions. Under other economic constraints, these strategies remain robust. This paper expands the research framework of modern portfolio theory, contributing to the development of artificial intelligence and quantitative investment.

Let $\mathbb{F}_{q}$ be the finite field of $q$ elements, and $\mathbb{F}_{q^{n}}$ be its extension of degree $n$. An element $\alpha\in \mathbb{F}_{q^{n}}$ is called a normal element of $\mathbb{F}_{q^{n}}/\mathbb{F}_{q}$ if $\{\alpha,\alpha^{q},\ldots, \alpha^{q^{n-1}}\}$ constitutes a basis of $\mathbb{F}_{q^{n}}/\mathbb{F}_{q}$. Normal elements over finite fields have proved very useful for fast arithmetic computations with potential applications to coding theory and to cryptography. The minimal polynomial of a normal element is certainly an irreducible polynomial with nonzero trace, while the converse does not hold in general. Using linearized polynomials, we give some necessary and sufficient conditions for this problem, which extend the known results.

This paper compares and analyzes the differences in stock pricing between news sentiment and social media sentiment in two different time dimensions, daily and monthly, using individual sentiment data from the Thomson Reuters MarketPsych Indices and trading data from the US stock market from 2010 to 2019. The empirical results indicate that social media sentiment performs better at the daily level than news sentiment, and news sentiment has a stronger explanatory power on stock returns at the monthly level than social media sentiment. Specifically, at the daily level, this paper constructs news sentiment factor and social media sentiment factor, and finds that social media sentiment factor still exhibits significant excess returns under the Fama-French five-factor model, while news sentiment factor no longer exhibits excess returns. In addition, social media sentiment factor can explain most market anomalies at the daily level, while news sentiment factor cannot. In order to investigate the reasons, this paper conducts a Granger causality test, indicating that the response speed of social media sentiment factor is 3 to 4 trading days faster than that of news sentiment factor. At the monthly level, this paper finds that news sentiment improves its ability to explain anomalies, while the explanatory power of social media decreases significantly. In addition, for volatility anomalies and idiosyncratic volatility anomalies, the monthly news sentiment factor has a significant explanatory power, while the explanatory power of the monthly social media sentiment factor is not significant.

There are great differences between domestic and foreign enterprises in terms of business decisions, sensitivity to the international economic patterns, etc., which leads to their completely different characteristics in participating in the international industry relocation. Therefore, with the frequent outbreak of international emergencies that cause deep adjustment of global value chain, clarifying the heterogeneity of domestic and foreign enterprises in the international industry relocation will be an important prerequisite to promote the "dual circulation" development pattern and ensure the security of supply chain. This paper proposes a quantitative model to measure the magnitude of industry relocation that distinguishes between domestic and foreign enterprises. Based on that, the empirical study captures the scale, mode, industry heterogeneity and mutual substitution between China's domestic and foreign-funded enterprises in participating in international industry relocation during 2005--2016. The empirical evidence finds that: 1) From the magnitude perspective, both domestic and foreign enterprises in China are generally receiving production activities. However, the growth of relocation slowed down after 2014, followed with the trend of relocation outward. The magnitude of the international industrial relocation of domestic enterprises has always been about 80.0% of the total. However, in terms of the ratio of industrial relocation to output, domestic enterprises have always been much lower than foreign enterprises, and the difference reached 14.1 percentage points in 2005-2016. 2) From the mode perspective, domestic enterprises mainly participate in international industry relocation through intermediate products, while foreign enterprises participate more through final products. 3) From the industry perspective, domestic enterprises is dominated by the capital-intensive manufacturing, while foreign enterprises mainly focus on technology-intensive manufacturing and producer services. 4) Generally, China's domestic enterprises have a strong substitution effect on foreign enterprises in China. However, a "reverse substitution (foreign enterprises substitute domestic enterprises)" is continuously taken place in the technology-intensive manufacturing.

"The adjustment of coal-based electric energy transportation" plays a significant role in enhancing the ecological environment and reducing coal consumption in recipient areas. However, it faces challenges in practice. This study examines the "Structure adjustment of coal electric energy transport" from the "Sanxi Region" to the Beijing-Tianjin-Hebei region based on real-world experiences. By employing a multi-regional CGE model, this paper quantitatively analyzes the environmental, economic, and social impacts of this adjustment on both regions. The research reveals that the primary issue with the current transition is the imbalance of interests between the sending and receiving areas. Specifically, while the Beijing-Tianjin-Hebei region benefits from improved air quality, the "Sanxi Region" suffers from negative effects on both the atmosphere and economy. Considering China's 14th Five-Year Plan environmental protection goals, this paper suggests an optimal annual growth range for coal-based electric energy transportation from 2021 to 2025 of [14\%, 27\%]. Additionally, it proposes an optimized tax rate range for joint air pollution control and an economic compensation plan. This research offers a solution path and reference for overcoming challenges in the transformation of coal-based electric energy transportation and contributes to achieving ecological objectives in the Beijing-Tianjin-Hebei region.

This article aims to explore the impact of the internet on income inequality among rural households. Through the analysis of data from China Family Panel Studies, it is found that although the internet can significantly alleviate the inequality in total income and wage income among rural households, its effect on alleviating inequality in entrepreneurial income is limited, and it may exacerbate inequality in household property income. Based on this finding, this article analyzes the mechanism of its impact from the perspective of household income sources, revealing that the internet mainly reduces the wage income gap by pulling rural labor force into the non-agricultural sector, thereby alleviating household income inequality. Meanwhile, households with original capital accumulation are more likely to benefit from the internet, which exacerbates property income inequality. In addition, this article introduces the causal forest algorithm and, from the perspective of human capital, analyzes the heterogeneous effects of the internet on individual-level inequality in wage income and property income among rural households. The results show that the alleviation of wage income inequality is mainly manifested in households with low human capital, while the exacerbation of property income inequality is mainly manifested in households with high human capital.

This study constructs the digital innovation index of A-share listed companies from 2008 to 2020, and empirically examines the impact of the "specialization effect of intellectual property (IP) judicial protection" brought by the establishment of IP courts on corporate digital innovation. We find that: 1) the establishment of IP courts has a significant positive effect on digital innovation in companies; 2) the establishment of IP courts mainly motivates digital business model innovation in companies; 3) the establishment of IP courts promotes digital innovation in companies through mechanisms such as optimizing the judicial environment, reducing spillover losses, and alleviating external financing constrains; 4) the promotion effect of the establishment of intellectual property courts on digital innovation is more pronounced in small, non-state-owned, and low-competition industry firms; 5) the establishment of IP courts significantly increases the market value of firms' digital innovation (especially digital business model innovation).

In the digital economy, the emergence of digital currencies has attracted considerable attention from both investors and researchers. However, their high volatility characteristics present new challenges in investment decision-making and risk assessment. To capture the characteristics comprehensively, this paper proposes a novel approach for constructing confidence regions for interval-valued variables based on the exponentially decay weighted bootstrap. The coverage area of the confidence regions and tail quantiles provide new indicators for assessing the volatility and tail risks in the market. Empirical results using Bitcoin as a case study demonstrate the proposed approach outperforms other traditional point-based methods such as exponential weighted moving average in measuring the uncertainty and intraday price volatility. Furthermore, the derived tail quantiles exhibit superior predictive performance for tail risk compared to Value-at-risk methods and the exponential weighted moving average, as evidenced by various tests. The proposed methodology not only contributes a new statistical tool for analyzing digital currency volatility but also provides novel perspectives for extreme risk management in financial markets.

Green development involves a wide range and covers a large range, so the difference in interest demands makes the government, enterprises and financial institutions unable to reach an effective consensus in the game. This study constructs a tripartite evolutionary game model based on green preference perspective, and analyzes the relationships among green regulation, green transition, and green bond investment. The study found that the green preference of government, enterprises and financial institutions has different effects on green development. Enterprise green preference plays a decisive role in green transformation. Firstly, when the green preference of the enterprise is large, even if the government does not carry out green regulation or financial institutions do not invest in green bonds, the enterprise will still carry out green transformation production. However, when the green preference of other participants is not large enough, the phenomenon that the government makes green regulatory decisions but has no policy effect will occur. Secondly, when the size of the green preference of enterprises is in a specific range, while the green preference of financial institutions and the government is large, there are two possibilities: The simultaneous success or failure of green transition and green bond issuance. Finally, the main conclusions of this paper are verified by numerical simulation.

In the background of the rise of the anti-globalization trend in the postepidemic era, China's economic development is expected to rely more on the increase in the degree of dependence on the pull of domestic demand, so the study on how to promote the level of consumption of the residents and the expansion of domestic demand is also becoming more and more critical. The deep integration of digital economic development and traditional industries can release a sizable "digital dividend", colossal energy, is the expansion of domestic demand, the realization of the "domestic cycle" of the critical potential driving force. Given this, based on the China Family Panel Studies (CFPS) database, this paper constructs the digital economy development level index at the provincial level in China. It empirically examines the theoretical analysis and empirical test on the effect of digital economy development on residents' household consumption. The study finds that: (ⅰ) Digital economy development can promote residents' household and per capita consumption. This conclusion still holds after a series of robustness tests. (ⅱ) The development of the digital economy can positively impact residents' consumption level, mainly through improving the quality of residents' income. However, optimizing the consumption environment is not the main reason for the digital economy to promote consumption.(ⅲ) From the heterogeneity analysis, digital economy development has a more noticeable effect on the consumption enhancement of regions with low unemployment rates and households with low labor costs. (ⅳ) This paper further discusses the impact of digital economic development on the consumption structure and finds that digital economic development makes it diffcult to enhance residents' subsistence consumption but significantly increases the developmental consumption expenditures of income groups at all levels and also substantially promotes the enjoyment expenditures of high-income households. The findings of this paper provide theoretical support and a decision-making basis for further utilizing digital economic development to release consumption potential.

Let $T\in \mathcal{B(H)}$ be a bounded linear operator on a complex Hilbert space $\mathcal{H}$. The properties of the generalized pencil $T=P +\alpha Q+\beta PQ$ of pair $(P, Q)$ of projections at $(\alpha, \beta)\in \mathbb{C}^2$ are investigated. Using Halmos decomposition theory for orthogonal projections we give some equivalent conditions for which $T$ is the generalized pencil and study the spectrum properties of this generalized pencil $T$. We prove that the generalized pencil $T$ is similar to a diagonal operator under some conditions. The spectrum relations among the generalized pencil $T$ and projections $P$, $Q$ are established. Further, we give the necessary and sufficient conditions under which the generalized pencil $T$ is a Fredholm operator, a compact operator or a selfadjoint operator, respectively. Finally, the generalized pencils of pairs of idempotents are studied.