Because of the harmful influence of CO₂ emissions on the environment and humans, issues related to CO₂ emissions have received considerable attention in recent years. Based on the pollution haven hypothesis and pollution halo effect, the uncertain effect of bilateral foreign direct investment (FDI) on CO₂ emissions has recently been in focus. Moreover, because of the opposing capital flow of bilateral FDI, the interaction between inward FDI (IFDI) and outward FDI (OFDI) might have a trade-off effect on CO₂ emissions. The accurate forecasting of CO₂ emissions in China in light of effect of the bilateral FDI is important since the government can use it to regulate emissions’ reduction. The grey multivariable Verhulst model (GMVM) was formulated in this paper with the goal of forecasting CO₂ emissions in China by considering the nonlinear, independent, and interaction-related effects of bilateral FDI on them. To enhance the accuracy of prediction, this paper used the Fourier series and the grey prediction model for residual modifications. The empirical results showed that the IFDI and the item of the interaction of bilateral FDI promoted CO₂ emissions, whereas OFDI reduced them in China. These results also verified the higher precision of the improved GMVM relative to other models. This paper also used improved GMVM to further forecast CO₂ emissions and provided suggestions for the Chinese government to plan for foreign investment, including selectively implementing bilateral FDI, and focusing on the trade-off in its interaction-related effects.

Since the implementation of the Belt and Road Initiative, China’s total amount of outward foreign direct investment (OFDI) has increased each year and this has caused its relationship with carbon emissions (CO₂e) to receive great attention recently. Forecasting China’s CO₂e accurately by considering the impact of OFDI is important since the government can use it to formulate an appropriate emissions plan to fulfill its carbon reduction commitments. Because the relationship between OFDI and CO₂e has nonlinear characteristics, a nonlinear grey multivariable model with fractional-order accumulation (NFGM(1,N)) was proposed in this study. To enhance the prediction accuracy, an optimization process was used to determine the parameters. The outcomes of the variable fractional order showed that fractional-order accumulation can better extract the grey information hidden in the original data, which confirmed the principle of new information priority. The result of the power coefficient indicated a nonlinear relationship between the CO₂e and OFDI. Based on the prediction performance, the prediction accuracy of the NFGM(1,N) model was proven to be superior to those of the ARMA model, linear regression model, the GM(1,1), GM(1,N), and FGM(1,N) models. The empirical results also revealed that OFDI increased the CO₂e in China. The relationship between the CO₂e and OFDI exhibits a U-shaped development based on further predictions for the 2018–2030 period. Finally, some suggestions for long-term CO₂e reduction plans were provided in this paper.

The quality of a country’s business environment speaks volumes about its government’s capacity and competitiveness. Unfortunately, the current system only evaluates countries and cities, overlooking the business environments of individual provinces. To address this issue, this study utilizes a green and sustainable development approach to evaluate the business environments of 30 provinces/municipalities in China. By incorporating ecological and environmental protection and sustainable development indicators, a novel green business environment index is constructed and analyzed to determine its impact on macroeconomic sustainable development and micro-enterprise operation. Taking into account the business environment index established by the World Bank and other organizations, this evaluation system adds ecological and environmental indicators specific to each province/municipality in China from the year 2011 to 2020. The result is a provincial green business environment evaluation index system consisting of 5 primary indicators and 30 secondary indicators. Principal component analysis (PCA) is then applied to rank the green business environment for each province/municipality. Furthermore, the overall green business environment of the Eastern region is superior to that of the Central and Western regions, highlighting the uneven development of the business environment in China.

The tourism industry has become a major contributor to the economic growth. However, because of the outbreak of the coronavirus disease (COVID-19) pandemic, the year 2020 became an extremely difficult year for the global tourism industry. Since the development of the tourism industry depends largely on changes in travel sentiment, it is important to analyze these changes in light of the pandemic. To determine the development trends of travel sentiment, a hybrid grey prediction model was used to predict travel sentiment globally and in the top 10 destination countries considering the shock effect of COVID-19 and vaccination. The results showed that the grey prediction models integrated with residual modification model contributed to improving the prediction accuracy. In addition, COVID-19 and vaccination were found to have opposite effects on travel sentiment. Based on the predictions, governments should strengthen pandemic prevention and control and administer vaccines to restore travel sentiment and promote tourism recovery.

Against China’s dual-carbon and first-class business environment strategies, the green business environment serves as a core institutional driver of corporate social responsibility (CSR). Prior research relies on linear models or static fsQCA and overlooks the multi-dimensional, time-varying complexity of green business environment. Based on institutional and ecological modernization theories, this paper establishes a 5-dimension, 29-indicator evaluation index. Using 2011–2024 panel data of 30 Chinese provinces, the global principal component analysis (GPCA) was adopted to measure regional green business environment, and dynamic fsQCA to identify CSR driving configurations. The empirical results revealed a steady improvement in the green business environment alongside distinct east-west spatial disparities. No single factor acts as a necessary condition for high-CSR performance, and five equifinal driving paths are classified into government-led, social-driven, and two-dimensional synergistic models. Provincial spatial heterogeneity exerts a more prominent effect than temporal heterogeneity, and all configurational paths become more stable after 2021. This study proposes a hybrid analytical framework combining GPCA and dynamic fsQCA, and provides differentiated governance suggestions to advance regional CSR development.