Heteroscedasticity of time series is an important issue addressed in relation to the nonlinearity and complexity of time series. Previous studies have focused on time series heteroscedasticity during a long-term period but have rarely analyzed it from a nonlinear dynamic perspective. This paper proposes a new model for converting a time series into a complex network. Our proposed model can examine not only the heteroscedasticity of a short-term series but also the dynamic evolution process of this heteroscedasticity. Using four typical crude oil time series as sample data, we construct four networks. A network node denotes the types of fluctuation patterns corresponding to the symbolization of the heteroscedastic features of a short-term fluctuation series based on the autoregressive generalized autoregressive conditional heteroscedasticity model, and a weighted edge represents the evolution direction and frequency between two patterns. Our findings show that the choice of the length of a short-term period depends on the diversity of these patterns. The identification of the nodes with greater out-strength or greater betweenness centrality can help us to understand the different roles of fluctuation patterns in the evolution process. We propose a method for predicting the most probable target nodes from a source node. The analysis of clustering effects can help in detecting the fluctuation patterns between different clusters. This paper investigates the evolution dynamic mechanism of the heteroscedastic features of a short-term time series, which can help researchers and investors deeply understand the dynamic process of time series.

Industrial carbon dioxide (CO₂) emissions are mainly derived from fossil energy use, which is composed of procedures involving extraction of energy from the natural system as well as its exchange and consumption in the social system. However, recent research on low-carbon transitions considers the cost of energy commodities from a separate perspective—a biophysical or monetary perspective. We introduce the energy intensity ratio (EIR), which is a novelty perspective combining biophysical and monetary metrics to estimate the cost of energy commodities in the low-carbon energy transitions. This combination is essential, since the feedback of energy into the biophysical system will influence the performance of energy in the economic system and vice versa. Based on the Logarithmic Mean Divisia Index (LMDI), we developed the EIR-LMDI method to explain the changes in CO₂ emissions. The changes in CO₂ emissions caused by the EIR are the net energy effect. In China, the net energy effect kept CO₂ emissions at a compound annual growth rate of 6.15% during 2007–2018. Especially after 2014, the net energy effect has been the largest driver of the increase in CO₂ emissions. During the study period, high net energy usually indicated high CO₂ emissions. Coal is the most important energy commodity and dominates the net energy effect; the least volatile component is the EIR of natural gas. The EIR affects CO₂ emissions by the price crowding-out effect and the scale expansion effect, which make the process of low-carbon transition uncertain. The results illuminate that policymakers should monitor the net energy effect to prevent it from offsetting efforts to reduce energy intensity.

China considers the healthy and sustainable development of the natural gas market to be crucial for achieving carbon neutrality and has been actively reforming its natural gas market to optimize the energy and economic structure. While previous studies have discussed the effectiveness of policy measures, there is a lack of simulation research and quantitative analysis on the impact of reform measures in China. This study addresses this gap by constructing a numerical simulation model based on China’s long-distance pipeline network and natural gas market, calibrated to 2019 as a pre-reform baseline and extended to the partially reformed market of 2024–2025. The model includes a base scenario to replicate real market conditions and two policy scenarios that incorporate market-oriented reform measures such as deregulation of prices, pipeline separation and interconnection. The effects of these measures on gas allocation and social welfare are examined. The results indicate that (1) pipeline separation and price deregulation increase social welfare, with welfare shifting from consumers to producers and distributors; (2) natural gas consumption and price changes exhibit pronounced regional heterogeneity, even though prices rise overall, reflecting the complexity of policy effects; (3) the reform follows a path of diminishing returns, and the current stage policy already captures about half of the welfare gain and most of the price adjustment, while shielding consumers from much of the surplus loss. Finally, we conclude with policy implications for China’s natural gas market reform. As these reform measures are now being implemented, the quantified welfare and price effects also offer a timely, model-based reference for assessing China’s ongoing gas-market marketization.