The digital economy has become an important driving force for the steady development of China's economy, and enterprise innovation is a key element for an enterprise's survival and development. This paper constructs a mathematical model to measure the scale of digital economic development and the efficiency of enterprise innovation. It builds a fixed effects model and mediated effects model to study the effect of the development of the digital economy on enterprise innovation based on data from 30 provinces from 2012 to 2020. The results show that (1) there is a significant positive effect of the digital economy on enterprise innovation with an impact coefficient of 0.028, and the economic meaning of the coefficient is that for every 1-point increase in the digital economy index, the ratio of R&D capital expenditures to the enterprise's operating income increases by 0.028% points. This finding remains significant in the robustness test. (2) A further test of the mediating effect finds that the digital economy can drive enterprise innovation by reducing financing constraints. (3) In the regional heterogeneity analysis, it is found that the effect of the digital economy in promoting enterprise innovation is more prominent in the central region, and the impact coefficients are 0.04, 0.06, 0.025, and 0.024 for the eastern, central, western, and northeastern regions, respectively. Taking the central region as an example, the economic meaning of the coefficient is that for every 1-point increase in the digital economy index, the ratio of R&D capital expenditures to the enterprise's operating income increases by 0.06% points. The findings of this paper are of practical significance to enterprises in enhancing their innovation capabilities and promoting the high-quality development of China's economy.

Taking long-term high-frequency electricity price data as the research content, this paper proposes seasonal and trend decomposition using loess-temporal convolutional network-neural basis expansion analysis for an interpretable time series forecasting (STL-TCN-NBEATS) model to solve the problems of low forecast accuracy caused by high volatility, high frequency and nonlinearity and poor interpretability of the deep learning model. By comparing the forecast effects of the temporal convolutional network-long short-term memory (TCN-LSTM), LSTM and other models, the main conclusions are as follows: (1) The hybrid model, STL-TCN-NBEATS, selected in this paper can effectively solve the problem of low forecast accuracy after reasonable selection of model parameters. The evaluation indexes of the root mean square error (RMSE) and the mean absolute percentage error (MAPE) were 3.7441 and 4.5044, respectively, which were 3.1416 and 2.1336 lower than those of the second-best model (TCN-LSTM). Compared with the autoregressive integrated moving average model (ARIMA), the accuracy was improved by approximately 49.18% (RMSE) and 60.35% (MAPE). (2) The STL-TCN-NBEATS model has better feature extraction ability, so it can obtain higher forecast accuracy. Since the construction of the TCN introduces extended causal convolution and residual blocks, the deep learning network model has better processing ability and robustness for large sample time series. Moreover, the NBEATS network structure enables the model to be trained quickly, and the experimental results verify the effectiveness and high accuracy of this method. (3) The model not only has high precision but also has some interpretability. By decomposing time series data into a trend term, period term and remainder term, the NBEATS and the TCN are used to process the trend term, period term and remainder term, respectively, so that the hybrid model can forecast electricity prices according to the traditional time series processing mode.

The air quality index (AQI), as an indicator to describe the degree of air pollution and its impact on health, plays an important role in improving the quality of the atmospheric environment. Accurate prediction of the AQI can effectively serve people’s lives, reduce pollution control costs and improve the quality of the environment. In this paper, we constructed a combined prediction model based on real hourly AQI data in Beijing. First, we used singular spectrum analysis (SSA) to decompose the AQI data into different sequences, such as trend, oscillation component and noise. Then, bidirectional long short-term memory (BiLSTM) was introduced to predict the decomposed AQI data, and a light gradient boosting machine (LightGBM) was used to integrate the predicted results. The experimental results show that the prediction effect of SSA-BiLSTM-LightGBM for the AQI data set is good on the test set. The root mean squared error (RMSE) reaches 0.6897, the mean absolute error (MAE) reaches 0.4718, the symmetric mean absolute percentage error (SMAPE) reaches 1.2712%, and the adjusted R² reaches 0.9995.

The concentration series of PM_2.5 (particulate matter ≤ 2.5 μm) is nonlinear, nonstationary, and noisy, making it difficult to predict accurately. This paper presents a new PM_2.5 concentration prediction method based on a hybrid model of complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and bi-directional long short-term memory (BiLSTM). The new method was applied to predict the same kind of particulate pollutant PM₁₀ and heterogeneous gas pollutant O₃, proving that the prediction method has strong generalization ability. First, CEEMDAN was used to decompose PM_2.5 concentrations at different frequencies. Then, the fuzzy entropy (FE) value of each decomposed wave was calculated, and the near waves were combined by K-means clustering to generate the input sequence. Finally, the combined sequences were put into the BiLSTM model with multiple hidden layers for training. We predicted the PM_2.5 concentrations of Seoul Station 116 by the hour, with values of the root mean square error (RMSE), the mean absolute error (MAE), and the symmetric mean absolute percentage error (SMAPE) as low as 2.74, 1.90, and 13.59%, respectively, and an R² value as high as 96.34%. The “CEEMDAN-FE” decomposition-merging technology proposed in this paper can effectively reduce the instability and high volatility of the original data, overcome data noise, and significantly improve the model’s performance in predicting the real-time concentrations of PM_2.5.

At the 75th session of the United Nations General Assembly, China clearly put forward the goals of "carbon peak" in 2030 and "carbon neutrality" in 2060. Achievement of carbon targets. Therefore, the goal of this paper is to analyze the low-carbon development level of China's power industry and study the impact of carbon market policies on the low-carbon development level of the power industry. Based on this, this paper first constructs the low-carbon development evaluation index system of the power industry around the connotation of low-carbon development in the power industry and uses the global principal component analysis model to measure the low-carbon development level of China's power industry. Then, the dynamic change trend and spatial distribution characteristics of the low-carbon development level of China's power industry are analyzed using kernel density estimation and the K-means clustering method. Finally, propensity score matching and difference-in-difference methods are used to analyze the impact of carbon market policies on the low-carbon development level of China's power industry. The results show that, first, the low-carbon development level of China's power industry generally shows an upward trend and a polarized development trend. Second, the low-carbon development level of China's power industry has regional effects and gradient effects. The low-carbon development level of the power industry from high to low is the eastern region, central region and western region. Third, carbon market policies can help improve the low-carbon development level of China's power industry. The research results provide some reference and guidance for the evaluation of the low-carbon development level of China's power industry and the improvement of carbon market policies.

Green manufacturing has become a necessary way to promote new industrialization and realize the high-quality development of China’s manufacturing industry. Based on the panel data of 30 provinces in China from 2012 to 2022, this paper constructs a comprehensive evaluation index system for the green manufacturing development level and introduces the TOPSIS- Gray correlation method to comprehensively measure the green manufacturing development level of China as a whole and the four major regions in the eastern, central, western, and northeastern parts of the country. The regional differences, distribution dynamics and evolutionary trends of China's green manufacturing development level are also explored with the help of the Gini coefficient, kernel density estimation and Markov chain methods. Research Findings: (1) The green manufacturing development level in China is on an upward trend, with an overall spatial distribution pattern of “East is superior and West is inferior”. (2) There are regional differences in the green manufacturing development level in China, and the differences are widening, with interregional differences being the main reason for this overall difference. (3) The country as a whole, the central region and the western region are polarized to varying degrees, with the rest of the country showing an improvement in polarization. (4) Without considering spatial factors, the development of green manufacturing in each province experiences “club convergence” in the short term, and it is difficult to realize rapid development. Considering spatial factors, China's green manufacturing development level is generally characterized by “elevated in proximity to high levels and suppressed in proximity to low levels”, and in the long run, it shows a distribution trend toward the concentration of high values. The findings of this study can provide new ideas for promoting synergistic efficient development of green manufacturing in China.