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The first-order grey model is appropriate for monotonic time series, while the grey Verhulst model is appropriate for periodic time series. The grey Verhulst model is widely used for predicting practical nonlinear time series that contain fluctuations. Despite the successful application of the grey models in practice, researchers show that grey models still have room for improvement. Moreover, recent research shows that grey models are sensitive to initial conditions. In many practical problems, the value of initial conditions is not accurate and suffers from noise or approximation errors, resulting in inaccurate prediction. To address these difficulties, an improved grey Verhulst method using particle swarm optimization is proposed in this paper. The proposed model consists of two stages. In the first stage, a second-order polynomial with unknown coefficients is used to approximate the 1- AGO. In the second stage, the initial element of the time series is modified to improve the accuracy of the prediction. The particle swarm optimization method is used to search for the unknown coefficients. It is found that PSO is a suitable optimization method for the proposed method because it is stable and generates a sequence of points that converges to a globally optimal solution. To demonstrate the efficiency and stability of the proposed method, it was applied to five practical problems, namely, gas production in China, the number of hazardous chemical accidents, CO2 emissions in Russia, the number of domestic tourists in China, and traffic flows in Canada. Numerical results show that the method is more accurate and robust than existing methods. • The proposed method needs only four elements for predicting the future elements of time series. • The paper proposes a second order polynomial for approximating 1-AGO. • The method makes more accurate prediction than existed methods. • The proposed method is applied on various practical forecasting problems successfully. [ABSTRACT FROM AUTHOR]

Meeting energy needs and ensuring ecological sustainability are important tasks for policymakers. In particular, changing the energy mix used in daily electricity generation can have a major effect on ecological conditions, and this is a previously neglected research topic. Therefore, this paper aims to investigate the influence of daily electricity generation from nuclear power and renewables on the achievement of carbon neutrality targets in the four largest nuclear power countries (i.e., the U.S., China, France, and Russia). The study applies the wavelet-transform coherence (WTC), quantile-on-quantile regression (QQR), and Granger causality in quantiles (GCQ) approaches for the period from January 2, 2019 to December 29, 2022. The outcomes present that electricity generation from nuclear energy reduces carbon (CO 2) emissions only in Russia, while hydropower generation does not contribute to CO 2 emission reduction in any country. Solar electricity generation decreases CO 2 emissions in different quantiles in the U.S. and Russia, while electricity generation from wind power reduces CO 2 emissions in the U.S. and France. The empirical outcomes also reveal that expanding solar, wind, and nuclear power in the energy mix can enhance the potential of the U.S., France, and Russia to achieve carbon neutrality and secure a sustainable future. However, China is using nuclear and renewables inefficiently regarding carbon neutrality. Therefore, the empirical evidence for China is highly controversial compared to former studies. [Display omitted] • The study examines renewable and nuclear electricity effect on carbon neutrality. • The study focuses on top four major nuclear power countries. • The study applies nonlinear approaches by using high-frequency (daily) data. • Renewable and nuclear electricity have time, frequency, & quantile-varying effect. • The best electricity source change according to each country. [ABSTRACT FROM AUTHOR]

This paper takes both value-added trade and trade-implied CO 2 emission reduction responsibility into account, which constructs a unified conceptual framework to recalculate CO 2 emission reduction responsibility from the perspective of value-added trade. This allows policymakers to trace worldwide CO 2 emissions at multiple levels of trade, production, consumption, and shared principle alongside the world trade network. This paper employs the gross export decomposition methodology and the World Input-Output Database for calculations. Firstly, compared with traditional trade statistics, measuring embedded emissions in value-added trade can deduct the double-counted terms of CO 2 emissions due to intermediate products crossing several borders repeatedly. Secondly, the worldwide inter-country CO 2 emission footprints embedded in exports, imports, and net flows of value-added trade are traced in a geographical world map. It occurs that, China, the USA, Russia, and the EU are the top four largest emitters. Thirdly, network analysis is further utilized to capture bilateral implicit CO 2 emission relationships, e.g., the EU members' environmental impacts depend on intra-regional trade within the union. Finally, a comparison is made under three burden-sharing principles based on value-added trade. The shared responsibility offers a compromise between the producer's and the consumer's principle, which is considered to be fairer and more effective. • This paper calculates trade-implied CO 2 emission reduction responsibility from the perspective of value-added trade. • A gross export decomposition model is applied to deduct double-counted terms of implicit carbon embedded in traditional trade. • The worldwide inter-country CO 2 emission footprints are visualized. • Network analysis is conducted to identify the major carbon emitters and their complex relations. • Three burden-sharing criteria are computed through the statistics of value-added trade. [ABSTRACT FROM AUTHOR]