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Considering the small sample size and non-linear characteristics of historical energy consumption data from certain provinces in Southwest China, the authors propose a hybrid accumulation operator and a hybrid accumulation grey univariate model as a more accurate and reliable methodology for forecasting energy consumption. This method can provide valuable decision-making support for policy makers involved in energy management and planning.

The hybrid accumulation operator is proposed by linearly combining the fractional-order accumulation operator and the new information priority accumulation. The new operator is then used to build a new grey system model, named the hybrid accumulation grey model (HAGM). An optimization algorithm based on the JAYA optimizer is then designed to solve the non-linear parameters θ, r, and γ of the proposed model. Four different types of curves are used to verify the prediction performance of the model for data series with completely different trends. Finally, the prediction performance of the model is applied to forecast the total energy consumption of Southwest Provinces in China using the real world data sets from 2010 to 2020.

The proposed HAGM is a general formulation of existing grey system models, including the fractional-order accumulation and new information priority accumulation. Results from the validation cases and real-world cases on forecasting the total energy consumption of Southwest Provinces in China illustrate that the proposed model outperforms the other seven models based on different modelling methods.

The HAGM is used to forecast the total energy consumption of the Southwest Provinces of China from 2010 to 2020. The results indicate that the HAGM with HA has higher prediction accuracy and broader applicability than the seven comparative models, demonstrating its potential for use in the energy field.

The HAGM(1,1) is used to predict energy consumption of Southwest Provinces in China with the raw data from 2010 to 2020. The HAGM(1,1) with HA has higher prediction accuracy and wider applicability compared with some existing models, implying its high potential to be used in energy field.

Theoretically, this paper presents, for the first time, a hybrid accumulation grey univariate model based on a new hybrid accumulation operator. In terms of application, this work provides a new method for accurate forecasting of the total energy consumption for southwest provinces in China.

With the massive use of fossil energy polluting the natural environment, clean energy has gradually become the focus of future energy development. The purpose of this article is to propose a new hybrid forecasting model to forecast the production and consumption of clean energy.

Firstly, the memory characteristics of the production and consumption of clean energy were analyzed by the rescaled range analysis (R/S) method. Secondly, the original series was decomposed into several components and residuals with different characteristics by the ensemble empirical mode decomposition (EEMD) algorithm, and the residuals were predicted by the fractional derivative grey Bernoulli model [FDGBM (p, 1)]. The other components were predicted using artificial intelligence (AI) models (least square support vector regression [LSSVR] and artificial neural network [ANN]). Finally, the fitting values of each part were added to get the predicted value of the original series.

This study found that clean energy had memory characteristics. The hybrid models EEMD–FDGBM (p, 1)–LSSVR and EEMD–FDGBM (p, 1)–ANN were significantly higher than other models in the prediction of clean energy production and consumption.

Consider that clean energy has complex nonlinear and memory characteristics. In this paper, the EEMD method combined the FDGBM (P, 1) and AI models to establish hybrid models to predict the consumption and output of clean energy.

Accurate foreign tourist arrivals forecasting can help public and private sectors to formulate scientific tourism planning and improve the allocation efficiency of tourism resources. This paper aims to address the problem of low prediction accuracy of Chinese inbound tourism demand caused by the lack of valid historical data.

A novel hybrid Chinese inbound tourism demand forecasting model combining fractional non-homogenous discrete grey model and firefly algorithm is constructed. In the proposed model, all adjustable parameters of the fractional non-homogenous discrete grey model are optimized simultaneously by the firefly algorithm.

The data sets of annual foreign tourist arrivals to China are used to verify the validity of the proposed model. Experimental results show that the proposed method is effective and can be used as a useful predictor for the prediction of Chinese inbound tourism demand.

The method proposed in this paper is effective and can be used as a feasible approach for forecasting the development trend of Chinese inbound tourism.

Accurate prediction of seasonal power consumption trends with impact disturbances provides a scientific basis for the flexible balance of the long timescale power system. Consequently, it fosters reasonable scheduling plans, ensuring the safety of the system and improving the economic dispatching efficiency of the power system.

First, a new seasonal grey buffer operator in the longitudinal and transverse dimensional perspectives is designed. Then, a new seasonal grey modeling approach that integrates the new operator, full real domain fractional order accumulation generation technique, grey prediction modeling tool and fruit fly optimization algorithm is proposed. Moreover, the rationality, scientificity and superiority of the new approach are verified by designing 24 seasonal electricity consumption forecasting approaches, incorporating case study and amalgamating qualitative and quantitative research.

Compared with other comparative models, the new approach has superior mean absolute percentage error and mean absolute error. Furthermore, the research results show that the new method provides a scientific and effective mathematical method for solving the seasonal trend power consumption forecasting modeling with impact disturbance.

Considering the development trend of longitudinal and transverse dimensions of seasonal data with impact disturbance and the differences in each stage, a new grey buffer operator is constructed, and a new seasonal grey modeling approach with multi-method fusion is proposed to solve the seasonal power consumption forecasting problem.

The highlights of the paper are as follows:

1. A new seasonal grey buffer operator is constructed.

2. The impact of shock perturbations on seasonal data trends is effectively mitigated.

3. A novel seasonal grey forecasting approach with multi-method fusion is proposed.

4. Seasonal electricity consumption is successfully predicted by the novel approach.

5. The way to adjust China's power system flexibility in the future is analyzed.

A new seasonal grey buffer operator is constructed.

The impact of shock perturbations on seasonal data trends is effectively mitigated.

A novel seasonal grey forecasting approach with multi-method fusion is proposed.

Seasonal electricity consumption is successfully predicted by the novel approach.

The way to adjust China's power system flexibility in the future is analyzed.

The purpose of this study is to make a prediction of China's energy consumption structure from the perspective of compositional data and construct a novel grey model for forecasting compositional data.

Due to the existing grey prediction model based on compositional data cannot effectively excavate the evolution law of correlation dimension sequence of compositional data. Thus, the adaptive discrete grey prediction model with innovation term based on compositional data is proposed to forecast the integral structure of China's energy consumption. The prediction results from the new model are then compared with three existing approaches and the comparison results indicate that the proposed model generally outperforms existing methods. A further prediction of China's energy consumption structure is conducted into a future horizon from 2021 to 2035 by using the model.

China's energy structure will change significantly in the medium and long term and China's energy consumption structure can reach the long-term goal. Besides, the proposed model can better mine and predict the development trend of single time series after the transformation of compositional data.

The paper considers the dynamic change of grey action quantity, the characteristics of compositional data and the impact of new information about the system itself on the current system development trend and proposes a novel adaptive discrete grey prediction model with innovation term based on compositional data, which fills the gap in previous studies.

The time series forecasting is an essential methodology which can be used for analysing time series data in order to extract meaningful statistics based on the information obtained from past and present. These modelling approaches are particularly complicated when the available resources are limited as well as anomalous. The purpose of this paper is to propose a new hybrid forecasting approach based on unbiased GM(1,1) and artificial neural network (UBGM_BPNN) to forecast time series patterns to predict future behaviours. The empirical investigation was conducted by using daily share prices in Colombo Stock Exchange, Sri Lanka.

The methodology of this study is running under three main phases as follows. In the first phase, traditional grey operational mechanisms, namely, GM(1,1), unbiased GM(1,1) and nonlinear grey Bernoulli model, are used. In the second phase, the new proposed hybrid approach, namely, UBGM_BPNN was implemented successfully for forecasting short-term predictions under high volatility. In the last stage, to pick out the most suitable model for forecasting with a limited number of observations, three model-accuracy standards were employed. They are mean absolute deviation, mean absolute percentage error and root-mean-square error.

The empirical results disclosed that the UNBG_BPNN model gives the minimum error accuracies in both training and testing stages. Furthermore, results indicated that UNBG_BPNN affords the best simulation result than other selected models.

The authors strongly believe that this study will provide significant contributions to domestic and international policy makers as well as government to open up a new direction to develop investments in the future.

The new proposed UBGM_BPNN hybrid forecasting methodology is better to handle incomplete, noisy, and uncertain data in both model building and ex post testing stages.

The effective prediction of crude oil futures prices can provide a reference for relevant enterprises to make production plans and investment decisions. To the nonlinearity, high volatility and uncertainty of the crude oil futures price, a matrixed nonlinear exponential grey Bernoulli model combined with an exponential accumulation generating operator (MNEGBM(1,1)) is proposed in this paper.

First, the original sequence is processed by the exponential accumulation generating operator to weaken its volatility. The nonlinear grey Bernoulli and exponential function models are combined to fit the preprocessed sequence. Then, the parameters in MNEGBM(1,1) are matrixed, so the ternary interval number sequence can be modeled directly. Marine Predators Algorithm (MPA) is chosen to optimize the nonlinear parameters. Finally, the Cramer rule is used to derive the time recursive formula.

The predictive effectiveness of the proposed model is verified by comparing it with five comparison models. Crude oil futures prices in Cushing, OK are predicted and analyzed from 2023/07 to 2023/12. The prediction results show it will gradually decrease over the next six months.

Crude oil futures prices are highly volatile in the short term. The use of grey model for short-term prediction is valuable for research. For the data characteristics of crude oil futures price, this study first proposes an improved model for interval number prediction of crude oil futures prices.

This paper aims to develop a novel grey Bernoulli model with memory characteristics, which is designed to dynamically choose the optimal memory kernel function and the length of memory dependence period, ultimately enhancing the model's predictive accuracy.

This paper enhances the traditional grey Bernoulli model by introducing memory-dependent derivatives, resulting in a novel memory-dependent derivative grey model. Additionally, fractional-order accumulation is employed for preprocessing the original data. The length of the memory dependence period for memory-dependent derivatives is determined through grey correlation analysis. Furthermore, the whale optimization algorithm is utilized to optimize the cumulative order, power index and memory kernel function index of the model, enabling adaptability to diverse scenarios.

The selection of appropriate memory kernel functions and memory dependency lengths will improve model prediction performance. The model can adaptively select the memory kernel function and memory dependence length, and the performance of the model is better than other comparison models.

The model presented in this article has some limitations. The grey model is itself suitable for small sample data, and memory-dependent derivatives mainly consider the memory effect on a fixed length. Therefore, this model is mainly applicable to data prediction with short-term memory effect and has certain limitations on time series of long-term memory.

In practical systems, memory effects typically exhibit a decaying pattern, which is effectively characterized by the memory kernel function. The model in this study skillfully determines the appropriate kernel functions and memory dependency lengths to capture these memory effects, enhancing its alignment with real-world scenarios.

Based on the memory-dependent derivative method, a memory-dependent derivative grey Bernoulli model that more accurately reflects the actual memory effect is constructed and applied to power generation forecasting in China, South Korea and India.

In order to more accurately predict the dynamics of the e-commerce market and increase the comprehensive value of the circular e-commerce industry, proposes to use Grey system theory to analyze the circular economy of the e-commerce market.

Construct a Grey system theory model, analyze the big data of e-commerce and circular economy of the e-commerce market and predict the development potential of China's e-commerce market.

The results show that the Grey system theory model can play an important role in the data analysis of circular economy of the e-commerce market.

Use Grey model to analyze e-commerce data, discover e-commerce market rules and problems and then optimize e-commerce market.

Electricity consumption prediction has been an important topic for its significant impact on electric policies. Due to various uncertain factors, the growth trends of electricity consumption in different cases are variable. However, the traditional grey model is based on a fixed structure which sometimes cannot match the trend of raw data. Consequently, the predictive accuracy is variable as cases change. To improve the model's adaptability and forecasting ability, a novel fractional discrete grey model with variable structure is proposed in this paper.

The novel model can be regarded as a homogenous or non-homogenous exponent predicting model by changing the structure. And it selects the appropriate structure depending on the characteristics of raw data. The introduction of fractional accumulation enhances the predicting ability of the novel model. And the relative fractional order r is calculated by the numerical iterative algorithm which is simple but effective.

Two cases of power load and electricity consumption in Jiangsu and Fujian are applied to assess the predicting accuracy of the novel grey model. Four widely-used grey models, three classical statistical models and the multi-layer artificial neural network model are taken into comparison. The results demonstrate that the novel grey model performs well in all cases, and is superior to the comparative eight models.

A fractional-order discrete grey model with an adaptable structure is proposed to solve the conflict between traditional grey models' fixed structures and variable development trends of raw data. In applications, the novel model has satisfied adaptability and predicting accuracy.