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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.

This paper intends to construct a new adaptive grey seasonal model (AGSM) to promote the application of the grey forecasting model in quarterly GDP.

Firstly, this paper constructs a new accumulation operation that embodies the new information priority by using a hyperparameter. Then, a new AGSM is constructed by using a new grey action quantity, nonlinear Bernoulli operator, discretization operation, moving average trend elimination method and the proposed new accumulation operation. Subsequently, the marine predators algorithm is used to quickly obtain the hyperparameters used to build the AGSM. Finally, comparative analysis experiments and ablation experiments based on China's quarterly GDP confirm the validity of the proposed model.

AGSM can be degraded to some classical grey prediction models by replacing its own structural parameters. The proposed accumulation operation satisfies the new information priority rule. In the comparative analysis experiments, AGSM shows better prediction performance than other competitive algorithms, and the proposed accumulation operation is also better than the existing accumulation operations. Ablation experiments show that each component in the AGSM is effective in enhancing the predictive performance of the model.

A new AGSM with new information priority accumulation operation is proposed.

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.

Tourism demand forecasting is vital for the airline industry and tourism sector. Combination forecasting has the advantage of fusing several forecasts to reduce the risk of inappropriate model selection for analyzing decisions. This paper investigated the effects of a time-varying weighting strategy on the performance of linear and nonlinear forecast combinations in the context of tourism.

This study used grey prediction models, which did not require that the available data satisfy statistical assumptions, to generate forecasts. A quality-control technique was applied to determine when to change the combination weights to generate combined forecasts by using linear and nonlinear methods.

The empirical results showed that except for when the Choquet fuzzy integral was used, forecast combination with time-varying weights did not significantly outperform that with fixed weights. The Choquet integral with time-varying weights significantly outperformed that with fixed weights for all model combinations, and had a superior forecasting accuracy to those of other combination methods.

The tourism sector can benefit from the use of the Choquet integral with time-varying weights, by using it to formulate suitable strategies for tourist destinations.

Combining forecasts with time-varying weights may improve the accuracy of the predictions. This study investigated incorporating a time-varying weighting strategy into combination forecasting by using CUSUM. The results verified the effectiveness of the time-varying Choquet integral for tourism forecast combination.

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.

Electricity plays an essential role in nations' economic development. However, coal and renewables currently play an important part in electricity production in major world economies. The current study aims to forecast the electricity production from coal and renewables in the USA, China and Japan.

Two intelligent grey forecasting models – optimized discrete grey forecasting model DGM (1,1,α), and optimized even grey forecasting model EGM (1,1,α,θ) – are used to forecast electricity production. Also, the accuracy of the forecasts is measured through the mean absolute percentage error (MAPE).

Coal-powered electricity production is decreasing, while renewable energy production is increasing in the major economies (MEs). China's coal-fired electricity production continues to grow. The forecasts generated by the two grey models are more accurate than that by the classical models EGM (1,1) and DGM (1,1) and the exponential triple smoothing (ETS).

The study confirms the reliability and validity of grey forecasting models to predict electricity production in the MEs.