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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.

In the current study, two grey prediction models, Even GM (1, 1) and Non-homogeneous discrete grey model (NDGM), and ARIMA models are deployed to forecast cocoa bean production of the six major cocoa-producing countries. Furthermore, relying on Relative Growth Rate (RGR) and Doubling Time (D_t), production growth is analyzed.

The secondary data were extracted from the United Nations Food and Agricultural Organization (FAO) database. Grey forecasting models are applied using the data covering 2008 to 2017 as their performance on the small sample size is well-recognized. The models' performance was estimated through MAPE, MAE and RMSE.

Results show the two grey models fell below 10% of MAPE confirming their high accuracy and forecasting performance against that of the ARIMA. Therefore, the suitability of grey models for the cocoa production forecast is established. Findings also revealed that cocoa production in Côte d'Ivoire, Cameroon, Ghana and Brazil is likely to experience a rise with a growth rate of 2.52, 2.49, 2.45 and 2.72% by 2030, respectively. However, Nigeria and Indonesia are likely to experience a decrease with a growth rate of 2.25 and 2.21%, respectively.

For a sustainable cocoa industry, stakeholders should investigate the decline in production despite the implementation of advanced agricultural mechanization in cocoa farming, which goes further to put food security at risk.

The study presents a pioneering attempt of using grey forecasting models to predict cocoa production.

The purpose of this paper is to propose a model for effective data filling and precise prediction, which is used to solve the prediction problem of sequential data with the characteristics of poor information, high growth and containing extraordinary points.

After proving that the three principles of smooth sequence are not a sufficient condition for the judgement of sequence smoothness, judgement rules for sequence smoothness based on smoothness efficiency is introduced. Based on the non‐homogenous discrete grey model (NDGM) model which fits for high growth sequence, model error caused by equal weight mean value is analyzed, and mean value generation weight efficiency is optimized by the method of differential. Prediction steps that fit sequences with high growth, poor information and containing extraordinary points is established on the basis of equal weight mean value generation efficiency.

The results are convincing: previous judgement rules used for sequence smoothness do not fit for the high growth sequence, new judgement rules introduced are more effective for high growth sequence. Sequence filling algorithm based on differential ration not only improve the filling of high growth sequence, but also enhance the prediction precision of these sequences.

The method exposed in the paper can be used to solve the prediction problem of sequences with poor information, high growth and containing extraordinary points, and it was proved in the cases of large and medium company new products income and Ufida Software Company. What is more, the method is also helpful in aspects of corporate financial control and strategy‐making process.

The paper succeeds in proposing a new interpolation algorithm that is superior to ordinary mean value generation method in the aspects of generation and prediction and to grey interpolation algorithm in the aspect of information volume by defining sequence smoothness efficiency and introducing smoothness judgement rules that are easy to compute and fits for high growth sequence and not limited to monotonicity sequence.

The global warming, caused by the anthropogenic greenhouse gases, has been one of the major worldwide issues over the last decades. Among them, carbon dioxide (CO₂) is the most important one and is responsible for more than the two-third of the greenhouse effect. Currently, greenhouse gas emissions and CO₂ emissions – the root cause of the global warming – in particular are being examined closely in the fields of science and they also have been put on the agenda of the political leaders. The purpose of this paper is to predict the energy-related CO₂ emissions through using different discrete grey models (DGMs) in Turkey and total Europe and Eurasia region.

The proposed DGMs will be applied to predict CO₂ emissions in Turkey and total Europe and Eurasia region from 2015 to 2030 using data set between 1965 and 2014. In the first stage of the study, DGMs without rolling mechanism (RM) will be used. In the second stage, DGMs with RM are constructed where the length of the rolling horizons of the respected models is optimised.

In the first stage, estimated values show that non-homogeneous DGM is the best method to predict Turkey’s energy-related CO₂ emissions whereas DGM is the best method to predict the energy-related CO₂ emissions for total Europe and Eurasia region. According to the results in the second stage, NDGM with RM (k=26) is the best method for Turkey while optimised DGM with RM (k=4) delivers most reliable estimates for total Europe and Eurasia region.

This study illustrates the effect of different DGM approaches on the estimation performance for the Turkish energy-related CO₂ emission data.

The purpose of this paper is to understand the trend and forecast the number of tourists from different regions of the world to Mauritius.

The paper adopts two grey system models, the even model GM(1,1) and the non-homogeneous discrete grey model (NDGM), to forecast the total number of international tourism to Mauritius and its structure from different regions tourist arrivals to Mauritius for the next three years. Grey system theory models were used to account for uncertainties and the dynamism of the tourism sector environment. The two models were applied as a comparison to obtain more reliable forecasting figures.

The results demonstrate that both of the grey system models can be successfully applied with high accuracy for Mauritian tourism prediction, and also the number of tourist arrivals to Mauritius shows a continued augmentation for the upcoming years.

Forecasting is meaningful since the Government of Mauritius, private companies or any concerned authority can adopt the forecasting methods exposed in this paper for the development of the tourism sector through managerial and economic decision making.

Mauritius is a charming travel destination. Through this paper, it can be seen that future tourism travel to Mauritius has been successfully predicted based on previous data. Moreover, it seems that the grey system theory models have not been utilised yet as forecasting tools for the tourism sector of Mauritius as opposed to other countries such as China and Taiwan.

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.

To develop the theory and application of the grey prediction model, this investigation constructs a novel discrete grey Riccati model termed DGRM(1,1).

By examining a special kind of Riccati difference equation and the structure of the conventional discrete grey model (DGM), we advance a novel DGRM, and the model's prediction effect is evaluated by two numerical examples and an application case and compared with that of other conventional grey models.

The average relative simulation error of DGRM(1,1) does not change if the model is built after the original sequence has been transformed by a multiplier, and the new model is suitable to predict monotonically increasing, monotonically decreasing and unimodal sequences.

DGRM(1,1) is utilized to forecast the development cost of a small plane owned by the Aviation Industry Corporation of China (AVIC) with an original data sequence from 2006 to 2013. The outcomes indicate that DGRM(1,1) exhibits high precision and potential in development cost prediction.

Combining the Riccati difference equation with the conventional DGM, the author advances a new grey model that is suitable to predict three kinds of data series with different changing trends.

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.

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 purpose of this paper is to summarize progress of grey forecasting modelling, explain mechanism of grey forecasting modelling and classify exist grey forecasting models.

General modelling process and mechanism of grey forecasting modelling is summarized and classification of grey forecasting models is done according to their differential equation structure. Grey forecasting models with linear structure are divided into continuous single variable grey forecasting models, discrete single variable grey forecasting models, continuous multiple variable grey forecasting models and discrete multiple variable grey forecasting models. The mechanism and traceability of these models are discussed. In addition, grey forecasting models with nonlinear structure, grey forecasting models with grey number sequences and grey forecasting models with multi-input and multi-output variables are further discussed.

It is clearly to explain differences between grey forecasting models with other forecasting models. Accumulation generation operation is the main difference between grey forecasting models and other models, and it is helpful to mining system developing law with limited data. A great majority of grey forecasting models are linear structure while grey forecasting models with nonlinear structure should be further studied.

Mechanism and classification of grey forecasting models are very helpful to combine with suitable real applications.

The main contributions of this paper are to classify models according to models' structure are linear or nonlinear, to analyse relationships and differences of models in same class and to deconstruct mechanism of grey forecasting models.